In an elliptical orbit, where is the object moving fastest?

In an elliptical orbit, where is the object moving fastest?

• A. At apoapsis
• B. At periapsis
• C. At the semi-major axis
• D. At the farthest point from the Sun

Answer: (B)

In an elliptical orbit, speed is not constant because gravity does work as the object moves closer to or farther from the Sun. The speed is greatest at the closest approach to the Sun, where the gravitational pull is strongest. At this point, potential energy is most negative and the corresponding gain in kinetic energy makes the velocity peak. This idea is captured by the vis-viva relation, v^2 = μ(2/r − 1/a): with a fixed orbit (a is fixed), a smaller distance r to the Sun gives a larger v. The farthest point (apoapsis) is where the speed is smallest, since r is largest there.

In an elliptical orbit, speed is not constant because gravity does work as the object moves closer to or farther from the Sun. The speed is greatest at the closest approach to the Sun, where the gravitational pull is strongest. At this point, potential energy is most negative and the corresponding gain in kinetic energy makes the velocity peak. This idea is captured by the vis-viva relation, v^2 = μ(2/r − 1/a): with a fixed orbit (a is fixed), a smaller distance r to the Sun gives a larger v. The farthest point (apoapsis) is where the speed is smallest, since r is largest there.