Q. 25

Expert-verifiedFound in: Page 354

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

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

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 :

The mass of the planet is

Orbit distance = time period =

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.

The mass of the star is

94% of StudySmarter users get better grades.

Sign up for free