satelltie question

Question

A satellite is to be put into an elliptical orbit around a moon. 

 

The moon is a sphere with radius of 959 km. Determine an equation for the ellipse if the distance of the satellite from the surface of the moon varies from 357 km to 710 km.

Answer 1

Radius of the moon = 959 km.

A satellite is in elliptical orbit around the moon with the center of the moon at one focus.

The vertex is at the origin and the coordinates are (0,0).

Center is (h,k) = (0,0)

The vertical ellipse equation is

a = length of semi major axis and b = length of semi minor axis.

In this case

b = 959 km + 357 km = 1316 km.

 a = 959 km + 710 km = 1669 km.

Substitute the a,b and (h,k) in standard form.

The ellipse equation is .