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Calculator for maximum exposure time
of Milky Way Stars (on a fixed mount)

Select one of four ways to specify camera sensor size
1 Sensor size
Width mm
Sensor size
Height mm
2 Sensor
Width mm
Aspect Ratio
Width: Height
3 Crop Factor Aspect Ratio
Width: Height
4 Film and
Sensor Size Description
 
Mostly this is Film Size. Size of a CCD sensor is NOT the 1/x inch number (the size is WxH mm)
Focal Length
mm
Sensor Width
pixels
Seconds of time
A new Rule
Pixels of blur
X CoC blur
Celestial Declination
degrees

Please report ( Here ) any problems with the calculator, or with any aspect of this or any page. It will be appreciated, thank you.

We hear about the "500 Rule". It's a rough guide about maximum exposure time of star photographs due to trails when camera is on a fixed tripod. It says the maximum star exposure time (without excessive rotation trail due to a fixed mount) is the "Rule" number / focal length (for example, 500 Rule / 24 mm lens = 20.8 seconds maximum time). This involves a very big trade-off between enough exposure time for the stars, but less exposure time to reduce the motion blur.

However, that Rule was for 35 mm film, and it does not account for other sensor sizes. Using a cropped sensor must adjust for crop factor, either Rule / crop factor, or Rule / (focal length x crop factor) is the same thing. Then this difference makes any printed Rule number be ambiguous without explanation of how it applies to sensor size.

But this calculator needs the real focal length, so here, adjust for crop factor by dividing the Rule instead of multiplying the focal length.

Cropped sensors complicate the "Rule". The "(500): 333" Rule nomenclature used here is "(full frame): cropped" Rule (only shown with cropped sensors). The (500): 333 nomenclature here is an attempt to show rules for both sensors to clarify which is meant, using your specified sensor. If selecting a full frame sensor here, this conversion part is skipped. "Full frame" conventionally means the standard 35 mm film size comparison.

The "Rule" divides by Focal Length to get Seconds. But those seconds won't give the same trail effect on a smaller cropped sensor. If the same lens, the Earth rotates at the same rate across the pixels, but the cropped sensor is smaller. The star would cross the smaller sensor faster, so there is greater blur. And cropped DOF CoC is smaller for same reason. So if hoping for same limited blur effect when using a crop sensor, fewer seconds are necessary. This calculator does not know if you already divided your rule, so it never divides your stated rule. If using "Rule", you must divide that "Rule" by your crop factor first, and the calculator hopefully will guide you with that as you go. But the "Rule" is just one choice here, you can instead just use one of the three other option methods offered (seconds or pixels or X CoC), which have a more defined goal, and do not use a "Rule" as input (the computed Rule result will be shown though).

Declination of 0° computes the maximum length blur which occurs at the celestial equator, and so 0° declination is suggested as a general case to include the entire frame view. Rotation blur is technically zero at the pole at 90° declination (stars rotate around the pole, which is approx 0.7° from the North star Polaris). Plus and minus declination compute the same numbers here. The overhead directly above our head is celestial declination equal to our Earth latitude.

Pixels per degree and arcseconds per pixel can aid stellar angular measurements from the photo. But note the method is limited to spans of "small angles", not more than about 10° (but even 15° is still pretty close). The "flat" dimension in mm or pixels is the tangent of the same angle in the camera, and tangent is NOT a linear function for larger angles. This method is astronomy's platescale (stellar arc-seconds per flat plate mm) which is designed to measure on flat plates. Telescopes and even 200 mm telephotos only see a small angle, but wide angle lenses see much more. This dimensional property works to compute Small angles on any images that are not resampled, if you can enter the sensor and focal length properties used then.

Future images too. Wikipedia says the Sun's angular size is 31′31″ – 32′33″ (about 0.53°) and the Moon's size is 29′20″ – 34′6″ (also about the same). The distance to the elliptical orbits varies slightly with position, but both are close to 0.5°. So this pixels per degree number will tell you what size to expect of those on your sensor and lens. One half degree will fill half of that pixels per degree number of pixels.

Options 1-4 are four ways to specify camera sensor size. 1 and 3 seem most useful.

Aperture is not a factor of star trail length, but it affects exposure of stars with even greater significance. Effective aperture diameter is focal length / fstop Number. So a 14 mm f/2.8 lens is a 5 mm "telescope". A 28 mm f/2.8 lens is 10 mm diameter, and a 50 mm f/2 lens is a 25 mm "telescope". Larger telescopes are good, the Palomar telescope is 5.1 meters diameter. The 50 mm f/2 lens compares as 3.5 times more magnification (longer blur trails too) than 14 mm, but also five times diameter with 25 times more area, which I compute to be 2.5 x log10(25) = 3.5 magnitudes (of more faint stars) seen in the same exposure time. But you're surely talking about a tracking mount then. The 500 Rule of 10 seconds won't get it done.


