Rendezvous in Space! A couple of astronauts agree to rendezvous in space after hours. Their plan is to let gravity bring them together. One of them has a mass of 65 kg and the other a mass of 72 kg, and they start from rest 20.0 m apart. (a) Make a free-body diagram of each astronaut, and use it to find his or her initial acceleration. As a rough approximation, we can model the astronauts as uniform spheres. (b) 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.) (c) Would their acceleration, in fact, remain constant? If not, would it increase or decrease? Why?

Step 1 of 3 a) The gravitational attraction of the astronauts on each other causes them to accelerate toward each other. m A B F A F = GB r 11 2 2 65 kg×72 kg = 6.67 × 10 N.m /kg )( (20 m) = 7.807 × 10 10 N a = F A A ma 7.807×1010N 11 2 a A 65 kg = 1.2 × 10 m/s F B a B mB a = 7.807×1010N = 1.1 × 1011m/s 2 B 72 kg Step 2 of 3 b) x = x + a t for constant acceleration 0 2 x x = a t 2 and x = a t1 2 A 2 A B 2 B x + x = 20 m so A B 20 m = (a + a )t 2 2 a B 2×20 m t = 1.2×1011m/s +1.1 ×10m/s 6 = 1.32 × 10 s Which is equal to 15 days