Change in momentum for a satellite in circular orbit

[Peter Coe]

Homework Statement

A satellite is in a circular orbit passing over the North and South geographical poles as it orbits the Earth. It has a mass of 2200kg and its orbit height is 870km above the Earth's surface. What is the change in momentum of the satellite from when it passes over the equator heading North, to when it next passes over the equator?[/B]

Homework Equations

m (satellite) = 2.2 x 10^3 kg
M (Earth) = 5.98 x 10^24 kg
R = r(earth) + h(satellite) = 6.37 x 10^6 m + 8.7 x 10^5 m = 7.24 x 10^6 m
G = 6.673 x 10^-11 m^3 kg^-1 s^-2

v = SQR (G)(M)/R
a = v^2/R
F(centripetal) = (m(satellite) x v^2)/r
T = (2pi x R)/v

m(1)v(1)r(1) = m(2)v(2)r(2) due to conservation of angular momentum.

The Attempt at a Solution

So v = 7.424 x 10^3 m/s and a = 7.61 m/s. T = 6.127 x 10^3 s or 1.7 hours. Centripetal force = 1.67 x 10^16 N

And here is where I got stuck. Isn't velocity constant in circular orbit? So why is there a change in momentum? Many thanks in advance.

 

[Bandersnatch]

Isn't velocity constant in circular orbit? So why is there a change in momentum?

Is velocity a vector or a scalar?

 

[haruspex]

Isn't velocity constant in circular orbit?

No, speed is constant, but velocity amd momentum are vectors.
There is also the subtlety that the Earth is orbiting the sun, so the satellite's orbit is not a simple circle, but I doubt the question intends you to worry about that.

 

[Peter Coe]

So I'd be wrong to say that the magnitude of the relative velocity does not change in circular orbit? I'm aware the nature of the direction does, and that velocity is a vector quantity - but how does that produce a quantifiable change in momentum?

 

[Bandersnatch]

I'm aware the nature of the direction does, and that velocity is a vector quantity - but how does that produce a quantifiable change in momentum?

Say you have a billiards ball moving to the right with velocity V. It hits another ball, and as a result ends up moving to the left with the same magnitude of velocity, but opposite direction.
Do you think there was a change in momentum in this case or not?

 

[haruspex]

So I'd be wrong to say that the magnitude of the relative velocity does not change

No, you'd be right to say that, but the magnitude is the speed, and there is more to velocity than just speed.

velocity is a vector quantity - but how does that produce a quantifiable change in momentum?

Suppose a particle starts with velocity $\vec v$, and this consists of speed |v| in the +x direction. If it later still has speed |v| but is now traveling in the -x direction, what has been the change in velocity?

 

[Peter Coe]

No, you'd be right to say that, but the magnitude is the speed, and there is more to velocity than just speed.

Suppose a particle starts with velocity $\vec v$, and this consists of speed |v| in the +x direction. If it later still has speed |v| but is now traveling in the -x direction, what has been the change in velocity?

Say you have a billiards ball moving to the right with velocity V. It hits another ball, and as a result ends up moving to the left with the same magnitude of velocity, but opposite direction.
Do you think there was a change in momentum in this case or not?

Well the change in velocity/momentum would be a negative value relative to its original position. Ahhh, I see.. assign +ve and -ve.. Thanks