Measuring the blur trail:

This was to be M42 in Orion. Exposure was 20 seconds, ISO 3200. And f/2.8, 200 mm, so it is (20 x 200) = 4000 Rule full frame on fixed tripod. 4000 may be a bit too much. On a fixed mount, 20 mm would work better than 200 mm. :)   This length is 9.7x CoC mm. m42

At right is a 100% crop from it. Calculating above for 20 seconds (35.9 mm sensor width, 7360 pixels width, 1x crop factor), the result is 59.4 pixels of trail (99.6% length at 5.4° declination, cosine). Computing zero degrees would generally seem a better case about the entire field of view which often includes zero.

When the image is rotated 27° (to be horizontal), and enlarged to about 800% to see the pixels, I count a trail to be about 69x10 pixels (a tight marquee crop shows the count, or you can actually crop it and examine resulting size). But don't count the entire trail. Star blobs are round, so if the width of the line is 10 pixels (focus?), the additional blur trail of a round star is 69-10 = 59 pixels which agrees with the calculation. This addition is what is calculated. Counting is a bit arbitrary, there's always a couple of neighboring pixels and aliasing, etc., more or less.


VR Turn VR Off on the tripod. VR (Vibration Reduction) is Nikon's image stabilization method. Not intended for tripods, and worse, in very dark conditions, VR can cause a visible red streak seen in the star image. This is a Nikon D800 and 70-200 mm VR lens.

Also note the vignetting (dark corners). That's going to happen, and it's worse with wide angle at wide aperture (This one is 200 mm, f/2.8). The Adobe raw editor (ACR) has a great tool to fix that with one click (Lens Profile Corrections), but not bothered to do here.


500 Rule for photos of Milky Way Stars

The Earth rotates. A reasonably long star exposure on a tripod or other fixed mount will show an elongated star trail (blur) instead of a pin point dot. A longer lens seriously magnifies this movement, so usually a short wide lens is used for the Milky Way (also to show a lot of sky). However, a 14 mm lens at f/2.8 has an aperture diameter of 14/2.8 = 5 mm. A 50 mm lens at f/2 is 50/2 = 25 mm diameter, so while 50 mm magnifies the motion trailing (50/14 = 3.6x greater), its larger aperture can show a narrow view of substantially fainter stars.

There's a rule of thumb for Milky Way photography called the 500 Rule. This idea from 35 mm film days says 500 / focal length = seconds is the maximum exposure time still retaining sharp round stars (if using a fixed mount). But sensor size also affects magnification, and for a cropped sensor, this rule is 500 / (focal length x crop factor). However, this does not take megapixels into account, and more megapixels will show more pixels of trail. The 500 Rule is intended to be a compromise of the most exposure time vs. the least blur trail size, and typically Rule values from 400 to 600 are tried.

Why would we use one Rule vs another? For image quality of course, to be less affected by the blur trails caused by the Earth's rotation when camera is on a fixed mount. The purpose of this calculator is to give a reasonable expectation about what to expect from the blur trails. How many pixels long are the trails? However, it's a serious trade-off, because stars require quite a few seconds of exposure, and the Earth does rotate.

This calculator computes the fixed mount star trail blur based on your focal length, sensor size, pixel dimensions of your image, and of course shutter exposure time.
The resulting blur trail length is shown in degrees, mm, and in pixels of length. Pixels might mean the most to you, but there is added depth here of comparing this blur to the standard DOF CoC maximum acceptable limits for blur that we already use.
To plan your star session, you can choose to enter a shutter time, or a new Rule, or to limit the star blur trail to X pixels long, or to limit it's size on the sensor to be X times the CoC diameter (relative to the normal DOF limit).

The mm length of the elongated pixel trail is compared to standard Depth of Field CoC limit in mm, to judge how much it matters. The Depth of Field definition is an existing standard where the limit of 1x CoC diameter is the boundary where our eyes decide fuzzy instead of sharp enough (but it becomes much more evident at larger enlargements). A trail length of a few pixels may not always be quite as bad as it may sound, but many pixels will be a problem.

The "Rules"

Applying the "Rule" (for example Seconds = 500 / 24 mm) by using adjusted Rules for Crop factor of course computes different maximum exposure times for different sensors (not conflicting with the next statement), because the purpose of this Crop adjustment is to give comparable results. However, for the different exposure times computed for the different size sensors of the same megapixels and same lens, the calculator computes the same blur trail in both mm and pixels and same CoC multiple (if the Rule is converted for crop factor). The Earth rotates at the same rate, but the sensors are different sizes, and the Crop factor equalizes that aspect. But exposure must be compensated with higher ISO or wider aperture. For a 1.5 crop sensor, the fewer seconds of time required by the Rule is 0.58 EV less exposure than a 1.0 crop sensor. This is just saying that for a smaller cropped sensor, the same blur trail of the Rule requires less seconds of time, seconds / 1.5, which is 0.58 EV less exposure.

There's a chart summarizing how the rule affects these "changes" at the bottom of this page.

But for quality results (no visible blur trail), then the Rule becomes small, especially with cropped sensors, with inadequate exposure for the Milky Way stars. It's a difficult problem, because the Earth rotates.

