A comet's period and the area it sweeps
- Round
- Theory
- Points
- 4
- Level
- Bronze
- Taught in
- Section 3.1
Adapted from IOAA 2007 (Chiang Mai), theory problems 1.6 and 1.7. We have restated it in our own words and kept the original data. The solution was last checked on 21 October 2026.
A periodic comet goes round the Sun. At its furthest it is 31.5 au from the Sun and at its closest 0.5 au.
(a) What is the period of the comet? [2 points]
(b) What area, in square astronomical units per year, does the line joining the comet to the Sun sweep out? [2 points]
- By (3.1),
- By (3.2) in years and astronomical units,
- Also by (3.1),
- By the second law the area is swept at a steady rate, so the rate is
AnswerThe period is 64 years, and the line from the Sun sweeps out 3.12 au² every year. The eccentricity is
This problem also appears among the olympiad problems of Section 3.1, Kepler's laws and the ellipse, which teaches the ideas it uses. Equation and figure numbers refer to the course.