Gravitational acceleration in orbit An astronaut is working outside a spacecraft that is in orbit around the earth and is not attached to it. Why does the astronaut NOT drift away from the spacecraft?
A) The spacecraft and the astronaut are in orbit around the sun with the earth
B) The accelerations of the spacecraft and the astronaut are inversely proportional to their respective masses
The answer is B. Apparently A is true but irrelevant. But I do not understand how B is the answer?
 A: B isn't correct either. The accelerations of the astronaut and the spacecraft are actually independent of their respective masses (and that might be what the answer intended).
Remember that trajectories are determined by

*

*Acceleration


*Initial position


*Initial velocity
If these three things are the same for two objects, then they will traverse the same trajectory at the same rate. In this problem we can most likely assume that the astronaut and spacecraft are "starting" in the same position with the same velocity (how else would the astronaut work on the spacecraft?), so we just need to consider the accelerations of the astronaut and the spacecraft.
In terms of gravitational attraction, the gravitational force between two objects is directly proportional to the product of their masses. By Newton's second law, this then means that the acceleration due to gravity of an object is independent of that object's mass and is linearly proportional to the mass of the other object. For both the astronaut and the spacecraft this other object is the Earth.$^*$
The acceleration due to gravity also depends on the distance between the objects, but we have already stated the astronaut and the spacecraft start at the same position, so this is the same for both of them as well.
Therefore, in this case the astronaut and the spacecraft have the same acceleration, and thus will traverse the same trajectory at the same rate, and thus they stay close to each other.

$^*$Let's neglect the gravitational attraction between the astronaut and the spacecraft here: it is much less than the gravitational attraction these two have with the Earth.
