The Moon on Einstein's birthday
- Round
- Data analysis
- Points
- 8
- Level
- Bronze
- Taught in
- Section 2.8
Adapted from IOAA 2007 (Chiang Mai), data analysis problem 2. We have restated it in our own words. The original gave photographs of the Moon taken at the same hour each night, and we have replaced them with drawings worked out from the Moon's computed position. The solution was last checked on 17 October 2026.
Thailand, on UT+7, celebrated the 60th anniversary of King Bhumibol Adulyadej's accession to the throne from 8 to 13 June 2006. Figure 2.11 shows the Moon at 23:00 Thai time on each of those nights, with the fraction of its disc that was lit. Take Albert Einstein to have been born at noon on 14 March 1879 in Germany, on UT+1. Use the figure to find the Moon's age, the number of days since new Moon, at his birth. Show the method in detail and estimate the uncertainty of the result.
- The lit fraction is largest on 11 June, and the nights on either side nearly match, with 0.985 on 10 June against 0.988 on 12 June, and 0.949 on 9 June against 0.952 on 13 June. So the Moon was full close to 23:00 Thai time on 11 June, a little after it. We take full Moon at 16:00 UT on 11 June 2006.
- By (2.8), 11 June 2006 at 16:00 UT is JD 2 453 898.167. Noon on 14 March 1879 at UT+1 is 11:00 UT, which is JD 2 407 422.958. The two are 46 475.21 days apart.
- This is
- Full Moon comes half a month, 14.77 days, after new Moon, so at the birth the Moon was
- The time of full Moon read from the figure is uncertain by a few hours, about 0.1 day. A larger uncertainty comes from using the average month. Real full Moons come up to about 14 hours before or after the times that the average month gives, and the time from new Moon to full Moon varies from 13.9 to 15.6 days, so the age could be out by up to about a day.
AnswerThe Moon was about 20.7 days old, give or take a day, so it was a waning Moon a little before last quarter. The official solution, which takes full Moon at the start of 11 June, gives 20.9 days. The Moon's computed position puts the new Moon 21.3 days before the birth, inside our range.
This problem also appears among the olympiad problems of Section 2.8, Problems for Chapter 2, which teaches the ideas it uses. Equation and figure numbers refer to the course.