Chapter 13: Q. 27 (page 354)

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

Short Answer

Expert verified

The radius of the orbit of the satellite is $2.9 \times 10^{9} m .$

Step by step solution

Given information

Time period of the satellite = $1 d a y = 8.64 \times 10^{4} s .$

Calculation

According to the Kepler's third law, the time period is given by : $T^{2} = \frac{4 π^{2} R^{3}}{G M} .$

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 = $1.989 \times 10^{30} k g .$

Solving we get,

$T^{2} = \frac{4 π^{2} R^{3}}{G M} R^{3} = T^{2} \times \frac{G M}{4 π^{2}} R = {(T^{2} \times \frac{G M}{4 π^{2}})}^{1 / 3} R = {({(8.64 \times 10^{4} s)}^{2} \times \frac{(6.67 \times 10^{- 11} N m^{2} / k g^{2}) (1.989 \times 10^{30} k g)}{4 π^{2}})}^{1 / 3} R = 2.9 \times 10^{9} m$

Final answer

The radius of the orbit of the satellite is $2.9 \times 10^{9} m .$

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

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