Center of Gravity vs Center of Mass

7/30/2019 Center of Gravity vs Center of Mass

1/25

1

Center of Gravity vs Center of Mass

The center of mass and center of gravity are two concepts frequently encounters in the study of physic

These are also concepts that are most confused between, and often people use them interchangeably, whic

is erroneous. This article will explain the difference between center of mass and center of gravity and l

readers have a clearer understanding.

Center of mass of a rigid body is also called its center of gravity. However, this is true only in circumstance

where gravitational forces are uniform. Since gravitational force of earth is taken to be uniform at all place

the center of mass and the center of gravity are effectively same. Center of gravity is defined as the averag

location of the weight of an object. In the case of earth, since gravitational pull is same at all places, each maelement would weigh the same so the center of gravity is identical to the center of mass. However, in a no

uniform gravitational field, the center of gravity is not the same as the center of mass. Center of mass is

fixed property which is the average location of the mass of the body. It has nothing to do with gravity.

In the case of artificial satellites, gravitational pull is not uniform and in such conditions, center of gravi

refers to the mean location of the gravitational pull acting on the body of the satellite. This obviously resul

in slight difference between its center of mass and the center of gravity.

The center of mass of a body does not coincide with its center of gravity and this is a property that

exploited by sport car makers to keep the center of mass as low as possible to make the car have a bett

balance. The concept of difference between center of mass and center of gravity is also exploited by hig

jumpers when they perform Fosbury Flop and bend their bodies in such a way so as to clear the high ba

without touching it. They bend their bodies in such a way that they clear the bar despite their center of manot clearing the bar.

Center of Mass vs Center of Gravity

Center of mass and center of gravity are often taken as one in the study of physicsbecause of the uniform gravitational pull of earth.

However, in non uniform gravitational fields, center of mass is away from the centerof gravity

This fact is used by designers to make cars with a very low center of mass so as togive better balance.

OR

The center of mass is a geometrical measurement considering only mass distribution and not weightdistribution. Centre of mass is a mathematically defined point for an object, which is unaffected by external

field/force unless it is deformed by the external field/ force.

However, centre of gravity is a point from where net weight is assumed to act. Clearly it depends on gravity

which is an external force.

Normally, centre of mass and gravity are same, this is because Earths gravitational field is uniform.

Now, consider a situation in which gravitational field is non-uniform. Also, imagine a very long uniform rod

If you consider two parts of rod with same mass, the force of gravitation (weight) will be different on both

instead of same mass. Due to which, its centre of gravity and center of mass will be different.

Because of this, the position of centre of mass of this rod will be different from that of centre of weight.

Normally, on Earth gravity is uniform so center of mass and gravity are same for most of the objects. But

again be cautious!

APPLICATIONS

Finding the center of mass of a system is very useful in observing and recording many physical phenomena

Mathematically, the center of mass of a system is merely the result of a summation or integral where the

masses of differing points times their distance from the 'center' squared, and then an infinite amount of the


2/25

2

values are taken, the integral, and added together. Everyday activities can be explained better with the

concept of the center of mass.Gravity

The acceleration due to the gravitational force between an object and the earth is considered to be 9.8m/s^

or 32ft/s^2. Many people go under the assumption that everything in the earth's atmosphere is thought to

accelerate at this speed downwards, but it's untrue. This constant of gravity is the acceleration that the

center of mass of a system moves with, and not everything within that system has to move with that

acceleration. For instance, if a meter stick is raised about 40 degrees to the horizontal and a penny is atop th

highest point of the meter stick, the two objects will not fall at the same speed. The meter stick will fall fastein a vacuum, because the penny is part of the meter stick to begin with and then when the meter stick is

dropped, the center of mass travels faster than the penny, making it very evident as the penny just falls shor

of the same speed of the meter stick.

The Human Body

When jumping in the air, one would assume that the entire weight of the body has to lifted uniformly, but it

not true. The body has a center of mass just like anything else, and with the ability of the body to stretch, th

total height of someones jump is not necessarily the same height as the weight of their body. Usually when

someone jumps up they squat down to gain force through their legs and the ground, and while jumping,

stretch their arm up to it's highest point. The center of mass is usually around the waist(depends upon the

individual), thereby letting the jumper travel a larger distance upward without doing as much work. A grea

representation of the center of mass is the high jumper and how, through proper technique, they can elevattheir center of mass over the bar while letting the rest of their body just flex around the bar, creating a

technique that enables less work, and thereby a greater vertical distance to be achieved. When lifting a heav

object, one has the tendency to lean in the opposite direction of side where the object is being held. This is

because the body wants to achieve a balance that can enable it to move more uniformly. The center of mass

originally symmetrical with the body, but when, say a suitcase, is lifted with one arm, the body tends to lean

in the opposite direction, as to reform the center of mass with this new object introduced into the system.

Center of mass

Inphysics, the center of mass, or barycenter, of a distribution of mass in space is the unique point where

the weighted relative position of the distributed mass sums to zero. The distribution of mass is balancedaround the center of mass and the average of the weighted position coordinates of the distributed mass

defines its coordinates. Calculations inmechanicsare simplified when formulated with respect to the cente

of mass.

In the case of a singlerigid body, the center of mass is fixed in relation to the body, and if the body has

uniform density, it will be located at thecentroid. The center of mass may be located outside the physical

body, as is sometimes the case forhollowor open-shaped objects, such as ahorseshoe. In the case of a

distribution of separate bodies, such as theplanetsof theSolar System, the center of mass may not

correspond to the position of any individual member of the system.

The center of mass is a useful reference point for calculations inmechanicsthat involve masses distributed

space, such as thelinearandangular momentumof planetary bodies andrigid body dynamics. Inorbital

mechanics, the equations of motion of planets are formulated aspoint masseslocated at the centers of massThecenter of mass frameis aninertial framein which the center of mass of a system is at rest at with respe

the origin of the coordinate system.

History

The concept of "center of mass" in the form of the "center of gravity" was first introduced by the ancient

Greek physicist, mathematician, and engineerArchimedes of Syracuse. He worked with simplified

assumptions about gravity that amount to a uniform field, thus arriving at the mathematical properties of

what we now call the center of mass. Archimedes showed that thetorqueexerted on aleverby weights

resting at various points along the lever is the same as what it would be if all of the weights were moved to

single point their center of mass. In work on floating bodies he demonstrated that the orientation of a
http://en.wikipedia.org/wiki/Physicshttp://en.wikipedia.org/wiki/Physicshttp://en.wikipedia.org/wiki/Physicshttp://en.wikipedia.org/wiki/Mechanicshttp://en.wikipedia.org/wiki/Mechanicshttp://en.wikipedia.org/wiki/Mechanicshttp://en.wikipedia.org/wiki/Rigid_bodyhttp://en.wikipedia.org/wiki/Rigid_bodyhttp://en.wikipedia.org/wiki/Rigid_bodyhttp://en.wikipedia.org/wiki/Centroidhttp://en.wikipedia.org/wiki/Centroidhttp://en.wikipedia.org/wiki/Centroidhttp://en.wikipedia.org/wiki/Hollowhttp://en.wikipedia.org/wiki/Hollowhttp://en.wikipedia.org/wiki/Hollowhttp://en.wikipedia.org/wiki/Horseshoehttp://en.wikipedia.org/wiki/Horseshoehttp://en.wikipedia.org/wiki/Horseshoehttp://en.wikipedia.org/wiki/Planetshttp://en.wikipedia.org/wiki/Planetshttp://en.wikipedia.org/wiki/Planetshttp://en.wikipedia.org/wiki/Solar_Systemhttp://en.wikipedia.org/wiki/Solar_Systemhttp://en.wikipedia.org/wiki/Solar_Systemhttp://en.wikipedia.org/wiki/Mechanicshttp://en.wikipedia.org/wiki/Mechanicshttp://en.wikipedia.org/wiki/Mechanicshttp://en.wikipedia.org/wiki/Momentumhttp://en.wikipedia.org/wiki/Momentumhttp://en.wikipedia.org/wiki/Momentumhttp://en.wikipedia.org/wiki/Angular_momentumhttp://en.wikipedia.org/wiki/Angular_momentumhttp://en.wikipedia.org/wiki/Angular_momentumhttp://en.wikipedia.org/wiki/Rigid_body_dynamicshttp://en.wikipedia.org/wiki/Rigid_body_dynamicshttp://en.wikipedia.org/wiki/Rigid_body_dynamicshttp://en.wikipedia.org/wiki/Orbital_mechanicshttp://en.wikipedia.org/wiki/Orbital_mechanicshttp://en.wikipedia.org/wiki/Orbital_mechanicshttp://en.wikipedia.org/wiki/Orbital_mechanicshttp://en.wikipedia.org/wiki/Point_masshttp://en.wikipedia.org/wiki/Point_masshttp://en.wikipedia.org/wiki/Point_masshttp://en.wikipedia.org/wiki/Center_of_mass_framehttp://en.wikipedia.org/wiki/Center_of_mass_framehttp://en.wikipedia.org/wiki/Center_of_mass_framehttp://en.wikipedia.org/wiki/Inertial_framehttp://en.wikipedia.org/wiki/Inertial_framehttp://en.wikipedia.org/wiki/Inertial_framehttp://en.wikipedia.org/wiki/Archimedeshttp://en.wikipedia.org/wiki/Archimedeshttp://en.wikipedia.org/wiki/Archimedeshttp://en.wikipedia.org/wiki/Torquehttp://en.wikipedia.org/wiki/Torquehttp://en.wikipedia.org/wiki/Torquehttp://en.wikipedia.org/wiki/Leverhttp://en.wikipedia.org/wiki/Leverhttp://en.wikipedia.org/wiki/Leverhttp://en.wikipedia.org/wiki/Leverhttp://en.wikipedia.org/wiki/Torquehttp://en.wikipedia.org/wiki/Archimedeshttp://en.wikipedia.org/wiki/Inertial_framehttp://en.wikipedia.org/wiki/Center_of_mass_framehttp://en.wikipedia.org/wiki/Point_masshttp://en.wikipedia.org/wiki/Orbital_mechanicshttp://en.wikipedia.org/wiki/Orbital_mechanicshttp://en.wikipedia.org/wiki/Rigid_body_dynamicshttp://en.wikipedia.org/wiki/Angular_momentumhttp://en.wikipedia.org/wiki/Momentumhttp://en.wikipedia.org/wiki/Mechanicshttp://en.wikipedia.org/wiki/Solar_Systemhttp://en.wikipedia.org/wiki/Planetshttp://en.wikipedia.org/wiki/Horseshoehttp://en.wikipedia.org/wiki/Hollowhttp://en.wikipedia.org/wiki/Centroidhttp://en.wikipedia.org/wiki/Rigid_bodyhttp://en.wikipedia.org/wiki/Mechanicshttp://en.wikipedia.org/wiki/Physics


3/25

3

floating object is the one that makes its center of mass as low as possible. He developed mathematical

techniques for finding the centers of mass of objects of uniform density of various well-defined shapes.[1]

Later mathematicians who developed the theory of the center of mass includePappus of Alexandria,Guido

Ubaldi,Francesco Maurolico,[2]Federico Commandino,[3]Simon Stevin,[4]Luca Valerio,[5]Jean-Charles de la

Faille,Paul Guldin,[6]John Wallis,Louis Carr,Pierre Varignon, andAlexis Clairaut.[7]

Newton's second lawis reformulated with respect to the center of mass inEuler's first law.[8]

Diagram of an educational toy that balances on a point: the CM (C) settles below its support (P)[edit]Definition of center of mass

The center of mass is the unique point at the center of a distribution of mass in space that has the property

that the weighted position vectors relative to this point sum to zero.

