Question 117868This question is from textbook College Algebra
: Come with your responses to the following questions:
a) A satellite has an elliptical orbit around the earth with one focus at the earth’s center, E. 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 satellite’s orbit. (This is number 24 on page 491.)
b) As a follow up, develop two more examples with different values other than 800 and 200. Show your equations, work, and examples.
c) Compare your results and examples to the information found at the following site: http://ilrs.gsfc.nasa.gov/satellite_missions/slr_sats.html.
d) Look at the data under the table titled SLR Satellite Orbit Information, and see if you find any satellites that are close in terms of the eccentricity calculated for the initial problem. Note any that are close to the same eccentricity your team calculated.
This question is from textbook College Algebra
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Ok, here I come with a response to part a only.
Parts b, c, and d require your participation.
a)Find the eccentricity, e, of a satellite in an elliptical orbit around the earth.
We are given the distance from one focus (the earth's center) to the ellipse (orbit) as 4,800 miles. This comes from 4,000 miles for the earth's radius plus the apogee (greatest distance from the earth's surface to the satellite) of 800 miles.
We are also given the distance from the same focus (earth's center) to the ellipse (orbit) as 4,200 miles. This comes from 4,000 miles for the earth's radius plus the perigee (the smallest distance from the earth's surface to the satellite) of 200 miles.
First, some definitions related to an ellipse.
Let a = the distance, on the major axis, from the ellipse to the center.
Let c = the distance from one focus to the center.
Now you can see that the distance from the earth's center (focus) to the ellipse at the apogee along the major axis is given by (a + c), and the distance from the same focus to the ellipse at the perigee is given by (a - c).
Since we know these two distance we can calculate a and c.
Why do we want to do that, well...because eccentricity, e, is given by 
 Add these two equations to get...
 and...
 so then...
Eccentricity is:
 or...
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