2009
How the Sun's loss of mass widens Earth's orbit
- Round
- Theory
- Points
- 10
- Level
- Bronze
- Taught in
- Section 3.7
Adapted from IOAA 2009 (Tehran), theory problem 12. We have restated it in our own words and kept the original data. The solution was last checked on 21 October 2026.
The Sun loses mass because of the nuclear reactions at its centre. How much does the radius of Earth's orbit grow in 100 years because of this? Assume that Earth's orbit stays circular. Take the Sun's luminosity as
The Sun's luminosity is the energy it turns from mass each second. The change is slow, so angular momentum stays the same.
- The Sun turns mass into energy at the rate
- In 100 years that is
- The change is slow, so by (3.17),
AnswerEarth's orbit grows by about 1.0 m in 100 years, about 1 cm a year. The solar wind carries off about another third as much.
This problem also appears among the olympiad problems of Section 3.7, Two bodies, collisions and slow changes, which teaches the ideas it uses. Equation and figure numbers refer to the course.