The "500 Rule" was a simple guide (in older days for 35 mm film) calculating the maximum allowable exposure time of star photos due to the Earth’s rotation making star trails when camera is on a fixed tripod. Longer exposure causes the earth rotation to make longer circular star trails. Greater focal length magnifies the Earth’s rotation speed. But the original 500 Rule is Not about other sensor sizes of today, nor about computing a useful exposure time. The "Rule" is only about a maximum exposure time to prevent trail length due to the Earth's rotation.

  500 Rule:  Seconds = 500 / focal length

That was all there was to the original rule. The 500 Rule assumes 35 mm film popular at the time, or today for a Full Frame 1x crop factor. However, for other sensor sizes, the same allowable movement and corresponding Rule Number is computed as:

 For Crop Factor sensors:
  500 Rule:  Seconds = 500 / (Crop Factor x focal length)

The Rule will be more usable (longer exposure) when using a larger sensor. And a shorter lens for a wide sky view does compute a larger "rule" which computes more seconds (allowing more movement, which is harder to see in a wider frame), but a longer lens actually has a larger aperture diameter (at same f/stop, providing more exposure), so is a larger "telescope", so to speak. But this Rule is NOT AT ALL about a proper exposure, but is only about the movement trail it leaves. You will also have to use the ISO and f/stop that gives an acceptable exposure, and that gets much harder. The 500 Rule definitely does limit actual photographic exposure time. Some people use it as the 600 Rule because it specifies more time. Others more knowledgeable use it as the 400 Rule for less star trails but less exposure. For example, 500 Rule / (1.6 crop factor x 12 mm lens) = 21 seconds maximum time for perhaps acceptable absence of trail blur, but 21 seconds may need very high ISO and f/2.8 for an acceptable exposure of stars. A short lens works better for this (a short lens is less magnification of the Earth's rotation). A wide angle sky view with a short lens is a better view of the Milky Way anyway (because it is full sky large up there). And don't miss seeing  below  about an easy and inexpensive DIY rotation tracker.

But even when factoring in the crop factor (which is sensor size), the original Rule ignores all other factors. But if the shutter exposure is longer than a second or two, then the trail length is also longer than zero. Even photographing the Moon requires sunlight exposures because it moves (but it is illuminated by the same Sun that the Earth sees). However in today's cameras, a trail 5 or 6 pixels long is usually not noticeable unless viewing is enlarged more than usual. This calculator computes for sensor size and CoC and trail length, but the Rule does not specify a desired exposure. For exposure of stars in a dark sky on a fixed mount, using a 14 mm lens on a 1x sensor, I’d suggest planning to start at least about f/2.8 ISO 3200 and 30 seconds, which would be Rule 420 and 1.02X CoC and EV -2 (but 500 Rule allows 36 seconds, but which is only 1/4 EV more). 30 seconds is a little more motion, so will be best with a short lens (like 14 mm) for a lessor enlargement. For a 1.5x or 1.6x crop camera, a 9 mm lens would be about the same result, about Rule 260 to 290. Be aware that the Moon is not a star, but is illuminated by our own Sun, and a Full moon itself needs more nearly the same as other exposures in sunlight, which the moon is.

An example of Crop Factors shows the calculator concept here. There's a lot here, and you should notice some relationships in the data of this example.

The Rule 500 may be disappointing for a smaller sensor. The point is that for the 2x sensor, you can use a rule like Rule 500, and compute a longer exposure time like 55 seconds. For a 2x sensor and 9 mm lens, 55.56 seconds × 9 mm focal length is Rule 500, but the motion trail will be twice more than for a 1x sensor. It can use a Rule 200 for 23 seconds for acceptable blur, but that's not much exposure for motionless stars (but which can do the rotating rings around the North Star).

• First row is a full frame 1x camera and 500 Rule, like the old 35 mm film days.

  Second row is a 2x crop camera (called a Four Thirds model), and an Unadjusted 500 Rule (still 500, not the best choice, twice worse).

  Third row properly adjusts Crop 2x to Rule 250.

  Fourth row is Rule 412 adjusted to Rule 206 for crop factor 2x, which limits trail length to the normal 1x CoC limit as used to compute Depth of Field minimum acceptable sharpness.

  Rows 5 & 6 are the other 1.5x and 1.6x crops, with Rule adjusted for crop factor (500 / crop factor). I used the six significant digits just so the Earth's rotation could fully show to be the same exact value (but yes, I do know crop factor and focal length are Not normally more precise than a couple of digits).