[edit]A system of particles

In the case of a system of particles Pi, i=1, ..., n, each with mass mi that are located in space with

coordinates ri, i=1,...,n,, the coordinates R of the center of mass satisfy the condition,

Solve this equation for R to obtain the formula,

where M is the sum of the masses of all of the particles.

[edit]A continuous volume

If the mass distribution is continuous with the density (r) within a volume V, then the integral of theweighted position coordinates of the points in this volume relative to the center of mass R is zero, that is

Solve this equation for the coordinates R to obtain

where M is the total mass in the volume.

If a continuous mass distribution has uniformdensity, which means is constant, then the center of mass isthe same as thecentroidof the volume.[9]

[edit]Barycentric coordinates

The coordinates R of the center of mass of a two-particle system, P1 and P2, with masses m1 and m2 is given

by
http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEShore20089.E2.80.9311-1http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEShore20089.E2.80.9311-1http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEShore20089.E2.80.9311-1http://en.wikipedia.org/wiki/Pappus_of_Alexandriahttp://en.wikipedia.org/wiki/Pappus_of_Alexandriahttp://en.wikipedia.org/wiki/Pappus_of_Alexandriahttp://en.wikipedia.org/wiki/Guido_Ubaldihttp://en.wikipedia.org/wiki/Guido_Ubaldihttp://en.wikipedia.org/wiki/Guido_Ubaldihttp://en.wikipedia.org/wiki/Guido_Ubaldihttp://en.wikipedia.org/wiki/Francesco_Maurolicohttp://en.wikipedia.org/wiki/Francesco_Maurolicohttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEBaron200491.E2.80.9394-2http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEBaron200491.E2.80.9394-2http://en.wikipedia.org/wiki/Federico_Commandinohttp://en.wikipedia.org/wiki/Federico_Commandinohttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEBaron200494.E2.80.9396-3http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEBaron200494.E2.80.9396-3http://en.wikipedia.org/wiki/Simon_Stevinhttp://en.wikipedia.org/wiki/Simon_Stevinhttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEBaron200496.E2.80.93101-4http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEBaron200496.E2.80.93101-4http://en.wikipedia.org/wiki/Luca_Valeriohttp://en.wikipedia.org/wiki/Luca_Valeriohttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEBaron2004101.E2.80.93106-5http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEBaron2004101.E2.80.93106-5http://en.wikipedia.org/wiki/Jean-Charles_de_la_Faillehttp://en.wikipedia.org/wiki/Jean-Charles_de_la_Faillehttp://en.wikipedia.org/wiki/Jean-Charles_de_la_Faillehttp://en.wikipedia.org/wiki/Jean-Charles_de_la_Faillehttp://en.wikipedia.org/wiki/Paul_Guldinhttp://en.wikipedia.org/wiki/Paul_Guldinhttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEMancosu199956.E2.80.9361-6http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEMancosu199956.E2.80.9361-6http://en.wikipedia.org/wiki/John_Wallishttp://en.wikipedia.org/wiki/John_Wallishttp://en.wikipedia.org/wiki/John_Wallishttp://en.wikipedia.org/wiki/Louis_Carr%C3%A9_(mathematician)http://en.wikipedia.org/wiki/Louis_Carr%C3%A9_(mathematician)http://en.wikipedia.org/wiki/Louis_Carr%C3%A9_(mathematician)http://en.wikipedia.org/wiki/Pierre_Varignonhttp://en.wikipedia.org/wiki/Pierre_Varignonhttp://en.wikipedia.org/wiki/Pierre_Varignonhttp://en.wikipedia.org/wiki/Alexis_Clairauthttp://en.wikipedia.org/wiki/Alexis_Clairauthttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEWalton18552-7http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEWalton18552-7http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEWalton18552-7http://en.wikipedia.org/wiki/Newton%27s_second_lawhttp://en.wikipedia.org/wiki/Newton%27s_second_lawhttp://en.wikipedia.org/wiki/Euler%27s_laws#Euler.27s_first_lawhttp://en.wikipedia.org/wiki/Euler%27s_laws#Euler.27s_first_lawhttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEBeatty200629-8http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEBeatty200629-8http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEBeatty200629-8http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=2http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=2http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=2http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=3http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=3http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=3http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=4http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=4http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=4http://en.wikipedia.org/wiki/Densityhttp://en.wikipedia.org/wiki/Densityhttp://en.wikipedia.org/wiki/Densityhttp://en.wikipedia.org/wiki/Centroidhttp://en.wikipedia.org/wiki/Centroidhttp://en.wikipedia.org/wiki/Centroidhttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTELevi200985-9http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTELevi200985-9http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTELevi200985-9http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=5http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=5http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=5http://en.wikipedia.org/wiki/File:CoG_stable.svghttp://en.wikipedia.org/wiki/File:CoG_stable.svghttp://en.wikipedia.org/wiki/File:CoG_stable.svghttp://en.wikipedia.org/wiki/File:CoG_stable.svghttp://en.wikipedia.org/wiki/File:CoG_stable.svghttp://en.wikipedia.org/wiki/File:CoG_stable.svghttp://en.wikipedia.org/wiki/File:CoG_stable.svghttp://en.wikipedia.org/wiki/File:CoG_stable.svghttp://en.wikipedia.org/wiki/File:CoG_stable.svghttp://en.wikipedia.org/wiki/File:CoG_stable.svghttp://en.wikipedia.org/wiki/File:CoG_stable.svghttp://en.wikipedia.org/wiki/File:CoG_stable.svghttp://en.wikipedia.org/wiki/File:CoG_stable.svghttp://en.wikipedia.org/wiki/File:CoG_stable.svghttp://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=5http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTELevi200985-9http://en.wikipedia.org/wiki/Centroidhttp://en.wikipedia.org/wiki/Densityhttp://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=4http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=3http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=2http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEBeatty200629-8http://en.wikipedia.org/wiki/Euler%27s_laws#Euler.27s_first_lawhttp://en.wikipedia.org/wiki/Newton%27s_second_lawhttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEWalton18552-7http://en.wikipedia.org/wiki/Alexis_Clairauthttp://en.wikipedia.org/wiki/Pierre_Varignonhttp://en.wikipedia.org/wiki/Louis_Carr%C3%A9_(mathematician)http://en.wikipedia.org/wiki/John_Wallishttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEMancosu199956.E2.80.9361-6http://en.wikipedia.org/wiki/Paul_Guldinhttp://en.wikipedia.org/wiki/Jean-Charles_de_la_Faillehttp://en.wikipedia.org/wiki/Jean-Charles_de_la_Faillehttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEBaron2004101.E2.80.93106-5http://en.wikipedia.org/wiki/Luca_Valeriohttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEBaron200496.E2.80.93101-4http://en.wikipedia.org/wiki/Simon_Stevinhttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEBaron200494.E2.80.9396-3http://en.wikipedia.org/wiki/Federico_Commandinohttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEBaron200491.E2.80.9394-2http://en.wikipedia.org/wiki/Francesco_Maurolicohttp://en.wikipedia.org/wiki/Guido_Ubaldihttp://en.wikipedia.org/wiki/Guido_Ubaldihttp://en.wikipedia.org/wiki/Pappus_of_Alexandriahttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEShore20089.E2.80.9311-1


4/25

4

Let the percentage of the total mass divided between these two particles vary from 100% P1 and 0%

P2 through 50% P1 and 50% P2 to 0% P1 and 100% P2, then the center of mass R moves along the line from

P1 to P2. The percentages of mass at each point can be viewed as projective coordinates of the pointR on th

line, and are termed barycentric coordinates. This can be generalized to three points and four points to

define projective coordinates in the plane, and in space, respectively.

[edit]Systems with periodic boundary conditions

For particles in a system withperiodic boundary conditionstwo particles can be neighbors even though the

are on opposite sides of the system. This occurs often inmolecular dynamicssimulations, for example, in

which clusters form at random locations and sometimes neighboring atoms cross the periodic boundary.When a cluster straddles the periodic boundary, a naive calculation of the center of mass will be incorrect. A

generalized method for calculating the center of mass for periodic systems is to treat each

coordinate,xandyand/orz, as if it were on a circle instead of a line.[10]The calculation takes every

particle'sxcoordinate and maps it to an angle,

wherexmax is the system size in thexdirection. From this angle, two new points can be generated:

In the plane, these coordinates lie on a circle of radiusxmax. From the collection of and valuesfrom all the particles, the averages and are calculated. These values are mapped back into a new

angle, , from which thexcoordinate of the center of mass can be obtained:

The process can be repeated for all dimensions of the system to determine the complete center of mass. The

utility of the algorithm is that it allows the mathematics to determine where the "best" center of mass is,

instead of guessing or usingcluster analysisto "unfold" a cluster straddling the periodic boundaries. It must

be noted that if both average values are zero, , then is undefined. This is a correct result,

because it only occurs when all particles are exactly evenly spaced. In that condition, theirxcoordinates aremathematically identical in aperiodic system.

