Question

Need help with this question! Will attach pic! A satellite is to be put into an elliptical orbit around a moon as shown below.The moon is a sphere with radius of 1000 km. Determine an equation for the ellipse if the distance of the satellite from the surface of the moon varies from 953 km to 466 km

Answer 1

An equation for the ellipse ( standard form ):
x²/a²  +  y²/b² = 1
Here is:  a - semi-major axis and b - semi-minor axis.
Radius of the moon is 1,000 km and the distance from the surface of the moon to the satellite varies from 953 km to 466 km.
a = 1,000 + 953 = 1,953 km
b = 1,000 + 466 = 1,466 km
Answer:
The equation is  x² / 1,953²  + y² / 1,466² = 1
or: x²/3,814,209  +   y²/2,149,156  = 1