# Homework Help: Calculating Height, Velocity of mass in orbit.

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1. Dec 7, 2014

### chickenonrice

The problem is from a practice exam given to us by our professor to prepare for our final this coming week.

1. The problem statement, all variables and given/known data

A satellite in a circular geostationary orbit
above the Earth’s surface (meaning it has the
same angular velocity as the Earth) explodes
in to three pieces of equal mass. One piece
remains in a circular orbit at the same height
as the satellite’s orbit after the collision, but
the velocity of this piece is in the opposite direction
to the velocity of the satellite before
the explosion. After the explosion the second
piece falls from rest in a straight line directly
to the Earth. The third piece has an initial velocity in the same direction as the original direction of
the satellite, but now has a different magnitude of velocity. The diagram is obviously not remotely to
scale!
(a) At what height above the Earth does the satellite orbit?
(b) What is the magnitude of the velocity of the satellite along it’s original circular path?

2. Relevant equations
Fg = (GMeMs)/(R^2)
Ms*a = GMeMs / R^2
a= v^2/R
v = 2piR/Period
3. The attempt at a solution
I messed around with the equations to get =
v^2 = GMe/R
after which i used v = 2piR/Period.

To find the period, I did 24*60*60 / 1 complete oscillation (=86,400). The answer key for some reason is saying: 24*60*60/ 2 (=43,200) . That's something I am having trouble understanding.

Anyways, I continued with 43,200. I messed with the equations again to get:

v^2 = 4pi^2R^2 / (43,200^2) = GMe/R. I solved the equation, and got 2.66*10^7.

The answer key decided to multiply Me by .1. How come?

I am posting the answer key link here: http://www.ic.sunysb.edu/class/phy141md/doku.php?id=phy141:examprep:final10sols (it's the first problem)

2. Dec 7, 2014

### chickenonrice

JK. I figured it out! I was looking at the wrong solutions! Can a Mod Please delete this thread!!!