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Astro-photography with a tripod only - how long can I expose?

When doing night-time photography with a tripod only, the most important question is "how long can expose my picture before stars are turning into star trails?" or simply "what is the best exposure time?"

Of course.. the longer the better as more stars become visible. But if you expose too long then the earth's rotation quickly turns pinpoint stars into star trails. So what is the best compromise? The answer to this depends on many factors that play a role:
- focal length used
- position in the sky you are pointing at
- camera field of view
- camera's crop factor

Top-down as a rule of thumb, the following equation gives a good indication on what exposure time can be used to avoid star trails:

max_exposure_time = 500 / (focal_length * crop_factor) with max_exposure_time in seconds and focal_length in mm.

For example: using a fullframe camera (= crop_factor 1) with a 100mm lens results in 500 / (100 * 1) = 5sec maximum exposure time

Dependency on position in the sky

The equation above is a top-down rule of thumb that gives the maximum exposure time for the 'worst position in the sky' meaning the position in the sky where the celestial motion is the greatest. This is near the celestial equator. However when pointing at the North or South pole though, the movement of the stars is a lot smaller as the stars are rotating around the poles.
Hence when pointing at positions in the sky near the pole, even longer exposure times are possible. Pointing at the celestial pole, even a factor 2 of the maximum above may be possible.

Dependency on the focal length and field of view

Especially when using shorter focal lengths ie more wide angle lenses, keep in mind use the exposure time of that portion of the image that has the greatest movement. So for wide angle lenses I would recommend to rather stick to the rule of thumb above as to use the upper end of the range.In general, the dependency of the focal length is quite easy: the more zoom you use, the earlier you will see the movement of the stars.