A satellite is in a circular orbit around the Earth. If its speed is doubled, wh
Practice Questions
Q1
A satellite is in a circular orbit around the Earth. If its speed is doubled, what happens to the radius of its orbit?
It remains the same
It doubles
It increases by a factor of four
It decreases by a factor of four
Questions & Step-by-Step Solutions
A satellite is in a circular orbit around the Earth. If its speed is doubled, what happens to the radius of its orbit?
Step 1: Understand that a satellite in orbit moves in a circular path around the Earth.
Step 2: Know that the speed of the satellite is related to the radius of its orbit.
Step 3: Recall the formula for circular motion: the speed (v) of a satellite is related to the radius (r) and the gravitational force.
Step 4: When the speed of the satellite is doubled, we can express this as 2v.
Step 5: According to the formula, if the speed increases, the radius must decrease to maintain the balance of forces.
Step 6: The relationship shows that if the speed is doubled, the radius decreases by a factor of four (r becomes r/4).
Step 7: Conclude that doubling the speed of the satellite results in a smaller orbit.
Circular Motion and Orbital Mechanics – The relationship between the speed of a satellite and the radius of its orbit, governed by gravitational forces and centripetal acceleration.
