An object has a weight of 5.10 (N) AT SEA LEVEL. What is the acceleration due to gravity on the object if it is placed in a spaceship?

Answer 1

This does not make sense.
The only thing I can say is that it has a mass of
m = 5.10/9.81 = .52 kilograms
wherever it is.

Is the spaceship in a "zero gravity" orbit around earth?
In that case it still has a gravitational force depending on how far from the center of earth it is, but this force is exactly equal to mv^2/r, the centripetal force required to hold it in orbit, so there is no change in orbit radius.