Question

According to the text, an orbiting object having energy E < 0 follows an elliptical orbit. When we specify the numerical value for an object's energy, we are implic- itly comparing it to the energy the object has in some ref- erence situation. So, when we say that E < 0 in this case, we are comparing the energy of the orbiting object to the energy of an object with 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 r=[infinity].
E. Some other situation (specify).

Answer 1

The reference point for an orbiting object's energy E < 0 is when it is at rest infinitely far away where gravitational potential energy is zero, meaning the correct answer is D. At rest at r=[infinity].

Step-by-step explanation:

When we say that an orbiting object has energy E < 0, we are comparing its energy to the energy it would have when it is at rest infinitely far away from the primary (where there is no gravitational potential energy acting on it). This is because the gravitational potential energy approaches zero as the distance r approaches infinity, hence the total energy approaches zero. An object with negative total energy indicates it is in a bound orbit, such as an ellipse or a circle with the Earth, as opposed to zero energy which corresponds to an escape velocity or positive energy which corresponds to an object in an unbounded or hyperbolic trajectory.

The correct answer is thus D. At rest at r=[infinity]. This is the reference point where gravitational potential energy is considered zero, making it a logical baseline for comparing other energy states.