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This question mentions the "Rule of 600" for avoiding star-trails in astrophotography.

  • What is this rule?

  • How was it derived?

  • How should it be applied?

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4 Answers 4

up vote 33 down vote accepted

Stars move. Like with any other movement, what we care about is how much they move on the sensor during exposure: A movement that occurs only within a single pixel is not a movement the sensor can capture, i.e. the movement appears frozen.

But when movement takes a point across several pixels during the exposure, it will be visible as movement blur, in this case star trails. A rule like the "rule of 600" is similar in spirit to the "rule of 1/focal length" for handheld exposure, in that it attempts to give exposure times that yield approximately the same movement blur for most focal lengths.

The derivation is fairly simple:

  • The sky rotates 360 degrees in 24 hours, or 0.0042 arc degrees per second.
  • Assuming a full frame camera and a 24mm lens, we have a 73.7 degree horizontal view. (See wikipedia's Angle of view article.)
  • Assuming a 24 Mpx sensor (6000x4000, e.g. Nikon D600), those 73.7 degrees are projected on to 6000 horizontal pixels, giving 81.4 pixels per degree.
  • Assuming a 24mm lens, the "rule of 600" gives 600/24mm = 25 seconds exposure.
  • In 25 seconds the sky will move ~0.1 degrees.
  • For our 24 Mpx full frame camera with a 24mm lens, 0.1 degrees translates to 8.5 pixels.

By the 600 rule, those 8.5 pixels represent the maximum acceptable movement blur before star points turn into star trails. (That's what the rule says. Whether an 8-pixel smear is acceptable for a particular purpose is a different discussion.)

If we plug a 400mm lens into the same formulas, we get max 1.5 seconds exposure time and a 7.3 pixels movement during the exposure. So it's not an exact rule - the blur is slightly different for different focal lengths - but as a rule of thumb it's pretty close.

If we were using a 1.5x crop sensor with the same 24Mpx resolution (e.g. Nikon D3200) and used focal lengths to give equivalent angles of view, we would have e.g. 16mm focal length, 37.5 seconds exposure time and 12.7 pixels blur. That's 50% more blur.

In this case a "rule of 400" for the crop sensor camera would give the same blur as the "rule of 600" for the full frame example.

I suggest using "rule of 600" (or a stricter version with a smaller numerator) with the equivalent rather than the actual focal length, that way the rule gives the same results for smaller sensors. (E.g. 16mm on a 1.5x crop sensor is equivalent to 24mm on a full frame; use the "24mm equivalent" rather than the "16mm actual" focal length to calculate the max exposure time.)

Different stars move at different speeds relative to the Earth. The fastest movement is along the celestial equator, while the Pole star (Polaris for the Northern hemisphere) at the celestial pole hardly moves at all.

The effect can be seen in this picture from wikimedia commons: Polaris appears as a fixed point in the middle while other stars revolve around it, and the length of the star trails increase with their distance from Polaris.

Star trails around the celestial pole

The calculation above is for the worst-case scenario, when the picture includes stars that move along the celestial equator.

I guess the takeaway message is that the 600 in the "rule of 600" depends on camera resolution, sensor size, where in the sky you point the camera, and what you consider acceptable blur.

Use a smaller number if you want less blur.

Conversely, a higher number might be acceptable if you shoot a close crop of Polaris, use a low-resolution camera and/or target a low-resolution output format.

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Does it matter where in the sky the lens is pointed? Presumably stars near Polaris move a smaller linear amount..... – mattdm Dec 6 '12 at 4:11
@mattdm Yes, it matters, see the update. But the derivation is for the worst-case scenario. – j-g-faustus Dec 6 '12 at 7:02
Just a curious question, is the "megapixels" (resolution) truly affects the "Rule of 600"? Also kindly check this blog, davidkinghamphotography.com/blog/2012/11/… I'm a little confused... – Jez'r 570 Aug 14 '13 at 7:15
@Jez'r570 The "rule of 600" is like "1/focal length" for handheld shutter speed and "d/1500" for circle of confusion: The formulas ignore the resolution, and are calculated from how much detail you can see with the naked eye on a "standard size print" at "standard viewing distance". If standard size print and standard viewing distance is how you use your pictures, the camera resolution doesn't matter. – j-g-faustus Aug 14 '13 at 21:12
But if you want to use the extra resolution from a high-resolution camera, e.g. by cropping more, printing larger, viewing closer, or viewing at 100% on the computer, the higher resolution will reveal more blur, so you need a stricter rule. This goes for DOF and handholdable shutter speeds as well. – j-g-faustus Aug 14 '13 at 21:15

The rule of 600 states that to 'eliminate' star trails the exposure time in seconds should be 600 divided by the focal length of the taking lens. 20mm lens could go to 30 seconds, 300mm lens could go to 2 seconds.

Of course (like any motion blur) you will never eliminate star trails- you merely reduce the trail to an acceptable level for a given enlargement. The only perfect solution is a "perfectly aligned tracking equatorial mount" and there ain't no such thing.

The etiology is difficult if not impossible- it's sort of like 'Handhold no slower than 1/focal-length shutter speed'- a rule of thumb or common wisdom that works in many but not all cases.

