Q. 25

Expert-verified
Found in: Page 354

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

You are the science officer on a visit to a distant solar system. Prior to landing on a planet you measure its diameter to be and its rotation period to be You have previously determined that the planet orbits from its star with a period of . Once on the surface you find that the free-fall acceleration is What is the mass of (a) the planet and (b) the star?

a. The mass of the planet is

b. The mass of the star is

See the step by step solution

Step 1 : Given information a.

Radius of planet = , time period = , free-fall acceleration =

Step 2 : Calculation a.

Using the formula of gravitational law we get :

Where, F is gravitational force, M is mass of planet and r is the radius between masses.

Solving for acceleration we get :

Step 3 : Final answer a.

The mass of the planet is

Step 1 : Given information b.

Orbit distance = time period =

Step 2 : Calculation b.

Using Kepler's third law of planetary motion, the time period is given by :

Where, T is the time period, R is the radius of orbit of star, G is universal gravitational constant, M is mass of star.

Step 6 : Final answer b.

The mass of the star is