A satellite is in a circular orbit around the Earth. What is the expression for

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Question: A satellite is in a circular orbit around the Earth. What is the expression for the centripetal force acting on the satellite? (2022)

Options:

Correct Answer: All of the above

Exam Year: 2022

Solution:

All the given expressions represent the centripetal force acting on the satellite in different forms.

A satellite is in a circular orbit around the Earth. What is the expression for the centripetal force acting on the satellite? (2022)

A satellite is in a circular orbit around the Earth. What is the expression for the centripetal force acting on the satellite? (2022)

Step 1: Understand that a satellite in a circular orbit experiences a force that keeps it moving in a circle. This force is called centripetal force.
Step 2: Know that the formula for centripetal force (F_c) is given by F_c = (m * v^2) / r, where m is the mass of the satellite, v is its orbital speed, and r is the radius of the orbit.
Step 3: Recognize that the gravitational force between the Earth and the satellite provides the necessary centripetal force to keep the satellite in orbit.
Step 4: The gravitational force can be expressed as F_g = (G * M * m) / r^2, where G is the gravitational constant, M is the mass of the Earth, and m is the mass of the satellite.
Step 5: Set the centripetal force equal to the gravitational force: (m * v^2) / r = (G * M * m) / r^2.
Step 6: Simplify the equation by canceling out the mass of the satellite (m) from both sides, leading to v^2 = (G * M) / r.
Step 7: Use this relationship to express the centripetal force in terms of gravitational force or orbital parameters.

Centripetal Force – The force required to keep an object moving in a circular path, directed towards the center of the circle.
Gravitational Force – The attractive force between two masses, which in this case is the Earth and the satellite, providing the necessary centripetal force for the satellite's orbit.
Orbital Mechanics – The study of the motion of objects in space, particularly how gravitational forces affect their trajectories.