A satellite is in a circular orbit around the Earth. What is the relationship between its orbital speed (v) and the radius of the orbit (r)?
Practice Questions
1 question
Q1
A satellite is in a circular orbit around the Earth. What is the relationship between its orbital speed (v) and the radius of the orbit (r)?
v = sqrt(G * M / r)
v = G * M / r
v = r / G * M
v = G * r / M
The orbital speed of a satellite is given by v = sqrt(G * M / r), where M is the mass of the Earth.
Questions & Step-by-step Solutions
1 item
Q
Q: A satellite is in a circular orbit around the Earth. What is the relationship between its orbital speed (v) and the radius of the orbit (r)?
Solution: The orbital speed of a satellite is given by v = sqrt(G * M / r), where M is the mass of the Earth.
Steps: 7
Step 1: Understand that a satellite moves in a circular path around the Earth.
Step 2: Know that the speed of the satellite is called its orbital speed (v).
Step 3: Recognize that the radius of the orbit (r) is the distance from the center of the Earth to the satellite.
Step 4: Learn that the gravitational force between the Earth and the satellite keeps it in orbit.
Step 5: The formula for the orbital speed (v) is derived from the balance of gravitational force and the required centripetal force for circular motion.
Step 6: The formula is v = sqrt(G * M / r), where G is the gravitational constant and M is the mass of the Earth.
Step 7: This formula shows that as the radius (r) increases, the orbital speed (v) decreases.
