Question

Newton’s law of universal gravitation a. is equivalent to Kepler’s first law of planetary motion. b. can be used to derive Kepler’s third law of planetary motion. c. can be used to disprove Kepler’s laws of planetary motion. d. does not apply to Kepler’s laws of planetary motion.

Answer 1

Answer:

B. Can be used to derive Kepler's third law of planetary motion.

Explanation:

According to gravitational law, force of attraction exists between two bodies, with the force depending on the mass of the two bodies and distance between them.  It can be used to derive Kepler's third law, according to which

$\frac{mv^2}{r}=G\frac{Mm}{r^2}\\v =\frac{2\pi r}{T}\\ \Rightarrow \frac{T^2}{r^3}=\frac{4\pi^2}{GM}\\ T^2\propto r^3$

Answer 2

Newton published his law of universal gravitation almost a hundred
years later.  Using some calculus and some analytic geometry, which
any serious sophomore in an engineering college should be able to do,
it can be shown that IF Newton's law of gravitation is correct, then it MUST
lead to Kepler's laws.  Gravity, as Newton described it, must make the planets
in their orbits behave exactly as they do.