[edit]Center of gravity

Center of gravity is the point in a body around which theresultant torquedue to gravity forces vanish. Near

the surface of the earth, where the gravity acts downward as a parallel force field, the center of gravity and

the center of mass are the same.

The study of the dynamics of aircraft, vehicles and vessels assumes that the system moves in near-earth

gravity, and therefore the terms center of gravity and center of mass are used interchangeably.

In physics the benefits of using the center of mass to model a mass distribution can be seen by considering

theresultantof the gravity forces on a continuous body. Consider a body of volume V with density (r) at

each pointr in the volume. In a parallel gravity field the force fat each pointr is given by,

where dm is the mass at the pointr, g is the acceleration of gravity, and kis a unit vector defining the vertic

direction. Choose a reference pointR in the volume and compute theresultant forceand torque at this point

and

If the reference pointR is chosen so that it is the center of mass, then
http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=6http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=6http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=6http://en.wikipedia.org/wiki/Periodic_boundary_conditionshttp://en.wikipedia.org/wiki/Periodic_boundary_conditionshttp://en.wikipedia.org/wiki/Periodic_boundary_conditionshttp://en.wikipedia.org/wiki/Molecular_dynamicshttp://en.wikipedia.org/wiki/Molecular_dynamicshttp://en.wikipedia.org/wiki/Molecular_dynamicshttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-10http://en.wikipedia.org/wiki/Center_of_mass#cite_note-10http://en.wikipedia.org/wiki/Center_of_mass#cite_note-10http://en.wikipedia.org/wiki/Cluster_analysishttp://en.wikipedia.org/wiki/Cluster_analysishttp://en.wikipedia.org/wiki/Cluster_analysishttp://en.wikipedia.org/wiki/Periodic_boundary_conditions#Practical_implementation:_continuity_and_the_minimum_image_conventionhttp://en.wikipedia.org/wiki/Periodic_boundary_conditions#Practical_implementation:_continuity_and_the_minimum_image_conventionhttp://en.wikipedia.org/wiki/Periodic_boundary_conditions#Practical_implementation:_continuity_and_the_minimum_image_conventionhttp://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=7http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=7http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=7http://en.wikipedia.org/wiki/Resultant_forcehttp://en.wikipedia.org/wiki/Resultant_forcehttp://en.wikipedia.org/wiki/Resultant_forcehttp://en.wikipedia.org/wiki/Resultant_forcehttp://en.wikipedia.org/wiki/Resultant_forcehttp://en.wikipedia.org/wiki/Resultant_forcehttp://en.wikipedia.org/wiki/Resultant_forcehttp://en.wikipedia.org/wiki/Resultant_forcehttp://en.wikipedia.org/wiki/Resultant_forcehttp://en.wikipedia.org/wiki/Resultant_forcehttp://en.wikipedia.org/wiki/Resultant_forcehttp://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=7http://en.wikipedia.org/wiki/Periodic_boundary_conditions#Practical_implementation:_continuity_and_the_minimum_image_conventionhttp://en.wikipedia.org/wiki/Cluster_analysishttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-10http://en.wikipedia.org/wiki/Molecular_dynamicshttp://en.wikipedia.org/wiki/Periodic_boundary_conditionshttp://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=6


5/25

5

which means the resultant torque T=0. Because the resultant torque is zero the body will move as though it

is a particle with its mass concentrated at the center of mass.

By selecting the center of gravity as the reference point for a rigid body, the gravity forces will not cause the

body to rotate, which means weight of the body can be considered to be concentrated at the center of mass.

[edit]Linear and angular momentum

The linear and angular momentum of a collection of particles can be simplified by measuring the position

and velocity of the particles relative to the center of mass. Let the system of particles Pi, i=1,...,n be located athe coordinates ri and velocities vi. Select a reference pointR and compute the relative position and velocity

vectors,

The total linear and angular momentum vectors relative to the reference pointR are

and

IfR is chosen as the center of mass these equations simplify to

Newton's laws of motion require that for any system with no external forces the momentum of the system i

constant, which means the center of mass moves with constant velocity. This applies for all systems with

classical internal forces, including magnetic fields, electric fields, chemical reactions, and so on. More

formally, this is true for any internal forces that satisfyNewton's Third Law.[11]

[edit]Locating the center of mass

Main article:Locating the center of mass

Plumb line method

The experimental determination of the center of mass of a body uses gravity forces on the body and relies o

the fact that in the parallel gravity field near the surface of the earth the center of mass is the same as the

center of gravity.
http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=8http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=8http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=8http://en.wikipedia.org/wiki/Newton%27s_Third_Lawhttp://en.wikipedia.org/wiki/Newton%27s_Third_Lawhttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEKleppnerKolenkow1973117-11http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEKleppnerKolenkow1973117-11http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEKleppnerKolenkow1973117-11http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=9http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=9http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=9http://en.wikipedia.org/wiki/Locating_the_center_of_masshttp://en.wikipedia.org/wiki/Locating_the_center_of_masshttp://en.wikipedia.org/wiki/Locating_the_center_of_masshttp://en.wikipedia.org/wiki/File:Center_gravity_2.svghttp://en.wikipedia.org/wiki/File:Center_gravity_2.svghttp://en.wikipedia.org/wiki/File:Center_gravity_2.svghttp://en.wikipedia.org/wiki/File:Center_gravity_2.svghttp://en.wikipedia.org/wiki/File:Center_gravity_2.svghttp://en.wikipedia.org/wiki/File:Center_gravity_2.svghttp://en.wikipedia.org/wiki/File:Center_gravity_2.svghttp://en.wikipedia.org/wiki/File:Center_gravity_2.svghttp://en.wikipedia.org/wiki/File:Center_gravity_2.svghttp://en.wikipedia.org/wiki/File:Center_gravity_2.svghttp://en.wikipedia.org/wiki/File:Center_gravity_2.svghttp://en.wikipedia.org/wiki/File:Center_gravity_2.svghttp://en.wikipedia.org/wiki/File:Center_gravity_2.svghttp://en.wikipedia.org/wiki/File:Center_gravity_2.svghttp://en.wikipedia.org/wiki/Locating_the_center_of_masshttp://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=9http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEKleppnerKolenkow1973117-11http://en.wikipedia.org/wiki/Newton%27s_Third_Lawhttp://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=8


6/25

6

The center of mass of a body with an axis of symmetry and constant density must lie on this axis. Thus, the

center of mass of a circular cylinder of constant density has its center of mass on the axis of the cylinder. In

the same way, the center of mass of a spherically symmetric body of constant density is at the center of the

sphere. In general, for any symmetry of a body, its center of mass will be a fixed point of that symmetry.[12]

[edit]In two dimensions

An experimental method for locating the center of mass is to suspend the object from two locations and to

dropplumb linesfrom the suspension points. The intersection of the two lines is the center of mass.[13]

The shape of an object might already be mathematically determined, but it may be too complex to use a

known formula. In this case, one can subdivide the complex shape into simpler, more elementary shapes,whose centers of mass are easy to find. If the total mass and center of mass can be determined for each area

then the center of mass of the whole is the weighted average of the centers.[14]This method can even work

for objects with holes, which can be accounted for as negative masses.[15]

A direct development of theplanimeterknown as an integraph, or integerometer, can be used to establish

the position of thecentroidor center of mass of an irregular two-dimensional shape. This method can be

applied to a shape with an irregular, smooth or complex boundary where other methods are too difficult. It

was regularly used by ship builders to compare with the requireddisplacementandcentre of buoyancyof a

ship, and ensure it would not capsize.[16][17]

[edit]In three dimensions

An experimental method to locate the three dimensional coordinates of the center of mass begins by

supporting the object at three points and measuring the forces, F1, F2, and F3that resist the weight of theobject, W= -Wk(kis the unit vector in the vertical direction). Letr1, r2, and r3 be the position coordinates of

the support points, then the coordinates Rof the center of mass satisfy the condition that the resultant torqu

is zero,

or

This equation yields the coordinates of the center of mass R* in the horizontal plane as,

The center of mass lies on the vertical line L, given by

The three dimensional coordinates of the center of mass are determined by performing this experiment

twice with the object positioned so that these forces are measured for two different horizontal planes

through the object. The center of mass will be the intersection of the two lines L1 and L2 obtained from the

two experiments.

[edit]Applications

Estimated center of mass/gravity (blue sphere) of a gymnast at the end of performing a cartwheel. Notice

center is outside the body in this position.
http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEFeynmanLeightonSands196319.3-12http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEFeynmanLeightonSands196319.3-12http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEFeynmanLeightonSands196319.3-12http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=10http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=10http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=10http://en.wikipedia.org/wiki/Plumb_linehttp://en.wikipedia.org/wiki/Plumb_linehttp://en.wikipedia.org/wiki/Plumb_linehttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEKleppnerKolenkow1973119.E2.80.93120-13http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEKleppnerKolenkow1973119.E2.80.93120-13http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEKleppnerKolenkow1973119.E2.80.93120-13http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEFeynmanLeightonSands196319.1.E2.80.9319.2-14http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEFeynmanLeightonSands196319.1.E2.80.9319.2-14http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEFeynmanLeightonSands196319.1.E2.80.9319.2-14http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEHamill200920.E2.80.9321-15http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEHamill200920.E2.80.9321-15http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEHamill200920.E2.80.9321-15http://en.wikipedia.org/wiki/Planimeterhttp://en.wikipedia.org/wiki/Planimeterhttp://en.wikipedia.org/wiki/Planimeterhttp://en.wikipedia.org/wiki/Centroidhttp://en.wikipedia.org/wiki/Centroidhttp://en.wikipedia.org/wiki/Centroidhttp://en.wikipedia.org/wiki/Displacement_(ship)http://en.wikipedia.org/wiki/Displacement_(ship)http://en.wikipedia.org/wiki/Displacement_(ship)http://en.wikipedia.org/wiki/Centre_of_buoyancyhttp://en.wikipedia.org/wiki/Centre_of_buoyancyhttp://en.wikipedia.org/wiki/Centre_of_buoyancyhttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-16http://en.wikipedia.org/wiki/Center_of_mass#cite_note-16http://en.wikipedia.org/wiki/Center_of_mass#cite_note-16http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=11http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=11http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=11http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=12http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=12http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=12http://en.wikipedia.org/wiki/File:CofM.jpghttp://en.wikipedia.org/wiki/File:CofM.jpghttp://en.wikipedia.org/wiki/File:CofM.jpghttp://en.wikipedia.org/wiki/File:CofM.jpghttp://en.wikipedia.org/wiki/File:CofM.jpghttp://en.wikipedia.org/wiki/File:CofM.jpghttp://en.wikipedia.org/wiki/File:CofM.jpghttp://en.wikipedia.org/wiki/File:CofM.jpghttp://en.wikipedia.org/wiki/File:CofM.jpghttp://en.wikipedia.org/wiki/File:CofM.jpghttp://en.wikipedia.org/wiki/File:CofM.jpghttp://en.wikipedia.org/wiki/File:CofM.jpghttp://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=12http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=11http://en.wikipedia.org/wiki/Center_of_mass#cite_note-16http://en.wikipedia.org/wiki/Center_of_mass#cite_note-16http://en.wikipedia.org/wiki/Centre_of_buoyancyhttp://en.wikipedia.org/wiki/Displacement_(ship)http://en.wikipedia.org/wiki/Centroidhttp://en.wikipedia.org/wiki/Planimeterhttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEHamill200920.E2.80.9321-15http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEFeynmanLeightonSands196319.1.E2.80.9319.2-14http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEKleppnerKolenkow1973119.E2.80.93120-13http://en.wikipedia.org/wiki/Plumb_linehttp://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=10http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEFeynmanLeightonSands196319.3-12


7/25

7

Engineers try to design asports car's center of mass as low as possible to make the carhandlebetter.

