Astrophotography
- Round
- Theory
- Points
- 10
- Level
- Bronze
- Taught in
- Section 1.1
Adapted from the 2020 Global e-Competition on Astronomy and Astrophysics (Estonia, online), held in place of the IOAA that year, theory problem 1. We have restated it in our own words and kept the original data. The solution was last checked on 14 October 2026.
An astrophotographer on the equator uses a digital camera on a fixed tripod, with no tracking. The lens has a focal length of 150 mm and an aperture of 84 mm, and the light-collecting area of the sensor is a circle 22.5 mm across. The camera points straight up, at a star field at the zenith.
(a) Find the field of view, the angular width of the sky that falls on the sensor. [2 points]
(b) The pixels on the sensor are 3.23 µm apart. What is the longest exposure for which no star trails appear in a single frame? [5 points]
(c) For a better image the photographer takes many frames, each with the exposure from (b), and stacks them. The frames together span 30 s. What fraction of the field of view appears in every frame, and so gets the full benefit of stacking? [3 points]
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(a) The lens forms an image of the sky on the sensor, which sits at the focal length
The small-angle relation (1.1) gives almost the same,
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(b) In the same way one pixel covers
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The camera points at the zenith from the equator, so the middle of the field is on the celestial equator, and the stars in the field are within about 4.3° of it, half the field of view. For them the factor
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(c) Over the 30 s of the frames the field drifts by
Answer(a) The field of view is 8.58°. (b) The longest exposure is about 0.3 s. (c) About 98.5% of the field appears in every frame.
This problem also appears among the olympiad problems of Section 1.1, The celestial sphere, which teaches the ideas it uses. Equation and figure numbers refer to the course.