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Chapter 13: Q45P (page 381)

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

Short Answer

Expert verified

The mass of the Mars is 6.5脳1023kg.

Step by step solution

01

Step 1: Given

Radius,R=9.4脳106m

Period,7hours39minutes=2.754脳104s

02

Determining the concept

Using the formula for Kepler鈥檚 third law, we can find themass of Mars from the given radius and period. According to Kepler鈥檚 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=4蟺2GMR3

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

03

Determining themass of Mars

Now,

T2=4蟺2GMR3M=4蟺2R3GT24蟺29.4脳106m3G2.754脳104s2

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

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

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