Find the speed of a satellite in a circular orbit around the Earth with a radius 3.57 times the mean radius of the Earth. (Radiu
s of Earth = 6.37×10^3 km, mass of Earth = 5.98×10^24 kg, G = 6.67×10^-11 Nm^2/kg^2.)
2 answers:
In a circular orbit with a radius that is 3.57 times the mean radius of the Earth, a satellite moves at a speed of 132.43km/s.
In order to get the solution, we must understand the satellite's planetary motion equation.
<h3>What is the satellite's orbital motion equation?</h3>
- The earth's mass M and the satellite's mass M are attracted to one another by gravity.

- The term used to describe centripetal force of,

- When a satellite orbits the earth, these two forces are equivalent. Thus, the velocity will be,

As a result, we may estimate that the satellite will move at a speed of 132.43 km/s.
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Answer: The speed of a satellite in a circular orbit around the Earth with a radius 3.57 times the mean radius of the Earth is 4188.11 m/s.
Explanation: To find the answer, we need to know about the equation of motion of a satellite around earth.
<h3>What is the
equation of motion of a satellite around earth?</h3>
- We have gravitational force of attraction between the satellite of mass m and earth of mass M as,

- The expression for centripetal force of,

- These two forces are equal for a satellite around earth.

<h3>How to solve the problem?</h3>

- Thus, the speed of the satellite will be,

Thus, we can conclude that the speed of satellite will be 4188.11 m/s.
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