2015

The eccentricity of a satellite from its motion

Round: Theory
Points: 10
Level: Silver
Taught in: Section 3.3

Adapted from IOAA 2015 (Magelang), theory problem 5. We have restated it in our own words and kept the original data. The solution was last checked on 21 October 2026.

An observer wants an approximate value of the eccentricity of an artificial satellite's orbit. When the satellite is at apogee, it is seen to move through $Δ θ_{1} = 2^{'} 44^{″}$ in a short time. When the line from Earth to the satellite is at right angles to the major axis, so that the true anomaly is 90°, it moves through $Δ θ_{2} = 21^{'} 17^{″}$ in the same length of time. Take the observer to be at the centre of Earth. Find the eccentricity of the orbit.

I solved it without the solution

AnswerThe eccentricity is $e = 0.642$ .

This problem also appears among the olympiad problems of Section 3.3, The shape of an orbit, which teaches the ideas it uses. Equation and figure numbers refer to the course.