Question

A planet moves in an elliptical orbit around the sun. The mass of the sun is Ms . The minimum and maximum distances of the planet from the sun are R1 and R2, respectively. Using Kepler's 3rd law and Newton's law of universal gravitation, find the period of revolution of the planet as it moves around the sun. Assume that the mass of the planet is much smaller than the mass of the sun. Use for the gravitational constant. Express the period in terms of G, Ms,R1 , and R2.

Answer 1

Assume that the planet's mass is substantially lower than that of the sun. Use in relation to the gravitational constant. Describe the duration in terms of G, Ms,R1 , and R2 is  π√(R1+R2)³2GM.

By applying Newton's law, we can state that the centripetal force experienced by the planet due to its elliptical orbit will equalize the gravitational force exerted by the sun on the planet.

mv₂/(R1+R2)/2=GMm/(R1+R2/2)²

Here, m is the mass of the planet, v is the orbital velocity of the planet and G=6.67×10⁻¹¹N⋅m²⋅kg⁻² is the universal gravitational constant.

The period of revolution is given by,

P=2π(R1+R2)/v

Substituting we get,

P=2π((R1+R2)/2)√2GM/R1+R2

=π√(R1+R2)³2GM.

Hence, the time period of revolution is π√(R1+R2)³2GM.

Learn more about gravitational constant here:

https://brainly.com/question/858421

#SPJ4