Question

Why is Newton’s form of Kepler's third law so useful to astronomers?

Answer 1

Hint:According to this question we have to determine why Newton’s form of Kepler’s third law is so useful to an astronomer. To solve this question one must be aware of Newton’s form of Kepler’s third law. According to the modified third law, the sun and the planet orbited around a common center of mass for the planet-mass system. Using this we can determine why this law is useful.

 Complete step by step solution:
Kepler’s laws are useful as they describe the behavior of a celestial body around a massive body. These laws describe how planets, asteroids, or comets orbit the sun. These laws are not only applicable to our solar system but can also be used to describe the motion of binary stars around each other or even how stars orbit a black hole.
From the relation that every action has an equal and opposite reaction, Newton concluded that in the planet-sun system, the planet does not revolve around a stationary sun. So, Newton proposed that both the sun and the planet orbited around a common center of mass for the planet-mass system. Thereby, he modified Kepler’s third law.
 Newton’s generalized form of Kepler’s third law assists us to determine the masses of the objects from the orbital motion.

Note:There are three of Kepler’s laws of planetary motion. One, the orbit of every planet is elliptical with the sun at its focus. Two, according to the second law, an imaginary line that connects the sun and the planet sweeps equal area in equal times. And finally, the third law states that the planet’s orbital period when squared is proportional to the semi-major axis of its orbit when cubed.