Whenhigh jumpersperform a "Fosbury Flop", they bend their body in such a way that it clears the bar whil

its center of mass does not.[18]

[edit]Aeronautics

Main article:Center of gravity of an aircraft

The center of mass is an important point on anaircraft, which significantly affects the stability of the aircraf

To ensure the aircraft is stable enough to be safe to fly, the center of mass must fall within specified limits. I

the center of mass is ahead of the forward limit, the aircraft will be less maneuverable, possibly to the point

of being unable to rotate for takeoff or flare for landing.[19]

If the center of mass is behind the aft limit, theaircraft will be more maneuverable, but also less stable, and possibly so unstable that it is impossible to fly.

The moment arm of theelevatorwill also be reduced, which makes it more difficult to recover from

astalledcondition.[20]

Forhelicoptersinhover, the center of mass is always directly below therotorhead. In forward flight, the

center of mass will move aft to balance the negative pitch torque produced by applyingcycliccontrol to

propel the helicopter forward; consequently a cruising helicopter flies "nose-down" in level flight.

[edit]Astronomy

Two bodies orbiting a barycenter inside one body

Main article:Barycentric coordinates (astronomy)

The center of mass plays an important role in astronomy and astrophysics, where it is commonly referred tas the barycenter. The barycenter is the point between two objects where they balance each other; it is the

center of mass where two or more celestial bodiesorbiteach other. When amoonorbits aplanet, or a plane

orbits astar, both bodies are actually orbiting around a point that lies away from the center of the primary

(larger) body.[21]For example, the Moon does not orbit the exact center of theEarth, but a point on a line

between the center of the Earth and the Moon, approximately 1,710 km (1062 miles) below the surface of

the Earth, where their respective masses balance. This is the point about which the Earth and Moon orbit as

they travel around theSun. If the masses are more similar, e.g.,Pluto and Charon, the barycenter will fall

outside both bodies.[edit]

Question: Center of Gravity DefinitionThe term "center of gravity" has implications for all things related to posture, including postural issues such

asswaybackand designingposture exerciseprograms and more.

The center of gravity is a theoretical place in your body where your mass is considered to concentrate.Answer:

What do I mean by that? Well, here on earth, weight and mass are pretty much the same thing.

You can think ofmassas how much resistance your body has when moving - or the force of inertia as it

applies to your weight. (In outer space, you become weightless, but your mass stays the same. This is

because in outer space the force of gravity does not act on your body.)
http://en.wikipedia.org/wiki/Sports_carhttp://en.wikipedia.org/wiki/Sports_carhttp://en.wikipedia.org/wiki/Sports_carhttp://en.wikipedia.org/wiki/Car_handlinghttp://en.wikipedia.org/wiki/Car_handlinghttp://en.wikipedia.org/wiki/Car_handlinghttp://en.wikipedia.org/wiki/High_jumphttp://en.wikipedia.org/wiki/High_jumphttp://en.wikipedia.org/wiki/High_jumphttp://en.wikipedia.org/wiki/Fosbury_Flophttp://en.wikipedia.org/wiki/Fosbury_Flophttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEVan_Pelt2005185-18http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEVan_Pelt2005185-18http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEVan_Pelt2005185-18http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=13http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=13http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=13http://en.wikipedia.org/wiki/Center_of_gravity_of_an_aircrafthttp://en.wikipedia.org/wiki/Center_of_gravity_of_an_aircrafthttp://en.wikipedia.org/wiki/Center_of_gravity_of_an_aircrafthttp://en.wikipedia.org/wiki/Aircrafthttp://en.wikipedia.org/wiki/Aircrafthttp://en.wikipedia.org/wiki/Aircrafthttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEFederal_Aviation_Administration20071.4-19http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEFederal_Aviation_Administration20071.4-19http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEFederal_Aviation_Administration20071.4-19http://en.wikipedia.org/wiki/Elevator_(aircraft)http://en.wikipedia.org/wiki/Elevator_(aircraft)http://en.wikipedia.org/wiki/Elevator_(aircraft)http://en.wikipedia.org/wiki/Stall_(flight)http://en.wikipedia.org/wiki/Stall_(flight)http://en.wikipedia.org/wiki/Stall_(flight)http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEFederal_Aviation_Administration20071.3-20http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEFederal_Aviation_Administration20071.3-20http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEFederal_Aviation_Administration20071.3-20http://en.wikipedia.org/wiki/Helicopterhttp://en.wikipedia.org/wiki/Helicopterhttp://en.wikipedia.org/wiki/Helicopterhttp://en.wikipedia.org/wiki/Hover_(helicopter)http://en.wikipedia.org/wiki/Hover_(helicopter)http://en.wikipedia.org/wiki/Hover_(helicopter)http://en.wikipedia.org/wiki/Rotorheadhttp://en.wikipedia.org/wiki/Rotorheadhttp://en.wikipedia.org/wiki/Rotorheadhttp://en.wikipedia.org/wiki/Helicopter_flight_controls#Cyclichttp://en.wikipedia.org/wiki/Helicopter_flight_controls#Cyclichttp://en.wikipedia.org/wiki/Helicopter_flight_controls#Cyclichttp://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=14http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=14http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=14http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)http://en.wikipedia.org/wiki/Orbithttp://en.wikipedia.org/wiki/Orbithttp://en.wikipedia.org/wiki/Natural_satellitehttp://en.wikipedia.org/wiki/Natural_satellitehttp://en.wikipedia.org/wiki/Natural_satellitehttp://en.wikipedia.org/wiki/Planethttp://en.wikipedia.org/wiki/Planethttp://en.wikipedia.org/wiki/Planethttp://en.wikipedia.org/wiki/Starhttp://en.wikipedia.org/wiki/Starhttp://en.wikipedia.org/wiki/Starhttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEMurrayDermott199945.E2.80.9347-21http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEMurrayDermott199945.E2.80.9347-21http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEMurrayDermott199945.E2.80.9347-21http://en.wikipedia.org/wiki/Earthhttp://en.wikipedia.org/wiki/Earthhttp://en.wikipedia.org/wiki/Earthhttp://en.wikipedia.org/wiki/Sunhttp://en.wikipedia.org/wiki/Sunhttp://en.wikipedia.org/wiki/Sunhttp://en.wikipedia.org/wiki/Pluto#Charonhttp://en.wikipedia.org/wiki/Pluto#Charonhttp://en.wikipedia.org/wiki/Pluto#Charonhttp://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=15http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=15http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=15http://backandneck.about.com/od/posture/f/sway-back.htmhttp://backandneck.about.com/od/posture/f/sway-back.htmhttp://backandneck.about.com/od/posture/f/sway-back.htmhttp://backandneck.about.com/od/exerciseandsport/tp/Posture-Exercise.htmhttp://backandneck.about.com/od/exerciseandsport/tp/Posture-Exercise.htmhttp://backandneck.about.com/od/exerciseandsport/tp/Posture-Exercise.htmhttp://physics.about.com/od/glossary/g/mass.htmhttp://physics.about.com/od/glossary/g/mass.htmhttp://physics.about.com/od/glossary/g/mass.htmhttp://en.wikipedia.org/wiki/File:Orbit3.gifhttp://en.wikipedia.org/wiki/File:Orbit3.gifhttp://en.wikipedia.org/wiki/File:Orbit3.gifhttp://en.wikipedia.org/wiki/File:Orbit3.gifhttp://physics.about.com/od/glossary/g/mass.htmhttp://backandneck.about.com/od/exerciseandsport/tp/Posture-Exercise.htmhttp://backandneck.about.com/od/posture/f/sway-back.htmhttp://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=15http://en.wikipedia.org/wiki/Pluto#Charonhttp://en.wikipedia.org/wiki/Sunhttp://en.wikipedia.org/wiki/Earthhttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEMurrayDermott199945.E2.80.9347-21http://en.wikipedia.org/wiki/Starhttp://en.wikipedia.org/wiki/Planethttp://en.wikipedia.org/wiki/Natural_satellitehttp://en.wikipedia.org/wiki/Orbithttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=14http://en.wikipedia.org/wiki/Helicopter_flight_controls#Cyclichttp://en.wikipedia.org/wiki/Rotorheadhttp://en.wikipedia.org/wiki/Hover_(helicopter)http://en.wikipedia.org/wiki/Helicopterhttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEFederal_Aviation_Administration20071.3-20http://en.wikipedia.org/wiki/Stall_(flight)http://en.wikipedia.org/wiki/Elevator_(aircraft)http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEFederal_Aviation_Administration20071.4-19http://en.wikipedia.org/wiki/Aircrafthttp://en.wikipedia.org/wiki/Center_of_gravity_of_an_aircrafthttp://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit&section=13http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEVan_Pelt2005185-18http://en.wikipedia.org/wiki/Fosbury_Flophttp://en.wikipedia.org/wiki/High_jumphttp://en.wikipedia.org/wiki/Car_handlinghttp://en.wikipedia.org/wiki/Sports_car


8/25

8

Center of Mass - Theory and Application

Another way of looking at this is that the center of gravity (mass) is the point at which the body's mass is

equally balanced. This changes depending on one's position (arms up/down, leaning, etc). Dancers, gymnas

and tight-rope walkers are examples of how the human body compensates for changes in the center of

gravity to maintain balance.

