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Chapter 5: Q49. (page 134)

Calculate the period of a satellite orbiting the Moon, 95 km above the Moon鈥檚 surface. Ignore effects of the Earth. The radius of the Moon is 1740 km.

Short Answer

Expert verified

The period of a satellite is 7.05脳103s.

Step by step solution

01

Step 1. Given Data

The distance above the Moon鈥檚 surface is d=95km.

The radius of the Moon is r=1740km.

02

Step 2. Understanding the relation of speed of the satellite

In this problem, the time period of the satellite will be calculated by using the relation of the speed of the satellite in a circular orbit having radius r and mass m.

03

Step 3. Estimating the time period of the satellite

The relation of speed of a satelliteis given by,

v=Gmr+d2蟺r+dT=Gmr+dT=2蟺r+dGmr+d

Here, m is the mass of the Moon, G is the gravitational constant and T is the time period.

On plugging the values in the above relation.

T=2蟺1740km脳1000m1km+95km脳1000m1km6.67脳10-11N路m2/kg27.35脳1022kg1740km脳1000m1km+95km脳1000m1kmT=7.05脳103s

Thus, T=7.05脳103sis the required period of a satellite.

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