Shooting stars as points

Learning goal

You will be able to explain through the earth's rotation why stars stop being points in a long exposure and turn into small lines. You will quickly estimate with a simple rule how long a star can be exposed at most before it starts to leave a trail in the frame, according to the focal length and the sensor, and find a safer time with a more precise rule for high-resolution sensors. You will know why this time shortens quickly with long lenses, and why the part of the sky around the pole star turns more slowly. When you shorten the time, you will make up for the light you lose with a wider aperture and a higher ISO. In such a frame you will make sure a person standing in it doesn't move during this time, and light their face in its real tone with a small light.

The question

Your friend enlarges the Milky Way frame with the tree on the computer. The galactic core is in place, but every star has become a small, slanted line; the stars aren't points but like tiny commas. They had made a thirty-second exposure. In another frame they tried with fifty millimeters, the trails have grown almost twice as long. Someone at the club tells them "divide five hundred by the focal length," someone else shows a more complicated calculation on their phone. Why do stars turn into lines?

Context

In the previous lesson you planned the Milky Way's calendar in the sky, astronomical darkness and the new moon window (Lesson G.4). When meeting camera bodies, you learned that a small sensor narrows the framing and the crop factor that describes this (Lesson 3.3). In this track's first lesson you learned to find the exposure quickly in the dark with a high-ISO test shot, and to trade stop by stop between ISO and time (Lesson G.1).

The night sky looks still, but we stand on a turning planet. As the earth spins on its axis, the stars slide slowly across the sky; the eye doesn't notice this, but a shutter left open in front of the sensor for thirty seconds records this slide. This lesson takes up calculating how long you can stretch the exposure to record a star without a trail, and gathering enough light within this limit.

Simple explanation

Why do stars slide?

The earth turns once on its axis in about twenty-four hours; this means the sky slides roughly fifteen degrees every hour and a quarter of a degree every minute. The eye doesn't notice this movement, but the sensor records the path each star slides along during a long exposure. When this slide exceeds a few pixels of the sensor, the star stops being a point and turns into a small line. Because a long lens magnifies the sky more, the same slide leaves a longer trail on the sensor; that is why at fifty millimeters the lines are much longer than at fourteen millimeters.

The celestial pole is the point in the sky that the earth's axis of rotation points to; in the northern hemisphere it is right next to the pole star. The sky turns around this point. Stars near the pole slide slowly because they draw small circles, and can stay points in longer exposures; stars near the celestial equator, the region farthest from the pole, slide fastest. Because the galactic core stands in the south in the northern hemisphere, far from the pole, it is in the fast-sliding region.

How long can you expose?

The 500 rule is a simple rule that estimates the longest time, in seconds, at which stars stay points by dividing five hundred by the full-frame equivalent focal length. With a fourteen-millimeter lens on a full-frame camera this time is roughly thirty-five seconds, at twenty-four millimeters roughly twenty-one seconds. On a camera with a crop factor of one and a half, a twenty-four-millimeter lens behaves like thirty-six millimeters, so the time drops to roughly fourteen seconds.

This rule became common for film and low-resolution sensors. On today's high-resolution sensors, because the pixels are very small, the slide of the stars exceeds a few pixels in a shorter time; the time found with the 500 rule can leave visible lines when enlarged. That is why the 500 rule is a quick starting point, not an exact limit. In practice many photographers start from a safer place by shortening this time somewhat.

How is a more precise calculation made?

The NPF rule is a more precise rule that finds the longest time at which stars stay points by taking into account, besides the focal length, the aperture and the sensor's pixel size. In its simplified form, the time is found by dividing the sum of thirty-five times the f-number and thirty times the pixel size in microns by the focal length. At fourteen millimeters, at f/2.8 and with six-micron pixels, this time is roughly twenty seconds; at twenty-four millimeters it is close to twelve seconds. The same values gave thirty-five and twenty-one seconds in the 500 rule. Many sky apps make this calculation by themselves.

Shortening the time loses light; working close to the widest aperture and raising the ISO make up for this loss. If there is a person in the frame, they must not move during this time: standing motionless for twenty seconds is hard, and even breathing can blur the face slightly. Asking the person to lean against a rock or a tree, and lighting their face for a second or two at the end of the exposure with a small light, keeps the face sharp. The light quickly shines too bright on light skin, while on dark skin it often falls short; adjusting the light's duration and distance to the skin shows it in its real tone.

