Consider a spacecraft in an elliptical orbit around the earth. At the low point, or perigee, of its orbit, it is 500 above the earth's surface; at the high point, or apogee, it is 4000 above the earth's surface.

Using conservation of angular momentum, find the ratio of the spacecraft's speed at perigee to its speed at apogee.

I know Conservation of momentum at perigree and apogee is L=M*V*r :M = mass, V = velocity, r = radius. But i dont know the velocity.. or L..

Question

Consider a spacecraft in an elliptical orbit around the earth. At the low point, or perigee, of its orbit, it is 500  above the earth's surface; at the high point, or apogee, it is 4000  above the earth's surface.

Using conservation of angular momentum, find the ratio of the spacecraft's speed at perigee to its speed at apogee.

I know Conservation of momentum at perigree and apogee is L=M*V*r :M = mass, V = velocity, r = radius. But i dont know the velocity.. or L..

anonymous · Answer

we know that semimajor axis is a = (1/2)[(Re + hp)+(Re +ha)]
                                                  = 9.13*106 m
Re = radius of earth = 6380 km = 6380000 m
hp = height of perigee = 500 km = 500000 m
ha = height of apogee = 5000 km = 5000000 m
M = mass of the earth = 5.98*1024 kg
G = 6.67*10-11 Nm2/kg2
we know that time period of revolution of the spacecraft is T= 2πa3/2/√GM
  Then T = 2π*(9.13*106 )3/2/√6.67*10-11 *5.98*1024
            = 8.67*103 sec

anonymous · Answer

We know that according to conservation of angularmomentum
    mvprp  =mvara
vp = spacecraft's speed at perigee
va=spacecraft's speed at apogee
Then vp /va  =ra/rp  = (Re+ha)/(Re +hp)   = 6380+5000/6380+500  =1.654

anonymous · Answer

Thank you :)