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I am running downstairs for a SECOND to go see if it's still snowing...if you happen to read this right now and you go in the chat room and I'm not responding, that's why. I'll be back right away.
I'm back now...

Talking to myself, too...

Hey, any of you guests who've been around here could help out if you wanted...please...
ok, so here's me being desperate. I've covered 4 sheets of paper in useless calculations on this stupid problem, and so, I am giving up. On the small chance that maybe somebody around here will look at this and go, "oh I know how to do that" (*glances at Golly and two know physics at somewhat, right?*) I'm going to post the problem. Any ideas are helpful...I'm totally out at this point. Grondy, you can delete this whole bit after tomorrow if you want, ok?

here's the monster:
A satellite of mass m is in an elliptical orbit around the earth, which has a mass Me and a radius Me. The orbit varies from closest apporach of a at point A to maximum distance of b from the center of the Earth at point B . At point A, the speed of the satellite is Vo. Assume that the gravitational potential energy Ug = 0 when masses are an infinite distance apart. Express your answers in terms of a, b, m, Me, Re, Vo, and G. As the satellite passes point A, a rocket engine on the satellite is fired so that its orbit is changed to a circular orbit of radius a about the center of the Earth. Determine the work done by the rocket engine to effect this change.

blah...have fun...I'm pretty sure there's a simple way to do this, I'm just not seeing it.
Hmm, don't have my books here, but I'll think about the problem & get back to you. Give me an hour or so. I wish you had posted this earlier, Grondy & ! were on the chatline yesterday until past midnight. Sad Smilie
Lemme see what I can do.
I just saw the due date - don't think you're gonna get this in time. But just in case you do:

Here's a rough guide & some formulas that I can remember:

Mass of satellite = m
Mass of Earth = Me
Elliptical orbit distance: Perihelion = a; Aphelion = b
Circular orbit distance, r = a
Elliptical orbit velocity of satellite at perihelion = Vo
Elliptical orbit velocity of satellite at aphelion = V1
Circular orbit velocity of satellite = V
Gravitational constant = G

1) Assuming that the gravitational potential energy Ug = 0 when masses are an infinite distance apart, then
U(r) = - (intergral of, from infinity to r} F.dr =
F.dr = -GMe.m/r^2
So, U(r) = - (GMe.m)/ r

2) Velocity of satellite (circular orbit) = V1 = square root of (GMe/r)

3) For elliptical orbit:
Solving the equation of (1) conservation of angular momentum (m.Vo.a = m.V1.b), and
(2) conservation of energy (Eo = E1), where E = (1/2 . m.V^2 - (G.Me.m)/ r
Velocity of satellite (elliptical orbit) at perihelion squared = Vo^2 = 2.G.Me.((b/(a.(a+b))

V^2 = Vo^2 . a . (a+b)/ (2b) ----- (i)

4) Energy for circular orbit = Ec = -(G.Me.m)/2a ----------- (ii)

5) Energy for elliptical orbit = Ee = - (G.Me.m)/(a+b) --------------( iii)

6) U = Gravitational potential energy
K = kinetic energy = (1/2). m.v^2
E = total energy = K + U ----------- (iv)

7) Change in potential energy between staellite & surface of Earth at a = delta U
delta U = G. Me. m. (a-Re)/(a.Re)

8) So the work performed equals change in energy

U(elliptical at perihelion) - U(circular) = equations (iii) -(ii)

See if it works...from here I can see that your results from (8) would yield m, Me, Vo, a, b & G. I haven't tried simplifying & subsituting equation (7) - maybe that's where you can get the term Re in your equation.

Good luck...hope this helps.

MTFBWY Smile Smilie
Sorry I couldn't help Chikakat. Sad Smilie Looks like Ungoliant has provided a very elegant solution which makes sense to me. Smile Smilie It would have taken me days to come up with it as my toolbox has become rust encrusted from lack of use.
thanks so much anyway, Ungoliant... I really really really appreciate the help! Big Smile Smilie Big Smile Smilie Big Smile Smilie

didn't quite make the due date, but least I understand the problem now...I think I ended up making up some stuff that was pretty close to what you said...hopefully I'll get some credit for that Wink Smilie
No problem, glad to be able to help. Glad you didn't manage to use it 'cos I mistyped (8), supposed to be E(ellipse,perihelion) - E (circular) = (iii) - (ii)...but works out ok in the end. Smile Smilie
Ungoliant: I was impressed. How long did it take you to set up your solution? Did you do it from your head or did you have to dig out some textbooks?

Of course when I took physics, Kennedy hadn't yet told NASA to shoot for the moon and my physics books hadn't the slightest hint about astrophysics being merely the tying together of the force of attraction between two or more bodies(gravity), the conservation of energy (momentum), and eliptical geometry in at least three dimensional space. Smile Smilie
Why, thanks Grondie. Yeah, I had to do my brother's Physics homework last year, so that's how I had the formulas. Chika's problem was similar to one of his questions, so it only took a couple of hours. But it took a lot longer last year...almost the whole day!

Yeah - but at least you saw the moon landing. I was only a few months old then...wish my parents had gotten down to business earlier. Smile Smilie
I flunked for Physics, so you wouldn't have wanted my help! And your monster is chinese to me! Smile Smilie
Tommy: I flunked physics too, the first time I tried it in University. The population of my high school was smaller than that first year physics class and the professor kept saying greek things like 'cross and dot' instead of 'sin and cos' and then having to learn to think in the metric system rather than the English system; I was just in over my head. I later retook it and squeaked through.
yeah i knew that!!!!!
but seriously AAAAAAAAAHHHHHHHHHHHHHH!!!!!!!!!