Eccentricity = c/a 
where c is the distance from the center to the focus of the ellipse 
a is the distance from the center to a vertex 

Here is a sketch:



On this graph 1 unit = 1000 miles. The circle represents 
the earth with the center at the origin. so point P has
coordinates (4,0) and point Q has coordinates (-4,0) 

The green ellipse represents the orbit of the satellite. 

Where 1 unit = 1000 miles. So the satellite is 800 miles or 0.8 units
from the earth's surface at point M, and 200 miles or 0.2 units from 
the earth's surface at point N. PM is 800 miles or 0.8 units and
QN is 200 miles or 0.2 units. 

So the coordinates of M are (4.8,0)
and the coordinates of N are (-4.2,0)  

Unfortunately the software does not close the green ellipse at its 
vertices, but its vertices are at M and N. The center of the ellipse,
R, is the midpoint between M and N, so we use the midpoint formula

midpoint = (, ),

midpoint = (,) = (0.3,0)

and find that the center of the ellipse is R(0.3,0)

Since the focus of the ellipse is at the center of the earth (0,0) 
and the center of the ellipse is at R(0.3,0), the value of c
is c=0.3 units (distance from center to focus).  That is c = 300 miles.

the value of a is a=  (the distance from the ellipse's center
(.3,0) to vertex M(4.8,0) is 4.8-.3 or 4.5 units, or a = 4500 miles.

Therefore the eccentricity =  

Edwin