Usually the center of gravity is located in front of your sacrum bone, at about the second sacral level. (The

sacrum is made up of five bones fused together vertically.) So when you are on planet earth your weight, or

mass, is thought to be concentrated at this point in front of yoursacrum. The downward pull of gravity (line

of gravity) passes through this point, as well.To understand the difference between theory and practical application of this concept, lets compare thehuman body to a baseball for a minute. From a point in the exact center, the baseball is of equal weight and

shape all the way around, is it not? So, with any movement of the ball, this center point moves right along

with it. Easy.

But when we consider center of gravity in the human body, things get more complicated. As we mentioned

before, because the body has moving parts (arms, legs, head, various areas of the trunk), every time you do,

well, anything, the shape of your overall form changes. And if you carry something like a suitcase or grocery

bag or if you wear abackpack, this adds weight, which changes the center of gravity, too.

So, we can say that the center of gravity is a constantly changing point in the body that represents where th

weight (mass) of the rest of your body is equally balanced in every direction. This point can and does chang

based on what youre carrying and how youre carrying it, as well as the position you take and themovements you make.My personal take on it this: In an ideal situation I like to think of the center of gravity as the place from whic

you can operate your whole body as a unit, while gracefully coordinating the movement of appendages as

you go.

When calculating in single particle systems such as an atom or a defined point, the physical shape and

geometry of its mass is insignificant. However in real life, no object is simply a particle and possess a great

complications in its physical geometry. When dealing with such problems, we calculate the kinematics

relative to its center of mass. But not only is the center of mass used for physical objects, also for multi-

particle systems which can be treated as a single entity and the dynamics of each particle is calculated

relative to the system's center of mass.COM IN ASTRONOMY

Inastronomy,barycentric coordinates are non-rotating coordinates with origin at thecenter of massof

two or more bodies.

The barycenter (or barycentre; from the Greek -heavy+ -centre + -ic[1]) is the point betweetwo objects where they balance each other. For example, it is the center of mass where two or more celestia

bodiesorbiteach other. When amoonorbits aplanet, or a planet orbits astar, both bodies are actually

orbiting around a point that is not at the center of the primary (the larger body). For example, the moon doe

not orbit the exact center of theEarth, but a point on a line between the center of the Earth and the Moon,

approximately 1,710 km below the surface of the Earth, where their respective masses balance. This is the

point about which the Earth and Moon orbit as they travel around theSun.
http://backandneck.about.com/od/s/g/sacrumsacral.htmhttp://backandneck.about.com/od/s/g/sacrumsacral.htmhttp://backandneck.about.com/od/s/g/sacrumsacral.htmhttp://backandneck.about.com/od/childrensissues/tp/Backpacks-Back-Packs-Back-Pain.htmhttp://backandneck.about.com/od/childrensissues/tp/Backpacks-Back-Packs-Back-Pain.htmhttp://backandneck.about.com/od/childrensissues/tp/Backpacks-Back-Packs-Back-Pain.htmhttp://en.wikipedia.org/wiki/Astronomyhttp://en.wikipedia.org/wiki/Astronomyhttp://en.wikipedia.org/wiki/Astronomyhttp://en.wikipedia.org/wiki/Center_of_masshttp://en.wikipedia.org/wiki/Center_of_masshttp://en.wikipedia.org/wiki/Center_of_masshttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#cite_note-1http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#cite_note-1http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#cite_note-1http://en.wikipedia.org/wiki/Orbithttp://en.wikipedia.org/wiki/Orbithttp://en.wikipedia.org/wiki/Orbithttp://en.wikipedia.org/wiki/Natural_satellitehttp://en.wikipedia.org/wiki/Natural_satellitehttp://en.wikipedia.org/wiki/Planethttp://en.wikipedia.org/wiki/Planethttp://en.wikipedia.org/wiki/Planethttp://en.wikipedia.org/wiki/Starhttp://en.wikipedia.org/wiki/Starhttp://en.wikipedia.org/wiki/Starhttp://en.wikipedia.org/wiki/Earthhttp://en.wikipedia.org/wiki/Earthhttp://en.wikipedia.org/wiki/Earthhttp://en.wikipedia.org/wiki/Sunhttp://en.wikipedia.org/wiki/Sunhttp://en.wikipedia.org/wiki/Sunhttp://en.wikipedia.org/wiki/Sunhttp://en.wikipedia.org/wiki/Earthhttp://en.wikipedia.org/wiki/Starhttp://en.wikipedia.org/wiki/Planethttp://en.wikipedia.org/wiki/Natural_satellitehttp://en.wikipedia.org/wiki/Orbithttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#cite_note-1http://en.wikipedia.org/wiki/Center_of_masshttp://en.wikipedia.org/wiki/Astronomyhttp://backandneck.about.com/od/childrensissues/tp/Backpacks-Back-Packs-Back-Pain.htmhttp://backandneck.about.com/od/s/g/sacrumsacral.htm


9/25

9

Contents

[hide]

1 Two-body problem

1.1 Examples

1.2 Inside or outside the Sun?

1.3 Animations

2 Relativistic corrections

3 Selected barycentric orbital elements

4 References

[edit]Two-body problem

The barycenter is one of thefociof theelliptical orbitof each body. This is an important concept in the field

ofastronomy,astrophysics, and the like (seetwo-body problem). In a simple two-body case, r1, the distance

from the center of the primary to the barycenter is given by:

Ifa is the semi-major axis of the system, r1 is thesemi-major axisof the primary's orbit around the

barycenter, and r2 = ar1 is the semi-major axis of the secondary's orbit. When the barycenter islocated within the more massive body, that body will appear to "wobble" rather than following a discernible

orbit.[edit]Examples

The following table sets out some examples from theSolar System. Figures are given rounded to

threesignificant figures. The last two columns show R1, the radius of the first (more massive) body,

and r1/R1, the ratio of the distance to the barycenter and that radius: a value less than one shows that the

barycenter lies inside the first body.

Examples

Larger

body

m1

(mE=1)

Smaller

body

m2

(mE=1)

a

(km)

r1

(km)

R1

(km)r1/R1

Remarks

Earth 1 Moon 0.0123 384,000 4,670 6,380 0.732

The Earth has a perceptible "wobble"; seetides.

Pluto 0.0021 Charon0.000254

(0.121 mPluto)19,600 2,110 1,150 1.83

Both bodies have distinct orbits around the barycenter, and as such Pluto and Charon were considered

adouble planetby many before the redefinition ofplanetin August 2006.

Sun 333,000 Earth 1150,000,000

(1AU)449 696,000 0.00064

The Sun's wobble is barely perceptible.

Sun 333,000 Jupiter318

(0.000955 mSun)

778,000,000

(5.20 AU)742,000 696,000 1.07

The Sun orbits a barycenter just above its surface.[2]

[edit]Inside or outside the Sun?

Ifm1m2 which is true for the Sun and any planet then the ratio r1/R1 approximates to:

Hence, the barycenter of the Sun-planet system will lie outside the Sun only if:
http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#Two-body_problemhttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#Two-body_problemhttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#Exampleshttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#Exampleshttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#Inside_or_outside_the_Sun.3Fhttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#Inside_or_outside_the_Sun.3Fhttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#Animationshttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#Animationshttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#Relativistic_correctionshttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#Relativistic_correctionshttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#Selected_barycentric_orbital_elementshttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#Selected_barycentric_orbital_elementshttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#Referenceshttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#Referenceshttp://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit&section=1http://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit&section=1http://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit&section=1http://en.wikipedia.org/wiki/Focus_(geometry)http://en.wikipedia.org/wiki/Focus_(geometry)http://en.wikipedia.org/wiki/Focus_(geometry)http://en.wikipedia.org/wiki/Elliptic_orbithttp://en.wikipedia.org/wiki/Elliptic_orbithttp://en.wikipedia.org/wiki/Elliptic_orbithttp://en.wikipedia.org/wiki/Astronomyhttp://en.wikipedia.org/wiki/Astronomyhttp://en.wikipedia.org/wiki/Astronomyhttp://en.wikipedia.org/wiki/Astrophysicshttp://en.wikipedia.org/wiki/Astrophysicshttp://en.wikipedia.org/wiki/Astrophysicshttp://en.wikipedia.org/wiki/Two-body_problemhttp://en.wikipedia.org/wiki/Two-body_problemhttp://en.wikipedia.org/wiki/Two-body_problemhttp://en.wikipedia.org/wiki/Semi-major_axishttp://en.wikipedia.org/wiki/Semi-major_axishttp://en.wikipedia.org/wiki/Semi-major_axishttp://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit&section=2http://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit&section=2http://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit&section=2http://en.wikipedia.org/wiki/Solar_Systemhttp://en.wikipedia.org/wiki/Solar_Systemhttp://en.wikipedia.org/wiki/Solar_Systemhttp://en.wikipedia.org/wiki/Significant_figureshttp://en.wikipedia.org/wiki/Significant_figureshttp://en.wikipedia.org/wiki/Significant_figureshttp://en.wikipedia.org/wiki/Kilometrehttp://en.wikipedia.org/wiki/Kilometrehttp://en.wikipedia.org/wiki/Kilometrehttp://en.wikipedia.org/wiki/Earthhttp://en.wikipedia.org/wiki/Earthhttp://en.wikipedia.org/wiki/Moonhttp://en.wikipedia.org/wiki/Moonhttp://en.wikipedia.org/wiki/Tidehttp://en.wikipedia.org/wiki/Tidehttp://en.wikipedia.org/wiki/Tidehttp://en.wikipedia.org/wiki/Plutohttp://en.wikipedia.org/wiki/Plutohttp://en.wikipedia.org/wiki/Charon_(moon)http://en.wikipedia.org/wiki/Charon_(moon)http://en.wikipedia.org/wiki/Double_planethttp://en.wikipedia.org/wiki/Double_planethttp://en.wikipedia.org/wiki/Double_planethttp://en.wikipedia.org/wiki/Planethttp://en.wikipedia.org/wiki/Planethttp://en.wikipedia.org/wiki/Planethttp://en.wikipedia.org/wiki/Sunhttp://en.wikipedia.org/wiki/Sunhttp://en.wikipedia.org/wiki/Astronomical_unithttp://en.wikipedia.org/wiki/Astronomical_unithttp://en.wikipedia.org/wiki/Jupiterhttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#cite_note-NASA2005-2http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#cite_note-NASA2005-2http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#cite_note-NASA2005-2http://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit&section=3http://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit&section=3http://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit&section=3http://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit&section=3http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#cite_note-NASA2005-2http://en.wikipedia.org/wiki/Jupiterhttp://en.wikipedia.org/wiki/Astronomical_unithttp://en.wikipedia.org/wiki/Sunhttp://en.wikipedia.org/wiki/Planethttp://en.wikipedia.org/wiki/Double_planethttp://en.wikipedia.org/wiki/Charon_(moon)http://en.wikipedia.org/wiki/Plutohttp://en.wikipedia.org/wiki/Tidehttp://en.wikipedia.org/wiki/Moonhttp://en.wikipedia.org/wiki/Earthhttp://en.wikipedia.org/wiki/Kilometrehttp://en.wikipedia.org/wiki/Significant_figureshttp://en.wikipedia.org/wiki/Solar_Systemhttp://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit&section=2http://en.wikipedia.org/wiki/Semi-major_axishttp://en.wikipedia.org/wiki/Two-body_problemhttp://en.wikipedia.org/wiki/Astrophysicshttp://en.wikipedia.org/wiki/Astronomyhttp://en.wikipedia.org/wiki/Elliptic_orbithttp://en.wikipedia.org/wiki/Focus_(geometry)http://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit&section=1http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#Referenceshttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#Selected_barycentric_orbital_elementshttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#Relativistic_correctionshttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#Animationshttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#Inside_or_outside_the_Sun.3Fhttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#Exampleshttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#Two-body_problemhttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)


