CHAPTER 8 NOTES

KONICHEK

• I. Kepler's Laws of planetary motion.

• A. Was seeking an explanation of why Mars orbit was off of path of a circle as predicted by Brahe.

• B. Brought astronomy from a qualitative/ observational science to a quantitative/ measurement science

•

KEPLER

KEPLER’S FIRST LAW

• The planets move in elliptical orbits with the sun as 1 foci

Kepler’s second law-Law of areas

• Planets will sweep equal area in equal times

KEPLER’S THIRD LAW- The square of the periods is

proportional to the cube of the average radius of the orbit

B SAMPLE PROBLEM- The moon Io B SAMPLE PROBLEM- The moon Io is 4.2 units from the center of is 4.2 units from the center of Jupiter. It has a period of 1.8 days. Jupiter. It has a period of 1.8 days. The measurement of Ganymede’s The measurement of Ganymede’s orbit is 10.7 units, find the periodorbit is 10.7 units, find the period

II. UNIVERSAL GRAVITATION-Isaac NewtonII. UNIVERSAL GRAVITATION-Isaac Newton A. Showed that if the planets are moving in elliptical orbits A. Showed that if the planets are moving in elliptical orbits

the net force acting on the planet must vary proportionally the net force acting on the planet must vary proportionally with the inverse square of the distancewith the inverse square of the distance

1. F 1/d1. F 1/d22 d is the average distance between the 2 d is the average distance between the 2 bodiesbodies

B. The product of the 2 masses involved also play a role.B. The product of the 2 masses involved also play a role. 1. Noted the falling of an apple from a tree and 1. Noted the falling of an apple from a tree and

surmised that the earth is attracting the apple, but the apple is surmised that the earth is attracting the apple, but the apple is also attracting the earth...even if it is very littlealso attracting the earth...even if it is very little

2. Noted that the force of attraction is directly 2. Noted that the force of attraction is directly proportional to the product of the masses.proportional to the product of the masses.

C. Law of Universal Gravitation- The force of attraction is proportional to the product of the masses and inversely proportional to the square of the distance.

1. F=G M1M2/r2

a. G= 6.67x10-11NM2/Kg2

b. Cavendish experiment determined the value of G

CAVENDISH EXPERIMENT

The apparatus constructed by Cavendish was a The apparatus constructed by Cavendish was a torsion balancetorsion balance made of a six-foot wooden rod made of a six-foot wooden rod suspended from a wire, with a 2 inch diameter suspended from a wire, with a 2 inch diameter 1.61 pound 1.61 pound leadlead sphere attached to each end. sphere attached to each end. Two 12 inch 348 pound lead balls were located Two 12 inch 348 pound lead balls were located near the smaller balls, about 9 inches away, and near the smaller balls, about 9 inches away, and held in place with a separate suspension held in place with a separate suspension system. The experiment measured the faint system. The experiment measured the faint gravitational attraction between the small balls gravitational attraction between the small balls and the larger ones.and the larger ones.

III. Using the law of universal gravitationIII. Using the law of universal gravitation A. Planets and satellitesA. Planets and satellites B. Newton reasoned if a bullet shot out of a gun with enough B. Newton reasoned if a bullet shot out of a gun with enough

force from a high mountaintop it would go into orbit about the earthforce from a high mountaintop it would go into orbit about the earth 1. The parabolic motion of the projectile would be identical to 1. The parabolic motion of the projectile would be identical to

the curvature of the earth.the curvature of the earth. 2. An object with a horizontal velocity of 8Km/s will keep the 2. An object with a horizontal velocity of 8Km/s will keep the

same altitude and circle the earth. same altitude and circle the earth. C. V=C. V= D. Finding the velocity of a satellite-A satellite is 225Km above D. Finding the velocity of a satellite-A satellite is 225Km above

the earth’s surface. What is the orbital velocity?the earth’s surface. What is the orbital velocity?

E. Able to derive Keplers 3rd lawE. Able to derive Keplers 3rd law

PROBLEMS ARISE IN PROBLEMS ARISE IN PARADISE-LETS PARADISE-LETS INVESTIGATEINVESTIGATE

Theoretical concernsTheoretical concerns There is no immediate prospect of identifying There is no immediate prospect of identifying

the mediator of gravity. Attempts by physicists the mediator of gravity. Attempts by physicists to identify the relationship between the to identify the relationship between the gravitational force and other known gravitational force and other known fundamental forces are not yet resolved, fundamental forces are not yet resolved, although considerable headway has been although considerable headway has been made over the last 50 years (See: made over the last 50 years (See: Theory of everythingTheory of everything and and Standard ModelStandard Model). ). Newton himself felt the inexplicable Newton himself felt the inexplicable action at a distanceaction at a distance to be unsatisfactory (see " to be unsatisfactory (see "Newton's reservationsNewton's reservations" below)." below).

Newton's theory requires that gravitational Newton's theory requires that gravitational force is transmitted instantaneously. Given force is transmitted instantaneously. Given classical assumptions of the nature of classical assumptions of the nature of space and time before the development of space and time before the development of general relativity, a propagation delay general relativity, a propagation delay leads to unstable orbits. leads to unstable orbits.

• Disagreement with observation• Newton's theory does not fully explain

the precession of the perihelion of the orbits of the planets, especially of planet Mercury. There is a 43 arc second per century discrepancy between the Newtonian prediction, which arises only from the gravitational tugs of the other planets, and the observed precession

The predicted deflection of light by The predicted deflection of light by gravity using Newton's theory is only gravity using Newton's theory is only half the deflection actually observed. half the deflection actually observed. General relativity is in closer General relativity is in closer agreement with the observations.agreement with the observations.

The observed fact that gravitational and inertial masses are the same for all bodies is unexplained within Newton's system. General relativity takes this as a postulate. See equivalence principle