   Chapter 7, Problem 43P

Chapter
Section
Textbook Problem

A satellite of Mars, called Phoebus, has an orbital radius of 9.4 × 106 m and a period of 2.8 × 104 s. Assuming the orbit is circular, determine the mass of Mars.

To determine
The mass of Mars.

Explanation

Given info: The gravitational constant is 6.67×1011Nm2/kg2 , the orbital period of Phoebus is 2.8×104s , and the orbital radius of the satellite is 9.4×106m .

Explanation: From Kepler’s third law, the square of the period of a satellite of Mars called Phoebus is T2=(4π2GMMars)r3 and this expression is rearranged for the mass of Mars.

The formula for the mass of Mars is,

MMars=(4π2GT2)r2

• G is gravitational constant.
• T is period of the satellite.
• r is orbital radius of the satellite.

Substitute 6.67×1011Nm2/kg2 for G , 2

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