Suppose one of the Global Positioning System satellites has a speed of 4.48 km/s at perigee and a speed of 3.6
Suppose one of the Global Positioning System satellites has a speed of 4.48 km/s at perigee and a speed of 3.64 km/s at apogee. If the distance from the center of the Earth to the satellite at perigee is 2.00×104 what is the corresponding distance at apogee? km
First use the energy equation at perigee to get the semimajor axis of the orbit:
v^2/2-mu/r=-mu/(2a)
v is velocity, r is orbital radius, a is semimajor axis, mu=3.986*10^5 for Earth.
Rearranging: a=-mu/2*(v^2/2-mu/r)^-1
Next you find the eccentricity of the orbit:
rp=a*(1-e)
e=1-rp/a
Now you can find the radius at apogee:
ra=a*(1+e)