### Subject: Calculate the mass of the Earth given the speed and distance from the cente

Date: Sat Dec 29 17:21:53 2007
Posted by No name entered.
Grade level: 10-12 School: No school entered.
City: No city entered. State/Province: No state entered. Country: No country entered.
Area of science: Physics
ID: 1198974113.Ph
Message:
```
A satellite orbits the Earth in an elliptical orbit.  At perigee its distance
from the center of the earth is 22,500 km and its speed is 4280 m/s.  At
apogee its distance from the center of the Earth is 24,100 km and its speed is
3990 m/s.  Using this information, calculate the mass of the Earth.

My thoughts:

Well, I think I can set up this equation
m_s m_e         v^2
G -------- = m_s -----
r^2            r

since the m_s (mass of the satellite) terms cancel, we have

m_e = v^2 r/G, with v = 4280 m/s and r = 22,500 km.

So I don't know why the books also tells us about the condition at apogee (I
haven't checked if this also holds for apogee).

What makes me uncomfortable is the satelite's orbit is elliptical instead of
circular, so I'm not sure if the centripetal acceleration also works for
elliptical orbit.

```

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