10/25

10

That is, where the planet is heavy andfar from the Sun.

If Jupiter hadMercury's orbit (57,900,000 km, 0.387 AU), the Sun-Jupiter barycenter would be only 5,500 k

from the center of the Sun (r1/R1 ~ 0.08). But even if the Earth hadEris'orbit (68 AU), the Sun-Earth

barycenter would still be within the Sun (just over 30,000 km from the center).

To calculate the actual motion of the Sun, you would need to sum all the influences from all

theplanets,comets,asteroids, etc. of theSolar System(seen-body problem). If all the planets were aligned

on the same side of the Sun, the combined center of mass would lie about 500,000 km above the Sun's

surface.

The calculations above are based on the mean distance between the bodies and yield the mean value r1. But

all celestial orbits are elliptical, and the distance between the bodies varies between theapses, depending otheeccentricity,e. Hence, the position of the barycenter varies too, and it is possible in some systems for the

barycenter to be sometimes inside and sometimes outside the more massive body. This occurs where:

Note that the Sun-Jupiter system, with eJupiter = 0.0484, just fails to qualify: 1.05 1.07 > 0.954.[edit]Animations

Images are representative (made by hand), not simulated.

wo bodies of similar mass

biting a common

arycenter (similar to the90

ntiopesystem)

Two bodies with a difference

in mass orbiting a common

barycenter external to both

bodies, as in thePlutoCharonsystem

Two bodies with a major difference in

mass orbiting a common barycenter

internal to one body (similar to

theEarthMoonsystem)
http://en.wikipedia.org/wiki/Mercury_(planet)http://en.wikipedia.org/wiki/Mercury_(planet)http://en.wikipedia.org/wiki/Mercury_(planet)http://en.wikipedia.org/wiki/Eris_(dwarf_planet)http://en.wikipedia.org/wiki/Eris_(dwarf_planet)http://en.wikipedia.org/wiki/Planethttp://en.wikipedia.org/wiki/Planethttp://en.wikipedia.org/wiki/Planethttp://en.wikipedia.org/wiki/Comethttp://en.wikipedia.org/wiki/Comethttp://en.wikipedia.org/wiki/Comethttp://en.wikipedia.org/wiki/Asteroidhttp://en.wikipedia.org/wiki/Asteroidhttp://en.wikipedia.org/wiki/Asteroidhttp://en.wikipedia.org/wiki/Solar_Systemhttp://en.wikipedia.org/wiki/Solar_Systemhttp://en.wikipedia.org/wiki/Solar_Systemhttp://en.wikipedia.org/wiki/N-body_problemhttp://en.wikipedia.org/wiki/N-body_problemhttp://en.wikipedia.org/wiki/N-body_problemhttp://en.wikipedia.org/wiki/Apsishttp://en.wikipedia.org/wiki/Apsishttp://en.wikipedia.org/wiki/Apsishttp://en.wikipedia.org/wiki/Eccentricity_(orbit)http://en.wikipedia.org/wiki/Eccentricity_(orbit)http://en.wikipedia.org/wiki/Eccentricity_(orbit)http://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit&section=4http://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit&section=4http://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit&section=4http://en.wikipedia.org/wiki/90_Antiopehttp://en.wikipedia.org/wiki/90_Antiopehttp://en.wikipedia.org/wiki/90_Antiopehttp://en.wikipedia.org/wiki/90_Antiopehttp://en.wikipedia.org/wiki/Plutohttp://en.wikipedia.org/wiki/Plutohttp://en.wikipedia.org/wiki/Charon_(moon)http://en.wikipedia.org/wiki/Charon_(moon)http://en.wikipedia.org/wiki/Earthhttp://en.wikipedia.org/wiki/Earthhttp://en.wikipedia.org/wiki/Moonhttp://en.wikipedia.org/wiki/Moonhttp://en.wikipedia.org/wiki/File:Orbit3.gifhttp://en.wikipedia.org/wiki/File:Orbit2.gifhttp://en.wikipedia.org/wiki/File:Orbit1.gifhttp://en.wikipedia.org/wiki/File:Orbit3.gifhttp://en.wikipedia.org/wiki/File:Orbit2.gifhttp://en.wikipedia.org/wiki/File:Orbit1.gifhttp://en.wikipedia.org/wiki/File:Orbit3.gifhttp://en.wikipedia.org/wiki/File:Orbit2.gifhttp://en.wikipedia.org/wiki/File:Orbit1.gifhttp://en.wikipedia.org/wiki/Moonhttp://en.wikipedia.org/wiki/Earthhttp://en.wikipedia.org/wiki/Charon_(moon)http://en.wikipedia.org/wiki/Plutohttp://en.wikipedia.org/wiki/90_Antiopehttp://en.wikipedia.org/wiki/90_Antiopehttp://en.wikipedia.org/wiki/File:Orbit3.gifhttp://en.wikipedia.org/wiki/File:Orbit2.gifhttp://en.wikipedia.org/wiki/File:Orbit1.gifhttp://en.wikipedia.org/wiki/File:Orbit3.gifhttp://en.wikipedia.org/wiki/File:Orbit2.gifhttp://en.wikipedia.org/wiki/File:Orbit1.gifhttp://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit&section=4http://en.wikipedia.org/wiki/Eccentricity_(orbit)http://en.wikipedia.org/wiki/Apsishttp://en.wikipedia.org/wiki/N-body_problemhttp://en.wikipedia.org/wiki/Solar_Systemhttp://en.wikipedia.org/wiki/Asteroidhttp://en.wikipedia.org/wiki/Comethttp://en.wikipedia.org/wiki/Planethttp://en.wikipedia.org/wiki/Eris_(dwarf_planet)http://en.wikipedia.org/wiki/Mercury_(planet)


11/25

11

[edit]Relativistic corrections

Inclassical mechanics, this definition simplifies calculations and introduces no known problems. Ingeneral

relativity, problems arise because, while it is possible, within reasonable approximations, to define the

barycenter, the associated coordinate system does not fully reflect the inequality of clock rates at different

locations. Brumberg explains how to set up barycentric coordinates in general relativity.[3]

The coordinate systems involve a world-time, i.e., a global time coordinate that could be set up bytelemetry

Individual clocks of similar construction will not agree with this standard, because they are subject to

differinggravitational potentialsor move at various velocities, so the world-time must be slaved to some

ideal clock; that one is assumed to be very far from the whole self-gravitating system. This time standard is

calledBarycentric Coordinate Time, "TCB".

[edit]Selected barycentric orbital elements

Barycentric osculating orbital elements for some objects in the Solar System:[4]

ObjectSemi-major axis

(inAU)

Apoapsis

(in AU)Orbital period in years

C/2006 P1 (McNaught) 2050 4100 92600

Comet Hyakutake 1700 3410 70000

C/2006 M4 (SWAN) 1300 2600 47000

(308933) 2006 SQ372 799 1570 22600

(87269) 2000 OO67 549 1078 12800

90377 Sedna 506 937 11400

2007 TG422 501 967 11200

For objects at such high eccentricity, the Sun's barycentric coordinates are more stable than heliocentric

coordinates.[5]

Top Research InstitutesIndian Institute of Technology (IIT), BombayIndian Institute of Science (IISc)(www.iisc.ernet.in)

Bhabha Atomic Research Centre (BARC)

Defence Research and Development Organization (DRDO)

Indian Space Research Organization (ISRO)

Tata Institute of Fundamental Research

Indian Institute of Astrophysics

Saha Institute of Nuclear Physics

All India Institute of Medical Sciences

wo bodies with similar mass orbiting a common barycenter,

ternal to both bodies, with eccentricelliptic orbits(a

mmon situation forbinary stars)

