Explaning Motion of a Man and Spacecraft Orbiting the Earth 
A man and spacecraft is orbiting around the earth. The man is outside the spacecraft and is not connected to the spacecraft in any way. The distance between the man and the spacecraft remain constant. Why don't they move apart?
a) The force   of  gravity acting  on  the astronaut   and spacecraft  is  negligible
b) The spacecraft  and the astronaut   are in  orbit   around  the Sun with    the Earth
c) The forces  due to  gravity acting  on  both    the astronaut   and the spacecraft  are the 
  same.
d) The accelerations   of  the astronaut   and the spacecraft  are inversely   proportional    to
  their   respective  masses.

This is clearly a poorly worded question which can be interpreted in several ways, especially the answer for part d. Several people (including several school and tuition teachers) are split on what the answer is. 
I believe that the answer is d. The reason that I say this is because it due to the fact that acceleration is inversely proportional to mass that results in man and the spacecraft having the same acceleration despite having having a different magnitude of gravitational force acting. Hence since they are accelerating at the same rate, they shouldn't move away from each other.
However others believe that the answer is b. I am not sure of their reasoning and I don't see how the fact that two objects orbiting the sun (which is completely irrelevant to the question) prove that they should be the same distance from each other. Am I missing some special effect that the sun has on objects orbiting the Earth?
Could anyone clear this up? Thanks
 A: Let's look at each answer in turn:

a) The force of gravity acting on the astronaut and spacecraft is negligible

Wrong. To be in orbit, gravity needs to be acting. If it were negligible, they would just head off in a straight line in space.

b) The spacecraft and the astronaut are in orbit around the Sun with the Earth

This is true, but irrelevant. Obviously, everything on and in orbit around the Earth is also in orbit around the Sun. And the Milky Way. And so on.. But that is not the reason they don't drift apart.

c) The forces due to gravity acting on both the astronaut and the spacecraft are the same.

Strictly, this is wrong. The force is proportional to their mass. If the ship is 100 times the mass of the man, the force on the ship is 100 times greater that that on the man. However, I think the questioner might've been trying to say something like the gravitational field strength is the same. So this is closest to the expected answer.

d) The accelerations of the astronaut and the spacecraft are inversely proportional to
  their respective masses.

Wrong. If you apply the same force to man and ship, you would find this was true, but we don't. The forces, as stated above, are different. The acceleration due to gravity is the same for both.
The question is terrible - none of the answers are unambiguously correct. One is true but irrelevant and the one that is supposed to be the correct answer (c), is badly phrased and wrong if taken literally.
A: None of the given answers are the correct explanation. The reason that the astronaut doesn't float away is because the acceleration due to gravity is the same for the astronaut and the spacecraft. It's what is keeping the spacecraft in orbit and it doesn't change just because the astronaut steps outside. The force of gravity on the astronaut and the spacecraft is proportional to their mass, and their acceleration is proportional to the force of gravity acting on them. But, their acceleration is also inversely proportional to their mass, so the acceleration is actually constant with respect to mass. That's why the astronaut doesn't float away.
A: The answer is (d) and there's nothing ambiguous about it.  $a=F/m$, true.  But Newton's law of gravitation has $F = GMm/r^2 \propto m$, so that $a = GM/r^2$.  Since $r$ is the same for both, their acceleration (centripetal) is the same.  Inversely proportional to their respective masses, yes, but still the same.
The inverse relationship between acceleration and mass is not the whole story: you also need the proportional relationship between force and mass.   But all the other answers are wrong, and (d) contains an essential part of the analysis.  It is the best answer.
Note in passing that the complete story also needs the equivalence of gravitational mass and inertial mass, something which is not necessarily true in classical non-relativistic mechanics, but is known to be true to a very high degree of precision by experiment.  Einstein's General Relativity says they should be exactly equal.
update after comments
Being inversely proportional to mass doesn't imply that they are not numerically equal. However, I see that what seems clear to me is being read differently by others.  Evidently, my head works the same way as the question's author.  But ... this is not a good situation for an exam question.  So I do agree now that it's a lousy question.
