An artificial satellite circles the Earth in a circular orbit at a location where the...

Question:

An artificial satellite circles the Earth in a circular orbit at a location where the acceleration due to gravity is {eq}7.43 \ m / s^2 {/eq}.

(a) Determine the orbital period of the satellite.

Gravitational force:

According to Newton's law of Gravitation, the force between the two masses is directly proportional to the product of the mass and inversely proportional to the square of the distance between them.

Answer and Explanation: 1

Given

Acceleration due to gravity {eq}\displaystyle g = 7.43 \ m/s^{2} {/eq}

Now, we know that the acceleration due to gravity

{eq}\displaystyle g = \dfrac{GM}{R^{2}} \\ 7.43 = \dfrac{6.67*10^{-11}*5.972*10^{24}}{R^{2}} \\ R = 7.321*10^{6} \ m {/eq}

where

  • M is mass of earth

Now, the orbital period of the satellite

{eq}\displaystyle T^{2} = \dfrac{4\pi^{2}R^{3}}{GM} \\ T^{2} = \dfrac{4\pi^{2}*(7.321*10^{6})^{3}}{6.67*10^{-11}*5.972*10^{24}} \\ T = 6237.34 \ s {/eq}


Learn more about this topic:

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Gravitational Pull of the Earth: Definition & Overview

from

Chapter 15 / Lesson 17
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Earth's gravitational pull is often misunderstood, but without it, life on Earth would be impossible. In this lesson, we'll define the gravitational pull and give some examples of how it is used. A quiz is provided to test your understanding.


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