Question

According to the text, an orbiting object having energy follows an elliptical orbit. When we specify the numerical value for an object's energy, we are implicitly comparing it to the energy the object has in some reference situation. So, when we say "in this case," we are comparing the energy of the orbiting object to the energy of an object of the same mass that is:

A. At rest at the primary's center.
B. At rest on the primary's surface.
C. In a circular orbit just above the primary's surface.
D. At rest at some other situation.

Answer 1

The reference situation for the object's energy in an orbital context is often being at rest infinitely far away from the primary, where gravitational potential energy is zero. However, for educational examples, the orbital energy is typically compared to an object at rest on the primary's surface.

Step-by-step explanation:

When specifying the numerical value for an object's energy in orbital motion, we are comparing it to a reference situation. In the context of satellites orbiting Earth and the discussion of orbital energy and gravitational potential energy, the reference situation often implied is that of the object being at rest infinitely far away from the primary, where the gravitational potential energy would be zero. Therefore, when describing the energy of an object in orbit as negative, we are saying it has less energy than it would if it were at rest at an infinite distance from the primary. However, the choice to compare it to a satellite at rest on the primary's surface is context-dependent and related to the example or problem being considered. For the specifics of the question asked, the comparison to an object at rest on the primary's surface (option B) makes the most sense, since in most educational settings, the reference point for the gravitational potential energy is taken to be zero at the surface of the primary, such as Earth's surface.