A satellite is in a circular orbit around the Earth. If its orbital radius is tr

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Question: A satellite is in a circular orbit around the Earth. If its orbital radius is tripled, how does the orbital speed change?

Options:

Correct Answer: It is reduced to one-third

Solution:

Orbital speed v = √(GM/R). If R is tripled, v becomes √(GM/(3R)) = v/√3, which is reduced to one-third.

A satellite is in a circular orbit around the Earth. If its orbital radius is tripled, how does the orbital speed change?

A satellite is in a circular orbit around the Earth. If its orbital radius is tripled, how does the orbital speed change?

Step 1: Understand that the orbital speed of a satellite is given by the formula v = √(GM/R), where G is the gravitational constant, M is the mass of the Earth, and R is the orbital radius.
Step 2: Identify that if the orbital radius R is tripled, it becomes 3R.
Step 3: Substitute 3R into the formula for orbital speed: v = √(GM/(3R)).
Step 4: Simplify the equation: v = √(GM/(3R)) = √(GM/R) * √(1/3).
Step 5: Recognize that √(GM/R) is the original speed v, so we can rewrite it as v/√3.
Step 6: Calculate the new speed: Since √3 is approximately 1.732, the new speed is v/√3, which means the speed is reduced.

Orbital Mechanics – Understanding the relationship between orbital radius and speed in circular orbits.
Gravitational Force – Application of gravitational constant and mass in determining orbital speed.
Mathematical Relationships – Manipulating equations to find how changes in radius affect speed.