A certain satellite travels in an approximately circular orbit of radius 2.0 * 106 m with a period of 7 h 11 min. Calculate the mass of its planet from this information.

Answer: Mass of the planet, M = 8.53 x 10^8kg

Explanation:

Given Radius = 2.0 x 106m

Period T = 7h 11m

Using the third law of kepler's equation which states that the square of the orbital period of any planet is proportional to the cube of the semi-major axis of its orbit.

This is represented by the equation

T^2 = (4π^2/GM) R^3

Where T is the period in seconds

T = (7h x 60m + 11m) (60 sec)

= 25860 sec

G represents the gravitational constant

= 6.6 x 10^-11 N. m^2/kg^2 and M is the mass of the planet

Making M the subject of the formula,

M = (4π^2/G) * R^3/T^2

M = (4π^2 / 6.6 x10^-11) * (2*106m) ^3 (25860s) ^2

Therefore Mass of the planet, M = 8.53 x 10^8kg