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?

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.

To determine the acceleration due to gravity on the object when placed in a spaceship, we need to understand that the object's weight is directly proportional to the acceleration due to gravity.

The weight of an object is given by the formula: Weight = mass * acceleration due to gravity.

Since the weight is given as 5.10 N at sea level, we can rearrange the formula to solve for the acceleration due to gravity:

Weight = mass * acceleration due to gravity

Dividing both sides of the equation by mass:

Weight / mass = acceleration due to gravity

Now we can plug in the given weight (5.10 N) and rearrange to solve for acceleration due to gravity:

acceleration due to gravity = Weight / mass

However, we don't have the mass of the object given. Without the mass, we can't calculate the acceleration due to gravity on the object. To determine the acceleration due to gravity on the object in the spaceship, we need to know the mass of the object.