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Chapter 13: Q. 27 (page 354)

A satellite orbits the sun with a period of 1day.What is the radius of its orbit?

Short Answer

Expert verified

The radius of the orbit of the satellite is2.9脳109m.

Step by step solution

01

Given information

Time period of the satellite =1day=8.64脳104s.

02

Calculation

According to the Kepler's third law, the time period is given by : T2=4蟺2R3GM.

Where, T is time period, R is the required radius of the orbit, G is the universal gravitational constant and M is mass.

We know, mass of the sun = 1.989脳1030kg.

Solving we get,

T2=4蟺2R3GMR3=T2脳GM4蟺2R=T2脳GM4蟺21/3R=8.64脳104s2脳(6.67脳10-11Nm2/kg2)(1.989脳1030kg)4蟺21/3R=2.9脳109m

03

Final answer

The radius of the orbit of the satellite is2.9脳109m.

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