2017

The fading of Supernova 1987A

Round: Theory
Points: 15
Level: Bronze
Taught in: Section 4.10

Adapted from IOAA 2017 (Phuket), theory problem 6. We have restated it in our own words and kept the original data. The solution was last checked on 20 October 2026.

Supernova 1987A was at its brightest, magnitude +3, on about 15 May 1987. It then faded, and by 4 February 1988 it could no longer be seen with the naked eye, whose limit is magnitude +6. Assume that its brightness $B$ fell exponentially with time $t$ , $B = B_{0} e^{- t / τ}$ , where $B_{0}$ and $τ$ are constants.

(a) Find $τ$ in days. (5 points)

(b) Find the last day on which the supernova could have been seen with a telescope 15.24 cm across that passes 70 per cent of the light falling on it. Take the diameter of the pupil of the eye as 0.6 cm. (10 points)

I solved it without the solution

AnswerThe time constant is about 96 days, and the supernova could be seen in the telescope until about 12 September 1989.

This problem also appears among the olympiad problems of Section 4.10, Problems for Chapter 4, which teaches the ideas it uses. Equation and figure numbers refer to the course.