Your starship, the Aimless Wanderer, lands on the mysterious planet Mongo. As chief scientist-engineer, you make the following measurements: A 2.50 kg stone thrown upward from the ground at 13.0 m/s returns to the ground in 4.50 s; the circumference of Mongo at the equator is 2.00×10^5km; and there is no appreciable atmosphere on Mongo. The starship commander, Captain Confusion, asks for the following information:

a. What is the mass of Mongo?
b. If the Aimless Wanderer goes into a circular orbit 30,000 km above the surface of Mongo, how many hours will it take the ship to complete one orbit?

(a) The mass of planet Mongo is  .

(b) The time taken by the ship to complete on orbit is about 11.08 hours.

Given data:

The mass of stone is, m =2.50 kg.

The speed of stone is, u = 13.0 m/s.

The time taken to return to ground is, t = 4.50 s.

The circumference of Mongo at equator is, .

(a) Use Newton's law of gravitation to obtain the mass of gravitation as,

........................................................(1)

Here,

g is the gravitational acceleration.

G is the universal gravitational constant.

The expression for the gravitational acceleration is,

Substitute the value in equation (1) as,

Thus, we can conclude that the mass of planet Mongo is  .

(b)

Now apply the Kepler's law to obtain the time period for completing the one orbit as with the 30000 km height as,

Thus, the time taken by the ship to complete one orbit is about 11.08 hours.

Learn more about the Kepler's Law here:

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