According to the text, an orbiting object having energy $E

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 implicitly comparing it to the energy the object has in some reference 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 $r=\infty$.
E) Some other situation (specify).

Quizplus · Accepted Answer

In celestial mechanics, an object with energy $E<0$ is bound in an elliptical orbit, and the reference point for $E=0$ is typically at $r=\infty$, where the gravitational potential energy is zero and the object would have no kinetic energy if it were at rest relative to the primary.

According to the Text, an Orbiting Object Having Energy E<0E<0E<0 Follows an Elliptical Orbit

According to the Text, an Orbiting Object Having Energy $E<0$ Follows an Elliptical Orbit