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Question 117277: I need some real help here. I have researched to find better explnations as to what the semi major axis is so I can do the math but I can't find it. I know the final answer should be between 0 and 1. This is the problem...
A satellite has an elliptical orbit around the earth with one focus at the earth's center, E. As indicated, the Earth's radius is 4000 miles, the highest point that the satellite is from the surface of the earth is 800 miles and the lowest is 200 miles. find the eccentricity of the satellites orbit.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A satellite has an elliptical orbit around the earth with one focus at the earth's center, E. As indicated, the Earth's radius is 4000 miles, the highest point that the satellite is from the surface of the earth is 800 miles and the lowest is 200 miles. find the eccentricity of the satellites orbit.
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Draw the picture.
At perigee the satellite is 4200 miles from the center of the earth.
At apogee the satellite is 4800 miles from the center of the earth.
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Apogee = c + a where c is the distance from center of the ellipse to focus
and a is the distance from center to satellite.
Perigee = -c + a
Note: Also, c is the semi-major axis of the ellipse.
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EQUATIONS:
a+c = 4800 miles
a-c = 4200 miles
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2a = 9000
a = 4500 miles
Then c = 300 miles
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eccentricity = c/a = 300/4500 = 1/15
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Note: You can find useful information on the ellipse, eccentricity, etc.
using Google; searth for eccentricity ellipse.
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Cheers,
Stan H.
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