Momentum Principle Related to Velocity

[cowmoo32]

Homework Statement

You will need to use the Momentum Principle to do the first part of this problem, and the Energy Principle to do the second part.

A satellite of mass 2500 kg orbits the Earth in a circular orbit of radius of 8.3 106 m (this is above the Earth's atmosphere).The mass of the Earth is 6.0 1024 kg.
What is the speed of the satellite?
I have the 2nd part of the problem, so all I need is the momentum principle

Homework Equations

Pfinal = Pinitial + Fnet*DeltaT
GMm/r^2

The Attempt at a Solution

I'm not sure how to start this one. The directions say that I'm supposed to use the momentum principle, but I'm not given the speed of the satellite. I was thinking maybe the derivative form of the momentum principle and find the perpendicular component of dP/dT, but I'm not sure how long it takes for the satellite to go around th earth. I'm completely stuck.

 

[Doc Al]

I have no idea what you mean by the "momentum principle". If you mean conservation of momentum, I don't see how that is relevant.

Instead, apply Newton's 2nd law to the satellite, recognizing that its motion is circular.

 

[cowmoo32]

By momentum principle I mean DeltaP = Fnet*DeltaT

 

[Doc Al]

OK, I see. Your initial thought was correct: Use F = dP/dt. (Note that this is another way of stating Newton's 2nd law.)

Use what you know (or should know) about circular motion to evaluate d(mv)/dt = m dv/dt.

 

[cowmoo32]

Here's the problem I have with using dP/dt: In order to find the velocity, or the change in momentum, I need to know the time it takes for one rotation around the earth...that's why I didn't use that formula in the first place. v = dr/dt, but again, I don't have dt.

 

[Doc Al]

Call the speed "v" and express dP/dt in terms of it (along with other known variables).

 

[cowmoo32]

v= dr/dt I can find dr because I know the radius of orbit, but I have no way of finding dt.

 

[Doc Al]

You can express the period (if you need it) in terms of v, since you know the radius of the orbit.

 

[cowmoo32]

I don't understand how you can express the period in terms of v if you don't know the time.

 

[cowmoo32]

Ok, I figured out the problem.

v = sqrt(G*Mearth/r)

 

[Doc Al]

Excellent.