MK Fisika Dasar 1 ENGE600003 4 sks

MK Fisika Dasar 1ENGE6000034 sksRachmat AndikaMultiferroic Research GroupDepartemen FisikaFMIPA - UIGravitation

MateriNewtons Gravitation LawWeightGravitational Potential EnergySatellite MotionKeplers Law and Planet Motion

Newtons Law of Universal Gravitation

Every particle in the Universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them

where G is a constant, called the universal gravitational constantMeasured experimentallyrachmat andika - rachmat.andika@sci.ui.ac.idNewtons Law of Universal GravitationThe magnitude of the force exerted by the Earth on a particle of mass m near the Earths surface is

Where ME is the Earths mass and RE its radius.The direction: toward the center of the Earth

A uniform spherical shell of matter attracts a particle that is outside the shell as if all the shells mass were concentrated at its centerShell theoremGravitation and the Principle of SuperpositionFor n interacting particles, we can write the principle of superposition for the gravitational force on particle 1 as

Example 1Three 0.300 kg billiard balls are placed on a table at the corners of a right triangle. Calculate the gravitational force on the cue ball (designated m1) resulting from the other balls !

HINT:Use vector expression and net gravitational force on particle

Free-Fall Acceleration and the Gravitational ForceRemember ! mg is defined as the weight of an object of mass m.

An object of mass m located a distance h above the Earths surface

Example 2Using the known radius of the Earth, 6.37x106 m, and the fact that g = 9.80 m/s2 at the Earths surface, find the average density of the Earth !HINT : - Use definition of density of an object

- Calculate ME by using the gravitational acceleration

- Combine those by substituting method to obtain the density of the EarthKeplers Laws and the Motion of PlanetsGeocentric model : the Earth as the center of the UniverseHeliocentric model: the Sun as the center of the Universe

1. All planets move in elliptical orbits with the Sun at one focus2. The radius vector drawn from the Sun to a planet sweeps out equal areas in equal time intervals3. The square of the orbital period of any planet is proportional to the cube of the semimajor axis of the elliptical orbitKEPLERs LawKeplers First Law1. All planets move in elliptical orbits with the Sun at one focus

focusMajor axis: the longest distance through the center between points on the ellipse, 2aMinor axis: the shortest distance through the center between points on the ellipse, 2bIn the elliptical orbit of a planet around the Sun, the Sun is at one focus of the ellipseThe eccentricity of an ellipse is defined as e = c/a, describes the general shape of the ellipse,0 < e < 1Sun: Aphelion >< PerihelionEarth: Apogee >< Perigee

Keplers second LawThe gravitational force acting on the planet is a central force directed toward to the Sun.

The angular momentum L of the planet is a constant of the motionThe radius vector from the Sun to any planet2. The radius vector drawn from the Sun to a planet sweeps out equal areas in equal time intervals

Keplers third lawGravitational force provides the centripetal acceleration of the planet as it moves in a circle

Where K = 2.97 x 10-19 s2/m33. The square of the orbital period of any planet is proportional to the cube of the semimajor axis of the elliptical orbit

The gravitational field

Gravitational Potential EnergyThe gravitational potential-energy function mgy for a particle-Earth system is valid only when the particle is near the Earths surface.Gravitational force is CONSTANT

The change in the gravitational potential energy of a system associated with a given displacement is defined as the negative of the work done by the gravitational

Gravitational Potential EnergyIf the system contains three particles, the gravitational potential energy is

Quick ExerciseA particle of mass m is displaced through a small vertical distance y near the Earths surface. Show that in this situation the general expression for the change in gravitational potential energy reduces to the familiar relationship U=mg y .

Energy in Planetary and Satellite motionObject of mass M is at rest (inertial reference frame), the total mechanical energy E of the two-object system

Total Energy for circular orbits

Total Energy for elliptical orbitsExample 3The space shuttle releases a 470-kg communications satellite while in an orbit 280 km above the surface of the Earth. A rocket engine on the satellite boosts it into a geosynchronous orbit at 4.23x107 m. How much energy does the engine have to provide?*Geosynchronous orbit :an orbit in which the satellite stays directly over a single on the EarthHINT: Determine the initial radius of the satellites orbit Obtain the initial and final energies Calculate the difference between those energiesEscape SpeedEscape speed is the minimum speed the object must have at the Earths surface in order to approach an infinite separation distance from the Earth.

vesc is independent of the mass of the object

Can we really escape from the Earth;s gravitational influence?Example 4 Calculate the escape speed from the Earth for a 5000 kg spacecraft and determine the kinetic energy it must have at the Earths surface in order to move infinitely far away from the Earth.Given the mass of the Earth: 5.98 x 1024 kg and its radius 6.37 x 106 m

Escape SpeedGenerally, escape speed from the surface of any planet of mass M and its radius R is

Black HoleSupernova : the catastrophic explosion of a very massive starIf the core has a mass less than 1.4 times the mass of Sun, it cools down and ends as a white dwarf starWhat if the core has a mass greater than this?

The collapse may continue until the star becomes a very small object in space: BLACK HOLE

What is the effect of black hole?The object will experiences an extremely strong gravitational force and is trapped forever

Black HoleThe escape speed for a black hole is very highIf the escape speed exceeds the speed of light, radiation from the object cannot escape

Object appears to be BLACKRs is called the Schwarzschild radiusEvent horizon is the imaginary surface

PREarth and Moons gravitational forceWhat will an object weigh on the Moons surface if it weighs 100 N on Earths surface?How many Earth radii must this same object be from the center of Earth if it is to weigh the same as it does on the Moon?Keplers LawsWhat linear speed must an Earth Satellite have to be in circular orbit at an altitude of 160 km above Earths surface?What is the period of revolution?