For two objects in space with very different masses, the gravitational force causes: a. a large linear acceleration of the more-massive object. b. no acceleration since the forces are equal and opposite. c. only the smaller object to accelerate. d. a net acceleration for the less-massive object.

The correct answer is D.

In fact, the gravitational force exerted by the massive object on the less-massive object is equal to the force exerted by the less-massive object on the massive object, and it is equal to

where m is the mass of the less massive object, M the mass of the massive object, G the gravitational constant and r the distance between the two objects.

For Newton's second law, the force acting on each of the objects is the mass of the object times its acceleration:


So the accelerations of the two objects are:



we can see from the two equations that
1) the acceleration of the massive object, , is very small because its mass M is big
2) the acceleration of the less-massive object, , is larger because its mass m is smaller

Therefore there will be a net acceleration produced on the less-massive object (and on the massive object, but it will be negligible)