A couple of astronauts agree to rendezvous in space after hours. Their plan is to let gravity bring them together. She has a mas
s of 64.0kg and he a mass of 76.0kg , and they start from rest 23.0m apart. Find his initial acceleration. Find her initial acceleration. 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.) Would their acceleration, in fact, remain constant?
Let's use Newton's Law of Universal Gravitation, which is expressed as<span>F=G<span><span><span>(m1</span><span>m2)/</span></span><span>r2</span></span></span>We can find the force of attraction between them. Then, to find the acceleration from<span>F=<span>m1</span><span>a1</span> <span>and</span> F=<span>m2</span><span>a2</span></span>I'll take it you know the equations of motion for constant acceleration. <span>y=<span>1/2</span>a<span>t^2</span></span>
Obviously, as they accelerate towards each other, the radius between
them decreases, meaning the force of gravitation between them increases,
meaning they accelerate faster.
