A satellite is in a circular orbit around the Earth. If the radius of the orbit is increased, what happens to the orbital speed of the satellite?
Practice Questions
1 question
Q1
A satellite is in a circular orbit around the Earth. If the radius of the orbit is increased, what happens to the orbital speed of the satellite?
Increases
Decreases
Remains the same
Depends on the mass of the satellite
Orbital speed (v) = √(GM/r). As r increases, v decreases.
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 increased, what happens to the orbital speed of the satellite?
Solution: Orbital speed (v) = √(GM/r). As r increases, v decreases.
Steps: 7
Step 1: Understand that a satellite orbits the Earth in a circular path.
Step 2: Know that the orbital speed of the satellite depends on two things: the gravitational constant (G) and the mass of the Earth (M), as well as the radius of the orbit (r).
Step 3: The formula for orbital speed (v) is v = √(GM/r).
Step 4: Notice that in this formula, the radius (r) is in the denominator (the bottom part).
Step 5: If the radius (r) increases (gets larger), the value of GM stays the same, but the overall fraction (GM/r) becomes smaller.
Step 6: Since v is the square root of (GM/r), if (GM/r) gets smaller, then v (the orbital speed) also gets smaller.
Step 7: Therefore, when the radius of the orbit increases, the orbital speed of the satellite decreases.
