How Do You Calculate the Net Force on a Satellite in Circular Orbit?

[iluvphys]

Hello friends, I have a question considering Newton in circular motion.

Homework Statement

Six artificial satellites complete one circular orbit around a space station in the same amount of time. Each satellite has mass m and radius of orbit L.
What is the net force of every single satellite?

e.g. - S1: m= 300kg L= 7500m

If I know how to work one of them out I can do the rest.

Homework Equations

F = mv^2/L

I know m, know L but have to figure out v.

The Attempt at a Solution

Well, I started writing down the equation for motion in a circle and got Fnet=mv^2/L.
I was hoping I could replace v with 2*pi*L/T.
However I don't know T. I am assuming that since the time taken for the round trips is the same for every satellite, I could assume T being 1 couldn't I?
Please help and thanks in advance.

 

[Redbelly98]

How about the equation for the force of gravity between two masses?

Also, what about the mass of the space station?

 

[thomate1]

Hello there, in response to your question, the net force acting on each satellite would be equal to the centripetal force required to keep them in circular motion. This force can be calculated using the equation F = mv^2/L, where m is the mass of the satellite, v is the velocity, and L is the radius of the orbit. Since all six satellites have the same mass and radius of orbit, the net force on each of them would be the same.

In order to calculate the velocity, we can use the formula for the period of a circular orbit, T = 2π√(L^3/GM), where G is the gravitational constant and M is the mass of the space station. Since the time taken for one orbit is the same for all satellites, we can use this equation to find the velocity for each satellite.

Therefore, the net force on each satellite would be F = m(2πL/T)^2/L, where T is the period calculated using the above equation. I hope this helps, and please let me know if you have any further questions. Good luck with your homework!