An unmanned satellite orbits the earth with a perigee radius of 10,000 km and an apogee radius of 100,000 km. Calculate: a. the eccentricity of the orbit
b. the semimajor axis of the orbit(km)
c. the period of the orbit(hours)
d. the specific energy of the orbit(km^2/s^2)
e. the true anomaly at which the altitude is 1000km (degrees)
f. Vr and V(perpendicular) at the points found in part (e) (km/s)
g. the speed at the perigee and apogee (km/s)

Solution :

Given :

radius of perigee, = 10,000 km

radius of apogee, = 100,000 km

a). Eccentricity of the orbit

or e = 0.818

b). Semi major axis of the orbit

     = 55,000 km

c). period of orbit

Replacing μ with

T = 35.64 hr

d). Specific energy of the orbit

e). the equation of the distance to the focus

θ = 1.002°

f).Calculating the angular momentum

or

Now calculate the radial velocity

Substituting for h,

Now calculating the azimuthal velocity

g). Velocity at perigee

Now calculate the velocity of the apogee