Two bo

with an

extrem

differen

in mass

orbitin

commo

barycen

internaone bod

(simila

theSun

Earthsy

m)
http://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit&section=5http://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit&section=5http://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit&section=5http://en.wikipedia.org/wiki/Classical_mechanicshttp://en.wikipedia.org/wiki/Classical_mechanicshttp://en.wikipedia.org/wiki/Classical_mechanicshttp://en.wikipedia.org/wiki/General_relativityhttp://en.wikipedia.org/wiki/General_relativityhttp://en.wikipedia.org/wiki/General_relativityhttp://en.wikipedia.org/wiki/General_relativityhttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#cite_note-3http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#cite_note-3http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#cite_note-3http://en.wikipedia.org/wiki/Telemetryhttp://en.wikipedia.org/wiki/Telemetryhttp://en.wikipedia.org/wiki/Gravitational_potentialhttp://en.wikipedia.org/wiki/Gravitational_potentialhttp://en.wikipedia.org/wiki/Gravitational_potentialhttp://en.wikipedia.org/wiki/Barycentric_Coordinate_Timehttp://en.wikipedia.org/wiki/Barycentric_Coordinate_Timehttp://en.wikipedia.org/wiki/Barycentric_Coordinate_Timehttp://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit&section=6http://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit&section=6http://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit&section=6http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#cite_note-barycenter-4http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#cite_note-barycenter-4http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#cite_note-barycenter-4http://en.wikipedia.org/wiki/Small_Solar_System_bodyhttp://en.wikipedia.org/wiki/Semi-major_axishttp://en.wikipedia.org/wiki/Semi-major_axishttp://en.wikipedia.org/wiki/Astronomical_unithttp://en.wikipedia.org/wiki/Astronomical_unithttp://en.wikipedia.org/wiki/Astronomical_unithttp://en.wikipedia.org/wiki/Apoapsishttp://en.wikipedia.org/wiki/Apoapsishttp://en.wikipedia.org/wiki/C/2006_P1http://en.wikipedia.org/wiki/C/2006_P1http://en.wikipedia.org/wiki/Comet_Hyakutakehttp://en.wikipedia.org/wiki/Comet_Hyakutakehttp://en.wikipedia.org/wiki/C/2006_M4_(SWAN)http://en.wikipedia.org/wiki/C/2006_M4_(SWAN)http://en.wikipedia.org/wiki/(308933)_2006_SQ372http://en.wikipedia.org/wiki/(308933)_2006_SQ372http://en.wikipedia.org/wiki/(308933)_2006_SQ372http://en.wikipedia.org/wiki/(87269)_2000_OO67http://en.wikipedia.org/wiki/(87269)_2000_OO67http://en.wikipedia.org/wiki/(87269)_2000_OO67http://en.wikipedia.org/wiki/90377_Sednahttp://en.wikipedia.org/wiki/90377_Sednahttp://en.wikipedia.org/wiki/2007_TG422http://en.wikipedia.org/wiki/2007_TG422http://en.wikipedia.org/wiki/2007_TG422http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#cite_note-Kaib2009-5http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#cite_note-Kaib2009-5http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#cite_note-Kaib2009-5http://www.iisc.ernet.in/http://www.iisc.ernet.in/http://www.iisc.ernet.in/http://en.wikipedia.org/wiki/Elliptic_orbithttp://en.wikipedia.org/wiki/Elliptic_orbithttp://en.wikipedia.org/wiki/Elliptic_orbithttp://en.wikipedia.org/wiki/Binary_starhttp://en.wikipedia.org/wiki/Binary_starhttp://en.wikipedia.org/wiki/Binary_starhttp://en.wikipedia.org/wiki/Sunhttp://en.wikipedia.org/wiki/Sunhttp://en.wikipedia.org/wiki/Earthhttp://en.wikipedia.org/wiki/Earthhttp://en.wikipedia.org/wiki/File:Orbit4.gifhttp://en.wikipedia.org/wiki/File:Orbit5.gifhttp://en.wikipedia.org/wiki/File:Orbit4.gifhttp://en.wikipedia.org/wiki/File:Orbit5.gifhttp://en.wikipedia.org/wiki/Earthhttp://en.wikipedia.org/wiki/Sunhttp://en.wikipedia.org/wiki/Binary_starhttp://en.wikipedia.org/wiki/Elliptic_orbithttp://www.iisc.ernet.in/http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#cite_note-Kaib2009-5http://en.wikipedia.org/wiki/2007_TG422http://en.wikipedia.org/wiki/90377_Sednahttp://en.wikipedia.org/wiki/(87269)_2000_OO67http://en.wikipedia.org/wiki/(308933)_2006_SQ372http://en.wikipedia.org/wiki/C/2006_M4_(SWAN)http://en.wikipedia.org/wiki/Comet_Hyakutakehttp://en.wikipedia.org/wiki/C/2006_P1http://en.wikipedia.org/wiki/Apoapsishttp://en.wikipedia.org/wiki/Astronomical_unithttp://en.wikipedia.org/wiki/Semi-major_axishttp://en.wikipedia.org/wiki/Small_Solar_System_bodyhttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#cite_note-barycenter-4http://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit&section=6http://en.wikipedia.org/wiki/Barycentric_Coordinate_Timehttp://en.wikipedia.org/wiki/Gravitational_potentialhttp://en.wikipedia.org/wiki/Telemetryhttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#cite_note-3http://en.wikipedia.org/wiki/General_relativityhttp://en.wikipedia.org/wiki/General_relativityhttp://en.wikipedia.org/wiki/Classical_mechanicshttp://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit&section=5


12/25

12

Indian Statistical Institute

Top 20 Scientific Research Institutes in India

1. Indian Institute of Science (Bangalore)

2. National Physical Laboratory (New Delhi)

3. Defence Research Development Organisation (New Delhi)

4. Institute of Physics (Bhubhaneswar)

5. Tata Institute of Fundamental Research (Mumbai)

6. Inter-University Centre for Astronomy and Astrophysics (Pune)

7. National Centre for Radio Astrophysics (Pune)8. Inter-University Consortium for DAE Facilities (Indore) Jawaharlal Nehru Centre for Advanced Scientific

Research (Bangalore)

9. Institute of Mathematical Sciences (Chennai)

10. Centre for Advanced Technology (Indore)

11. Indian Spare Research Organisation- (1) Physical Research Laboratory (Ahmedabad); and (2) Space

Physics Laboratory (Thiruvananthapuram)

12. Mehta Research Institute of Mathematics and Mathematical Physics (Allahabad)

13. Bhabha Atomic Research Centre (Mumbai)

14. Physical Research Laboratory (Ahmedabad)

15. Saha Institute of Nuclear Physics (Kolkata) S N Bose National Centre for Basic Sciences (Kolkata)

16. Raman Research Institute (Bangalore)17. Indira Gandhi Centre for Atomic Research (Kalpakkam, Tamil Nadu)

18. Atomic Minerals Directorate for Exploration and Research (Hyderabad).

19. Indian Institute of Astrophysics (Bangalore)

20. Institute of Plasma Research (Gandhinagar)

Launch Vehicles are used to transport and putsatellitesor spacecrafts into space. In India, the launch

vehicles development programme began in the early 1970s. The first experimental Satellite Launch

Vehicle (SLV-3) was developed in 1980. An Augmented version of this,ASLV, was launched successfully in

1992. India has made tremendous strides in launch vehicle technology to achieve self-reliance in satellite

launch vehicle programme with the operationalisation of Polar Satellite Launch Vehicle (PSLV) and

Geosynchronous Satellite Launch Vehicle (GSLV).PSLV represents ISRO's first attempt to design and develop an operational vehicle that can be used to

orbit application satellites. While SLV-3 secured for India a place in the community of space-faring

nations, the ASLV provided the rites of passage into launch vehicle technology for ISRO. And with PSLV, a

new world-class vehicle has arrived. PSLV has repeatedly proved its reliability and versatility by

launching 55satellites / spacecrafts ( 26 Indian and 29Foreign Satellites) into a variety of orbits so far.

ISRO also makes the Rohini series of sounding rockets used by the Indian and international scientific

community to launch payloads to various altitudes for atmospheric research and other scientific

investigations. These rockets are also used to qualify some of the critical systems used for advanced

launch vehicles.

Landmark achievements in ISRO's Launch Vehicle Development

PSLVhas 21 consecutively successful flights out of 22 launches

PSLV used for launching a total of 27 satellites for foreign customers under commercial

agreements, demonstrating its multi-satellite launch capability

PSLVused to launchSpace capsule Recovery Experiment(SRE-1),Chandrayaan-1and
http://www.isro.org/satellites/satelliteshome.aspxhttp://www.isro.org/satellites/satelliteshome.aspxhttp://www.isro.org/satellites/satelliteshome.aspxhttp://www.isro.org/Launchvehicles/launchvehicles.aspx#SLV3http://www.isro.org/Launchvehicles/launchvehicles.aspx#SLV3http://www.isro.org/Launchvehicles/launchvehicles.aspx#SLV3http://www.isro.org/Launchvehicles/launchvehicles.aspx#ASLVhttp://www.isro.org/Launchvehicles/launchvehicles.aspx#ASLVhttp://www.isro.org/Launchvehicles/launchvehicles.aspx#ASLVhttp://www.isro.org/pdf/foreignsatellite.pdfhttp://www.isro.org/pdf/foreignsatellite.pdfhttp://www.isro.org/pdf/foreignsatellite.pdfhttp://www.isro.org/Launchvehicles/PSLV/pslv.aspxhttp://www.isro.org/Launchvehicles/PSLV/pslv.aspxhttp://www.isro.org/Launchvehicles/PSLV/pslv.aspxhttp://www.isro.org/Launchvehicles/PSLV/pslv.aspxhttp://www.isro.org/Launchvehicles/PSLV/pslv.aspxhttp://www.isro.org/satellites/sre-1.aspxhttp://www.isro.org/satellites/sre-1.aspxhttp://www.isro.org/satellites/sre-1.aspxhttp://www.isro.org/satellites/chandrayaan-1.aspxhttp://www.isro.org/satellites/chandrayaan-1.aspxhttp://www.isro.org/satellites/chandrayaan-1.aspxhttp://www.isro.org/satellites/chandrayaan-1.aspxhttp://www.isro.org/satellites/sre-1.aspxhttp://www.isro.org/Launchvehicles/PSLV/pslv.aspxhttp://www.isro.org/Launchvehicles/PSLV/pslv.aspxhttp://www.isro.org/Launchvehicles/PSLV/pslv.aspxhttp://www.isro.org/pdf/foreignsatellite.pdfhttp://www.isro.org/Launchvehicles/launchvehicles.aspx#ASLVhttp://www.isro.org/Launchvehicles/launchvehicles.aspx#SLV3http://www.isro.org/satellites/satelliteshome.aspx


13/25

13

ISRO's exclusive meteorological satellite,KALPANA-1, proving its versatility

GSLVwith four successful flights of seven launches can launch 2 to 2.5 tonne satellite into Geo-

synchronous Transfer Orbit (GTO)

Successful testing of indigenously developed cryogenic upper stage on November 15, 2007.

