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Chapter 13: Q45P (page 381)

The Martian satellite Phobos travels in an approximately circular orbit of radius 9.4×106mwith a period of7h39min .Calculate the mass of Mars from this information.

Short Answer

Expert verified

The mass of the Mars is 6.5×1023kg.

Step by step solution

01

Step 1: Given

Radius,R=9.4×106m

Period,7hours39minutes=2.754×104s

02

Determining the concept

Using the formula for Kepler’s third law, we can find themass of Mars from the given radius and period. According to Kepler’s third law, the squares of the orbital periods of the planets are directly proportional to the cubes of the semi major axes of their orbits.

Formula is as follow:

T2=4π2GMR3

where, T is time, G is gravitational constant, M is mass and R is radius.

03

Determining themass of Mars

Now,

T2=4π2GMR3M=4π2R3GT24π29.4×106m3G2.754×104s2

Hence, the mass of the Mars is 6.5×1023kg.

Therefore, using the formula for Kepler’s third law, the mass of Mars from the given radius and period can be found.

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