If the period of a satellite in a circular orbit is T, what is the relationship between T and the radius r of the orbit?

1 question

1 item

Q: If the period of a satellite in a circular orbit is T, what is the relationship between T and the radius r of the orbit?

Solution: T = 2π√(r³/GM), thus T ∝ √r.

Steps: 6

Step 1: Understand that T is the period of the satellite, which is the time it takes to complete one full orbit.
Step 2: Recognize that r is the radius of the circular orbit, which is the distance from the center of the planet to the satellite.
Step 3: Know that the gravitational force provides the necessary centripetal force for the satellite to stay in orbit.
Step 4: Use the formula for the period of a satellite in a circular orbit: T = 2π√(r³/GM), where G is the gravitational constant and M is the mass of the planet.
Step 5: Notice that in the formula, T is proportional to the square root of r cubed (r³). This means if you change r, T will change based on this relationship.
Step 6: Conclude that T is proportional to the square root of r, written as T ∝ √r.