A perfectly white Moon
- Round
- Theory
- Points
- 10
- Level
- Bronze
- Taught in
- Section 6.3
Adapted from IOAA 2012 (Rio de Janeiro), theory problem S4. We have restated it in our own words. The original gives no data, so we add the full Moon's magnitude of −12.74 and its albedo of 0.14, the values the official solution uses. This albedo is a little higher than the geometric albedo of 0.12 found in this section from $H$. The solution was last checked on 23 October 2026.
What would the visual magnitude of the full Moon be if its albedo were 1? Take the full Moon's magnitude as −12.74 and its albedo as 0.14.
- The flux we receive is proportional to the albedo, so a white Moon would send
- By the magnitude scale,
- The shift is
AnswerA perfectly white full Moon would shine at magnitude −14.9, seven times brighter than the real one.
This problem also appears among the olympiad problems of Section 6.3, Phases and the brightness of planets, which teaches the ideas it uses. Equation and figure numbers refer to the course.