ISRO's Launch Fleet at a Glance

ISRO developed two experimental satellite launch vehicles,SLV-3andASLV

Polar Satellite Launch Vehicle(PSLV)commissioned in 1997

Geosynchronous Satellite Launch Vehicle (GSLV-Mk I) commissioned after second successful

flight in May 2003

GSLV - MK II will use indigenously developed cryogenic Upper Stage

GSLV - MK IIIis under development

SLV-3
http://www.isro.org/satellites/kalpana-1.aspxhttp://www.isro.org/satellites/kalpana-1.aspxhttp://www.isro.org/satellites/kalpana-1.aspxhttp://www.isro.org/Launchvehicles/GSLV/gslv.aspxhttp://www.isro.org/Launchvehicles/GSLV/gslv.aspxhttp://www.isro.org/Launchvehicles/launchvehicles.aspx#SLV3http://www.isro.org/Launchvehicles/launchvehicles.aspx#SLV3http://www.isro.org/Launchvehicles/launchvehicles.aspx#SLV3http://www.isro.org/Launchvehicles/launchvehicles.aspx#ASLVhttp://www.isro.org/Launchvehicles/launchvehicles.aspx#ASLVhttp://www.isro.org/Launchvehicles/launchvehicles.aspx#ASLVhttp://www.isro.org/Launchvehicles/PSLV/pslv.aspxhttp://www.isro.org/Launchvehicles/PSLV/pslv.aspxhttp://www.isro.org/Launchvehicles/GSLVMARKIII/mark3.aspxhttp://www.isro.org/Launchvehicles/GSLVMARKIII/mark3.aspxhttp://www.isro.org/Launchvehicles/GSLVMARKIII/mark3.aspxhttp://www.isro.org/Launchvehicles/PSLV/pslv.aspxhttp://www.isro.org/Launchvehicles/launchvehicles.aspx#ASLVhttp://www.isro.org/Launchvehicles/launchvehicles.aspx#SLV3http://www.isro.org/Launchvehicles/GSLV/gslv.aspxhttp://www.isro.org/satellites/kalpana-1.aspx


14/25

14

Satellite Launch Vehicle-3 (SLV-3), India's first experimental satellite

launch vehicle was successfully launched on July 18, 1980 from SHAR

Centre Sriharikota, when Rohini satellite, RS-1, was placed in orbit. SLV-3

was a 22 m long, all solid, four stage vehicle weighing 17 tonnes capable

of placing 40 kg class payloads in low earth orbit.

It employed an open loop guidance (with stored pitch programme) to

steer the vehicle in flight along pre-determined trajectory. The first

experimental flight of SLV-3, in August 1979, was only partiallysuccessful. Apart from the July 1980 launch, there were two more

launches held in May 1981 and April 1983, orbiting Rohini satellites

carrying remote sensing sensors.

ASLV

Augmented Satellite Launch Vehicle (ASLV) was developed to act as a low

cost intermediate vehicle to demonstrate and validate critical

technologies. With a lift off weight of 40 tonnes, the 23.8 m tall ASLV was

configured as a five stage, all-solid propellant vehicle, with a mission of

orbiting 150 kg class satellites into 400 km circular orbits. The strap-on

stage consisted of two identical 1m diameter solid propellant motors,Under the ASLV programme four developmental flights were conducted.

The first developmental flight took place on March 24, 1987 and the

second on July 13, 1988. ASLV-D3 was successfully launched on May 20,

1992, when SROSS-C (106 kg) was put into an orbit of 255 x 430 km.

ASLV-D4, launched on May 4, 1994, orbited SROSS-C2 weighing 106 kg. It

had two payloads, Gamma Ray Burst (GRB) Experiment and Retarding

Potentio Analyser (RPA) and functioned for seven years. ASLV provided

valuable inputs for further development.

The Polar Satellite Launch Vehicle,usually known by its abbreviation PSLV is the first operational launch

vehicle of ISRO. PSLV is capable of launching 1600 kg satellites in 620 km sun-synchronous polar orbit and

1050 kg satellite in geo-synchronous transfer orbit. In the standard configuration, it measures 44.4 m tall,

with a lift off weight of 295 tonnes. PSLV has four stages using solid and liquid propulsion systems alternate


15/25

15

The first stage is one of the largest solid propellant boosters in the world and carries 139 tonnes of propella

A cluster of six strap-ons attached to the first stage motor, four of which are ignited on the ground and two

are air-lit.

The reliability rate of PSLV has been superb. There had been 21 continuously successful flights of PSLV, till

September 2012 . With its variant configurations, PSLV has proved its multi-payload, multi-mission capabili

in a single launch and its geosynchronous launch capability. In the Chandrayaan-mission, another variant of

PSLV with an extended version of strap-on motors, PSOM-XL, the payload haul was enhanced to 1750 kg in620 km SSPO. PSLV has rightfully earned the status of workhorse launch vehicle of ISRO.

Typical Parameters of PSLV

Lift-off

weight295 tonne

Pay Load

1600 kg in to 620 km Polar

Orbit,

1060 kg in to Geosynchronous

Transfer Orbit (GTO)

Height 44 metre

PSLV Milestones

PSLV-C21launched SPOT 6 and PROITERES on September 09, 2012 (Successful)

PSLV-C19launchedRISAT-1on April 26, 2012 (Successful)

PSLV-C18launchedMegha-Tropiques,SRMSat,VesselSat-1andJugnuon October 12, 2011

(Successful)

PSLV-C17launchedGSAT - 12on July 15, 2011 (Successful)

PSLV-C16launchedRESOURCESAT - 2,YOUTHSATandX-SATon April 20, 2011 (Successful)

PSLV-C15launchedCARTOSAT-2B,ALSAT-2A, NLS 6.1 & 6.2andSTUDSATon July 12, 2010

(Successful)

PSLV-C14launchedOceansat - 2andSix Nanosatelliteson September 23, 2009 (Successful)

PSLV-C12launchedRISAT-2andANUSATon April 20, 2009 (Successfully)

PSLV-C11launchedCHANDRAYAAN-I, on October 22, 2008 (Successful)

PSLV-C9launchedCARTOSAT-2A,IMS-1and Eightnano-satellites on April 28, 2008

(Successful)

PSLV-C10launched TECSAR on January 23, 2008 (Successful)

PSLV-C8launched AGILE on April 23, 2007 (Successful)
http://www.isro.org/pslv-c21/PSLV-C21.aspxhttp://www.isro.org/pslv-c21/PSLV-C21.aspxhttp://www.isro.org/pslv-c19/PSLV-C19.aspxhttp://www.isro.org/pslv-c19/PSLV-C19.aspxhttp://www.isro.org/satellites/RISAT-1.aspxhttp://www.isro.org/satellites/RISAT-1.aspxhttp://www.isro.org/satellites/RISAT-1.aspxhttp://www.isro.org/pslv-c18/PSLV-C18.aspxhttp://www.isro.org/pslv-c18/PSLV-C18.aspxhttp://www.isro.org/satellites/megha-tropiques.aspxhttp://www.isro.org/satellites/megha-tropiques.aspxhttp://www.isro.org/satellites/megha-tropiques.aspxhttp://www.isro.org/satellites/srmsat.aspxhttp://www.isro.org/satellites/srmsat.aspxhttp://www.isro.org/satellites/srmsat.aspxhttp://www.isro.org/satellites/vesselsat-1.aspxhttp://www.isro.org/satellites/vesselsat-1.aspxhttp://www.isro.org/satellites/vesselsat-1.aspxhttp://www.isro.org/satellites/jugnu.aspxhttp://www.isro.org/satellites/jugnu.aspxhttp://www.isro.org/satellites/jugnu.aspxhttp://www.isro.org/pslv-c17/PSLV-C17.aspxhttp://www.isro.org/pslv-c17/PSLV-C17.aspxhttp://www.isro.org/satellites/gsat-12.aspxhttp://www.isro.org/satellites/gsat-12.aspxhttp://www.isro.org/satellites/gsat-12.aspxhttp://www.isro.org/pslv-c16/PSLV-C16.aspxhttp://www.isro.org/pslv-c16/PSLV-C16.aspxhttp://www.isro.org/satellites/resourcesat-2.aspxhttp://www.isro.org/satellites/resourcesat-2.aspxhttp://www.isro.org/satellites/resourcesat-2.aspxhttp://www.isro.org/satellites/youthsat.aspxhttp://www.isro.org/satellites/youthsat.aspxhttp://www.isro.org/satellites/youthsat.aspxhttp://www.isro.org/satellites/x-sat.aspxhttp://www.isro.org/satellites/x-sat.aspxhttp://www.isro.org/satellites/x-sat.aspxhttp://www.isro.org/pslv-c15/PSLV-C15.aspxhttp://www.isro.org/pslv-c15/PSLV-C15.aspxhttp://www.isro.org/satellites/cartosat-2b.aspxhttp://www.isro.org/satellites/cartosat-2b.aspxhttp://www.isro.org/satellites/cartosat-2b.aspxhttp://www.isro.org/satellites/alsat-nls.aspxhttp://www.isro.org/satellites/alsat-nls.aspxhttp://www.isro.org/satellites/alsat-nls.aspxhttp://www.isro.org/satellites/alsat-nls.aspxhttp://www.isro.org/satellites/alsat-nls.aspxhttp://www.isro.org/satellites/studsat.aspxhttp://www.isro.org/satellites/studsat.aspxhttp://www.isro.org/satellites/studsat.aspxhttp://www.isro.org/pslv-c14/PSLV-C14.aspxhttp://www.isro.org/pslv-c14/PSLV-C14.aspxhttp://www.isro.org/satellites/oceansat-2.aspxhttp://www.isro.org/satellites/oceansat-2.aspxhttp://www.isro.org/satellites/oceansat-2.aspxhttp://www.isro.org/satellites/cubesat-rubin.aspxhttp://www.isro.org/satellites/cubesat-rubin.aspxhttp://www.isro.org/satellites/cubesat-rubin.aspxhttp://www.isro.org/pslv-c12/PSLV-C12.aspxhttp://www.isro.org/pslv-c12/PSLV-C12.aspxhttp://www.isro.org/satellites/RISAT-2.aspxhttp://www.isro.org/satellites/RISAT-2.aspxhttp://www.isro.org/s

Center of Gravity vs Center of Mass

Documents

Transcript of Center of Gravity vs Center of Mass