2009
The height of a satellite from one sighting
- Round
- Theory
- Points
- 10
- Level
- Bronze
- Taught in
- Section 3.11
Adapted from IOAA 2009 (Tehran), theory problem 14. We have restated it in our own words and kept the original data. The solution was last checked on 21 October 2026.
A satellite goes round Earth on a circular orbit in the plane of the equator. An observer in Tehran, at latitude
Draw the triangle formed by Earth's centre, the observer and the satellite, and use the sine rule.
- In the plane of the meridian, the triangle has Earth's centre C, the observer O and the satellite S. The angle at C is the latitude, 35.6°, since S lies in the plane of the equator.
- The zenith is along CO carried on beyond O, so the angle at O inside the triangle is
- By the sine rule,
AnswerThe satellite is 3.98 Earth radii from Earth's centre.
This problem also appears among the olympiad problems of Section 3.11, Problems for Chapter 3, which teaches the ideas it uses. Equation and figure numbers refer to the course.