Av' A satellite is in a circular orbit (labeled 1) around the earth (mass M) at...

 

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Av' A satellite is in a circular orbit (labeled 1) around the earth (mass M) at radius R with speed Vinitial GM/R. We wish it to climb to a higher circular orbit, at radius R > R with speed final GM/R. We will do this by means of an elliptical Hohmann transfer orbit. The satel lite applies an impulse (a change of speed Av) at time zero, which puts it into the transfer orbit (labeled 2). On arriving at the new distance R it is at the apogee of the transfer orbit. It then applies an additional impulse Av', increasing its speed again, to enter the final circular orbit (la- beled 3). 3 R' R 2 a) What is the angular momentum 1 and energy e (per mass) of the transfer orbit? [This is readily found from your knowledge of R and R' and knowing the transfer orbit's formula for r(); see above.] b) What are the needed instantaneous changes of velocity Av and Av? All answers should be in terms of M, G, R and R'. To answer these questions you may find it useful to recall the formula for r(6) above. Hint: what are a and in terms of R and R'? Note that e must be negative. Av' A satellite is in a circular orbit (labeled 1) around the earth (mass M) at radius R with speed Vinitial GM/R. We wish it to climb to a higher circular orbit, at radius R > R with speed final GM/R. We will do this by means of an elliptical Hohmann transfer orbit. The satel lite applies an impulse (a change of speed Av) at time zero, which puts it into the transfer orbit (labeled 2). On arriving at the new distance R it is at the apogee of the transfer orbit. It then applies an additional impulse Av', increasing its speed again, to enter the final circular orbit (la- beled 3). 3 R' R 2 a) What is the angular momentum 1 and energy e (per mass) of the transfer orbit? [This is readily found from your knowledge of R and R' and knowing the transfer orbit's formula for r(); see above.] b) What are the needed instantaneous changes of velocity Av and Av? All answers should be in terms of M, G, R and R'. To answer these questions you may find it useful to recall the formula for r(6) above. Hint: what are a and in terms of R and R'? Note that e must be negative.