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 66.0kg and he a mass of 74.0kg , and they start from rest 21.0m apart. Find his initial acceleration. Find her initial acceleration.

Question

anonymous · Answer

Start with Newton's law of gravitation:

$$F=\frac{Gm_1m_2}{r^2}$$

where m1 and m2 are the masses of two objects, F is the force acting on each of them and r is the distance between them. G is the gravitation constant, and it has a rough value of 6.67*10^-11.
Then Newton's second law is 

$$F=ma$$
rearrange this to give
$$a=\frac{F}{m}$$

Which tells us that to find the acceleration of an astronaut, all we have to do is find the force acting on them and divide by their mass. Let's call the female astronaut number 1, and the male number 2.

$$a_1=\frac{F}{m_1}=\frac{Gm_1m_2}{r^2}\div m_1=\frac{Gm_2}{r^2}$$

Similarly, 
$$a_2=\frac{F}{m_2}=\frac{Gm_1m_2}{r^2}\div m_2=\frac{Gm_1}{r^2}$$

So you just have to plug in the values.