Visual evidence

Your friend looks at the data of the frame with the tree: full frame, twenty-four millimeters, f/2.8, thirty seconds. By the 500 rule it comes to about twenty-one seconds, by the NPF rule around twelve seconds; thirty seconds exceeded both.

On the next new moon night they go back to the same tree. They fit a fourteen-millimeter lens and shoot at f/2.8 and eighteen seconds, raising the ISO to 3200. In the enlarged frame the stars are small, round points; the galactic core again above the tree. They also turn one frame toward the pole star: there the stars are even sharper in the same time.

Selin leans against the tree and stands without moving for eighteen seconds. In the last two seconds of the exposure your friend holds a small, warm lamp to her face. In the first attempt the light fell short; when they bring the lamp half a meter closer, the warm brown of her cheeks and forehead comes out, her face sharp.

Common mistakes

Summary

Stars turn into lines because, as the earth turns, the sky slides roughly a quarter of a degree a minute and the open shutter records this slide; long lenses magnify the slide, while stars near the celestial pole slide more slowly. The longest time is found quickly with the 500 rule, and more precisely with the NPF rule, which also takes the sensor's pixel size and the aperture into account; the lost light is made up with a wide aperture and high ISO, and the person in the frame is shown sharp and in their real tone by leaning against something and having their face lit by a short light adjusted to their skin.

Mini assignment

In this assignment you will calculate and try out the star time for your own lenses.

1. For the focal lengths of the lenses you have, calculate with the 500 rule and with an app's NPF calculator the time at which stars stay points, and write it on a piece of paper.
2. On a dark night, with the same lens, shoot at the time you calculated and at twice that; enlarge the frames and compare the shape of the stars.
3. If you add a person to the frame, have them lean against something, light their face at the end of the exposure with a short light and adjust the light to their skin.

Check yourself

• At which time did the stars stay points, and at which did they turn into lines?
• How different are the times the 500 and NPF rules give on your camera?
• Is the face of the person in the frame sharp and in its real tone?

Glossary

Mini quiz

1. Why do stars turn into lines in a long exposure?

• A) Because the lens shakes
• B) Because the stars really move fast
• C) Because the sensor heats up
• D) Because the sky slides as the earth turns

2. On a full-frame camera with a twenty-four-millimeter lens, roughly how many seconds does the 500 rule give?

• A) Twenty-one seconds
• B) Ten seconds
• C) Fifty seconds
• D) Five seconds

3. Why can the 500 rule fall short on high-resolution sensors?

• A) Because the sensor is large
• B) Because the pixels are small, the slide exceeds a few pixels in a shorter time
• C) Because the ISO is high
• D) Because the lens is heavy

4. Which stars slide more slowly in the same time?

• A) Those near the celestial equator
• B) Those in the galactic core in the south
• C) Those near the celestial pole
• D) Those near the horizon

Answers

1. D — With the earth's rotation the sky slides roughly a quarter of a degree a minute and the sensor records this path.
2. A — Five hundred divided by twenty-four makes about twenty-one seconds.
3. B — On small pixels the same slide spreads over more pixels and the trail shows earlier.
4. C — Stars near the pole draw small circles and travel less in the same time.

Summary card

• The sky slides roughly a quarter of a degree a minute; a long exposure draws it.
• 500 rule: 500 ÷ (focal length × crop factor).
• NPF rule: more precise with aperture and pixel size; apps calculate it.
• With a long lens the time shortens; stars near the pole slide slowly.
• Make up for lost light with a wide aperture and ISO; have the person lean, light their face with a short light adjusted to their skin.

Bridge to the next lesson

Your friend can now keep the stars like points, but still compares their own Milky Way frame with the examples at the club: theirs are brighter, more detailed, the dust lanes more distinct. In their own hands is a kit zoom that doesn't open wider than f/4. At the club someone hands them a very wide-angle and very fast lens. How do you build your first Milky Way photo? The next lesson takes up the first Milky Way frame step by step, with a wide, fast lens, high ISO and the right exposure.