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## Homework Statement

Consider a spacecraft in an elliptical orbit around the earth. At the low point, or perigee, of its orbit, it is 400 km above the earth's surface; at the high point, or apogee, it is 4000 km above the earth's surface.

1. What is the period of the spacecraft's orbit?

## Homework Equations

Kepler's 3rd Law: T=(2*pi*a

^{3/2})/ sqrt(GM

_{E})

where a=semi-major axis

## The Attempt at a Solution

So the first thing I did was find the semi-major axis (value a of the eqn above):

(1/2)*(4000+400)=2200 km or 2.2*10

^{6}m

Then I plugged it into the equation along with the following constants:

G=6.67*10

^{-11}m

^{2}/kg

^{2},

M

_{E}=5.97*10

^{24}kg

T=(2*pi*2.2*10

^{(6)}

^{3/2})/ sqrt(6.67*10

^{-11}*5.97*10

^{24})= 1027 seconds

I checked the back of the book and the answer is wrong. I have no clue what I am doing wrong....:( Any help would be greatly appreciated.