Final answer:
The gravitational potential energy of an object increases as the height increases, based on the formula PEg = mgh.
Step-by-step explanation:
The relationship between an object's height and its gravitational potential energy (GPE) is that the gravitational potential energy increases with height. This is because GPE is calculated using the formula PEg = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height above the reference point. As an object is raised in height, the work done against gravity translates into an increase in GPE, hence the gravitational potential energy of an object is directly proportional to its height in a gravitational field.