The solution manual uses the following densities for low L, medium M and high H
ID: 1492721 • Letter: T
Question
The solution manual uses the following densities for low L, medium M and high H solar activity: Impulse Delta p has units of momentum, and by Newton's 2nd law, force is related to impulse by F = delta p/delta t, rightarrow delta p = F delta t where At is the duration of the impulse. Clearly impulse = force x time. To solve the exercise, calculate the spacecraft orbital velocity v for the given altitude. Use eq. 7.85 to calculate the drag force FD, and multiply by the given duration (t = 1 year = 3.16 x 107 s) to obtain the required impulse.Explanation / Answer
From newton's gravitational law,
F=GMm/r2 ; where M-mass of Earth; m-mass of the spacecraft ; r-altitude
From newton's second law , mv2/r =GMm/r2
v= sqrt{GM/r} ;r=550 x 103 m ; M=5.972 x 1024 kg
v=2.69 x 104 ms-1
No, From F= pACiv2 /2
a) low
F=2.391 x 10-4 ; impulse= F*3.16 x 107 =7555.56
b) medium
F= 3.188 x 10-3 ; impulse= 1.01 x 105
c) high
F=7.97 x 10-3 ; impulse=2.52 x 105