A discussion of the pros and cons (and math) can be found here: http://blog.starcircleacademy.com/2012/06/600-rule/

An interesting and more general discussion of star trails can be found here: http://blog.starcircleacademy.com/startrails/

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This rule applies to the shutter speed you should use when taking photographs of the night sky. The rule is as follows:

  • When using a lens of focal length L to take a long exposure photograph of the night sky (with a stationary camera), the maximum shutter speed you should use to avoid blurring of the stars is 600/L seconds.

For example, if using a 300mm lens, if you use a shutter speed of (600/300) = 2s or shorter, you should avoid seeing the stars as lines, rather than points, of light.

As far as I can tell there is no record of who came up with the rule or how it was derived, however it would most likely have been based on trial and error using 35mm film, with the inherently lower resolution (grain) and lower tolerance (frame size) than today's cameras, and rounded up (or down) to a nice round 600.

As for application, care should be taken. Modern digital sensors are much sharper than 35mm film, meaning there is less tolerance when it comes to motion blur. Additionally, most digital cameras these days have smaller sensors than the 36mm x 24mm of 35mm film, meaning there is EVEN LESS tolerance, so it should probably be adjusted to be more like a 400 rule when using these cropped-sensor cameras (that is, if you think 600 is still a valid value for full frame cameras, which is arguable). Conversely, if using medium format cameras, a larger number could be used.

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To further add to your point about the ineffectiveness of this with digital cameras, the number of megapixels make a difference. 36 MP are going to capture the movement in a shorter time than a 12 MP camera is. – Dan Wolfgang Dec 5 '12 at 20:50
I was going to make that point Dan but I hesitated; if you compare photos from 35mm film, a Canon 5D mk 1 (12mp) and a Nikon D800 (36mp), then you will see almost no difference in resolution at most common print sizes up to about 12" x 8", at which point the film will start to show grain (depending on the brand used), whereas the digital photos will be effectively identical up to much larger sizes. Certainly if you start looking at individual pixels there will be a noticeable difference between all three, but practically I don't think it will be as important in most cases. – NickM Dec 5 '12 at 20:54
One point the web site mentioned makes is that longer untracked exposures don't make the trails any brighter because the image of the star (assuming perfect focus) moves from photosite to photosite and only deposits so many photons into each. Higher resolution/smaller photosite sensors make this effect more pronounced. – BobT Dec 5 '12 at 21:00
At face value, you're right, Nick. The critical part I left out: focal length and positioning exaggerates this. If shooting at 24 mm (for example), a difference in pixel density will be unnoticed. When shooting at, say, 300 mm the pixel density is much more likely to be noticed. Point the camera 90 degrees from Polaris and you'll be capturing extreme movement, which is easily visible at much shorter shutter speeds. Which leads to: perhaps "where you point the camera" should be another answer here to somewhat debunk the "rule of 600." – Dan Wolfgang Dec 5 '12 at 21:15

It's worthwhile to calculate more precisely for how long you can expose before you get star trails. If you use a rule of thumb and/or trial and error methods until you get things right, you'll likely underestimate the maximum exposure time which ultimately leads to more noise as you'll go about producing the final image in a less than optimal way.

It is not difficult to calculate the maximum exposure time if you know beforehand what objects in the sky you want to photograph. The object is at a certain angle relative to the Earth's rotational axis, which is given by 90 degrees minus the so-called declination of the object. E.g. if the object of interest is the Andromeda galaxy, then [you can find here][1] that the declination is 41° 16′ 9″ therefore the angle w.r.t. the Earth's rotational axis is 48.731 degrees. If the field of view is large, you may not want star trails to appear to the South of Andromeda, so you then need to consider a larger angle. Suppose that you have decided that the angle is going to be and let's call this angle alpha.

We then need to know what the angular velocity of an object at angle alpha relative to the Earth's rotational axis is. If we project celestial objects on the unit sphere then the distance to the rotational axis is sin(alpha). The sphere rotates about its axis once every sidereal day which is 23 hours 56 minutes 4.01 seconds(this is slightly less than 24 hours because the Earth revolves around the Sun, so the Earth must revolve a bit more around its axis for the Sun to be in the same spot). This means that the velocity of the object is:

omega = 2 pi sin(alpha)/( 86164.01 seconds) = 7.2921*10^(-5) sin(alpha)/second

The camera sensor is at the center of the sphere so it is at a distance of 1 to the points on the sphere, this makes the velocity on the surface of the sphere also the relevant angular velocity in radians per second.

The angular resolution of the picture is given by the pixel size divided by the focal length. The pixel size can be calculated by taking the the square root of the ratio between the sensor size and the number of pixels. A typical crop sensor may have a pixel size of 4.2 micrometers. If the focal length is 50 mm, then the limiting angular resolution due to the finite pixel size will thus be 8.4*10^(-5) radians. Dividing this by the angular speed omega gives you the maximum exposure time above which star trails become visible in the ideal case. In general, for pixels of size s and focal length f, this is thus given by:

T = s/(4.2 micrometers) (57.6 mm/f)/sin(alpha) seconds

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