A couple of astronauts agree to rendezvous in space after hours. Their plan is t

Question

A couple of astronauts agree to rendezvous in space after hours. Their plan is to let gravity bring them together. She has a mass of 66.0 kg and he a mass of 70.0 kg , and they start from rest 21.0 m apart.

Part A

Find his initial acceleration

Part B

Find her initial acceleration

Part C

If the astronauts' acceleration remained constant, how many days would they have to wait before reaching each other? (Careful! They both have acceleration toward each other.)

Part D

Would their acceleration, in fact, remain constant?

Would their acceleration, in fact, remain constant?

Explanation / Answer

a) a = Gm/r² = 6.674e11 N·m²/kg² * 70kg / (21m)² = 10.6e-12 m/s²

b) a = GM/r² = 6.674e11 N·m²/kg² * 66kg / (21m)² = 9.98e-12 m/s²

c) She covers distance x; he covers 21m - x
(and you could figure out what x is using center of mass...)
him: s = 21m - x = ½at² = ½ * 10.6e-12m/s² * t²
her: S = x = ½at² = ½ * 9.98e-12m/s² * t²
Add these two eqns:
21m = ½(10.6 + 9.98)e-12m/s² * t²
t² = 2.04e12 s²
t = 1.428e6 s = 396.8 h = 16.5 days

PartD) As we assumed so, yes, it'll remain constant

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