Physics problem about artificial satellites

Question

Two artificial satellites a and b are in the same orbit with small distance between them (compared to Earth's radius R₀). After flying in the same orbit the distance between a and b changes periodically from L₁ (positions of satellites a₁ and b₁) to L₂ (positions of satellites a₂ and b₂). Find the biggest and the smallest distance from satellites to the center of the Earth R₁ and R₂ if the rotational period of the satellites is T.

Answer 1

This is an oscillation problem. Remember, the variable that gets overlooked is the radial distance from earth to the satellite.

So

The changing separation implies a small difference in orbital radius due to slight energy/phase mismatch, so:

1. When they are closest → smallest effective radius R₁
2. When farthest → largest effective radius R₂

^ This is just a proof of what the formula is. Use the below to plug and chug variables from the prompt in your practice guide or pretest.

R₂/R₁ = L₂/L₁