CoC is a limit on acceptable blurriness in Depth of Field calculations. Here, we merely use CoC as an existing size reference. also for the blur star trail due to the Earth's rotation motion. Depth of field is of course not an issue when focused on a star at infinity, but just being able to focus on a star is a major issue. Actually seeing any star in the viewfinder is difficult or impossible, but focusing is greatly aided if in Live View Mode, and then zooming in greatly on the rear LCD preview. Then you can see the bright ones to focus (manually focus for the brightest but smallest dot made by the star).

The trail surely will look a couple of pixels longer than calculated, due to the star dot straddling multiple pixels and affecting neighboring pixels. Any movement of one pixel obviously involves at least two pixels, another maybe at both of the start and end points, which calculation does not include. And of course, misfocus blur makes the blur pixels be larger dots too. The star dot is round, so its minimum length must be at least its width, so subtract the line width from the line length to get the extended blur trail length calculated. The calculator only calculates Width and horizontal dimensions, but magnification is the same in all directions.

It may matter if the camera times the shutter, or if you time it manually. Because, the camera's nominal shutter speed of 30 seconds is actually implemented to be 32 seconds (25 = 32, and nominal 15 seconds is actually 16). That's so our concept of 2x time being exactly 2x exposure will work (has to be 1, 2, 4, 8, 16, 32 steps.) Nominal 20 and 25 seconds are more as expected. You can compute with the correct time if you expect it. See chart of actual shutter speeds.


This calculator is NOT about proper exposure or ISO or aperture. It's only about focal length and sensor size and the Earths motion causing star trails if on a fixed mount. You will still need proper exposure, and for a dark sky and a short wide lens, I'd say start at ISO 3200, f/2.8, and about 20 seconds (you'd like the Milky Way to be longer). Since the earth rotates, some trail is of course inevitable without a tracking mount, and this will be a conflict.

This calculator is also NOT about intended long circular star trails (those are circular and rotate 15 degrees per hour). This goal is to compute movement of the Earth's rotation on a fixed mount.

A Better Solution

A fixed mount (like a camera tripod) is turned with the Earth as it rotates (one revolution per day). An "Equatorial mount" for telescopes lets the telescope or camera rotate on an axis parallel to the Earth's axis (axis is pointed to Polaris, the North Star, so it rotates same as Earth on its axis). This lets one simple rotation motion follow a star (instead of a complicated X and Y motion that is hard to perform precisely, called an alt-azimuth mount, i.e., like a regular camera tripod). On this equatorial axis, a motor (and gears) can keep turning the camera back at the same slow rate the the Earth turns forward, 15 degrees per hour, so that the camera is locked onto the same spot in the sky (with no relative motion). There is one inexpensive idea of this that is very popular.

If serious about it, you may want to investigate an easy-to-build barndoor hinge tracker for the camera. Look into that 17 page list, there are many versions shown. The distance from hinge to drive screw is a precise calculation to match the Earth's rotation to the screw thread pitch turning at one RPM. Some versions add a small one RPM motor and gears, but this one RPM can be manually adjusted as 1/4 turn every 15 seconds, which would then compute blur as 15 seconds (it can be maintained for a longer exposure of a minute or two, but don't shake the camera doing it).


Stars and Rules

If anyone is interested, here is how changes to Rule or Crop Factor affect these values.

These properties are about the rotation with time, and the length of the star trail, in degrees, mm, and pixels.

When all else is unchanged, Crop Factor changes only Pixels and X CoC. The mm path length stays the same, but of course the sensor is smaller, so it appears larger in the image.

A Rule adjusted for Crop Factor leaves those two unchanged, but changes all the others.

Changing only megapixels changes trail in pixels, but not on mm, or anything else, so the image looks the same (half the pixels of width, in half of the width, looks the same).


The value in any blank column is the SAME as the last value above it (it is unchanged).
Changes are shown as the columns progress downward.

Lens FL Width Rule Crop Seconds Degrees mm Pixels X CoC
20 6000 500 1 25 0.1042 0.03636 6.06 1.2x
2 12.12 2.4x
4 24.24 4.8x
8 48.48 9.7x
333.3 1.5 16.67 0.06944 0.02424 6.06 1.2x
312.5 1.6 15.62 0.0651 0.02273 6.06 1.2x
250 2 12.5 0.05208 0.01818 6.06 1.2x
100 5 5 0.02083 0.007272 6.06 1.2x
Half the pixel dimension is same but half smaller image
20 3000 500 1 25 0.1042 0.03636 3.03 1.2x
2 6.06 2.4x
4 12.12 4.8x
8 24.24 9.7x
2x focal length at half the exposure is same pixels and X CoC
40 6000 500 1 12.5 0.05208 0.03636 6.06 1.2x
2 12.12 2.4x
4 24.24 4.8x
8 48.48 9.7x
412 Rule gives 1 X CoC if adjusted for Crop
20 6000 413 1 20.65 0.08604 0.03003 5.01 1x
2 10.01 2x
4 20.02 4x
8 40.05 8x
275.3 1.5 16.67 0.05735 0.02002 5.01 1x
258.1 1.6 12.91 0.05377 0.01877 5.01 1x
Lens FL Width Rule Crop Seconds Degrees mm Pixels X CoC


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