A satellite is in a circular orbit around the Earth. If the radius of the orbit is tripled, how does the orbital speed change?
Practice Questions
1 question
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
Orbital speed v = √(GM/r). If r is tripled, v decreases by a factor of √3.
Questions & Step-by-step Solutions
1 item
Q
Q: A satellite is in a circular orbit around the Earth. If the radius of the orbit is tripled, how does the orbital speed change?
Solution: Orbital speed v = √(GM/r). If r is tripled, v decreases by a factor of √3.
Steps: 6
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.
