A satellite is in a circular orbit around the Earth. If the radius of the orbit
Practice Questions
Q1
A satellite is in a circular orbit around the Earth. If the radius of the orbit is tripled, how does the orbital speed change?
It triples
It doubles
It remains the same
It decreases by a factor of √3
Questions & Step-by-Step Solutions
A satellite is in a circular orbit around the Earth. If the radius of the orbit is tripled, how does the orbital speed change?
Correct Answer: Orbital speed decreases by a factor of √3.
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 radius of the orbit.
Step 2: Identify that if the radius r is tripled, we can express the new radius as r' = 3r.
Step 3: Substitute the new radius into the orbital speed formula: v' = √(GM/r').
Step 4: Replace r' with 3r in the formula: v' = √(GM/(3r)).
Step 5: Simplify the equation: v' = √(GM/r) * √(1/3) = v * (1/√3).
Step 6: Conclude that the new orbital speed v' is v divided by √3, meaning the orbital speed decreases by a factor of √3.
Orbital Mechanics – Understanding how the orbital speed of a satellite is related to the gravitational constant, mass of the Earth, and the radius of the orbit.
Inverse Square Law – Recognizing that as the radius increases, the orbital speed decreases due to the inverse relationship with the square root of the radius.