• The field named Seconds is Not about the photographic exposure, which is not determined by the Rule (but the longer the better for astrophotography, within reason). Instead Seconds is the Rule's time limit for the focal length that magnifies the Earth's rotational movement.
• Trail length: The rotation Trail length is the length dimension in mm on the sensor, and is also given as pixels on the sensor (pixels are not fractional, so round up). The trail is shorter if Rule is adjusted for smaller sensors, which however require corresponding greater enlargement to viewing size, so it comes out the same visual result again. The pixels (of same 6000x4000 number) are smaller on the smaller sensor.
• Lens mm (Focal Length): Cropped sensors routinely use a shorter equivalent focal length (shorter than the 1x sensor's focal length) to maintain the same Field of View size in both cameras, which is observed in this example too. Milky Way pictures will need a pretty wide view, and the shorter lens helps the Rule time limit.
• The 500 Rule divided by crop factor ( = 250 Rule here with 2x Crop) will give the same result as a 1x sensor and the 500 Rule (the trail is shorter on the smaller sensor, but the additional viewing enlargement result is the same). But the shorter focal length for the same Field of View used by a Crop Factor with an unadjusted 500 Rule (Second row again) will allow a longer maximum Rule exposure than is realistic, but that will be a longer rotation and a longer star trail blur, so the image quality will be less.
• It turns out that the 412 Rule adjusted for crop factor ( = 206 Rule here with 2x Crop) will limit the trail length to no more than the size of the maximum allowable CoC limit that also computes the Depth of Field range (acceptable Depth of Field stops when at CoC reaches 1x). That seems useful for stars too, because the Earth's rotation blurs the star dot. See the Crop Factor of many sensors and films,
  We can also use CoC to judge star rotation blur trail motion length too. As evidence of that suitability (for 35 mm film full frame at that time back then), the original 500 Rule was a close approximation, computing 1.22x CoC for full frame 35 mm film sensors. Still, some users always used the 400 Rule (0.97x CoC) to improve sharpness (assuming rule is adjusted for sensor crop factor). I'm suggesting Rule 412 is 1x CoC (considered acceptable sharpness for Depth of Field). And some like to use Rule 600 for more seconds of exposure, which is 1.42x CoC, a little outside the best sharpness. But (also depending on f/stop and ISO), star exposure may need more exposure time than the Rules allow on fixed mounts.

  Maybe more than you may want to know:

  Actually, specifications of sensor dimensions, crop factors, focal lengths, pixels, even CoC values, are all normally rounded values. So the computing precision is slightly rough, but the 1x CoC computes as Rule 411.47. But 412 is close enough, and a sharper result than 500.

  The relationship of CoC and star trails is that the factors of CoC, sensor size, crop factor and viewing enlargement are all determined by the sensor diagonal mm. The star trail is on the sensor dimension too. We may think sensor size is unimportant in today's digital, because digital doesn't have film grain to show. But sensor size is still quite important, because (regardless of the noise content of smaller sensors), the sensor diagonal determines how much external enlargement is required to view the DOF conventional standard 8×10 inch print. Enlargement determines how well we can see any detail or any blur. If you enlarge the sensor size 15x to view it, that viewing size divides the sensor resolution number by 15. Which is still usually adequate, except printing much larger than 8x10 inches can suffer.

  CoC is Circle of Confusion, the diameter of an out-of-focus "point" (a hypothetical point of zero size, but seen when not at the focused distance), which is determined in lens calculations. The CoC number we see published is a maximum CoC size limit determining what is seen as sharp, or not, which is routinely used in Depth of Field to calculate the DOF near and far span extents. This CoC limit also depends on sensor size, with smaller CoC on smaller sensors, because it is calculated as its size on the sensor, but is seen in the enlarged viewing size of a standard 8×10 inch print.

  CoC mm = (sensor diagonal mm / a constant determined by judging the blur size, but an exact blur size is very hard to judge). My calculator is using the CoC Divisor of 1442 which computes the standard CoC = 0.03 mm for full frame sensors (same as 35 mm film size). This CoC is sometimes seen as 0.0288 mm (from constant of 1500, which is another guess about sharpness), but it is 0.03 mm here, and routinely at most other places.

  If this CoC notion were 0.96x CoC instead of 1x, it would compare same as if the 0.0288 mm CoC, which is then 395 Rule (for a full frame sensor). Note that a Rule is seconds × focal length, which involves both.

  The mention of CoC here is NOT about Depth of Field. Depth of Field at Infinity focus for stars is mighty large. A short lens at widest aperture likely extends DOF back to only a few feet, or a longer lens may be a couple of thousand feet, depending on focal length and aperture. So Depth of Field is not a concern for focus at Infinity for stars, unless including foreground objects near you. Depth of Field calculators will show Hyperfocal, and you can enter 999999 feet there for the Infinity distance (189 miles). CoC is the size of mis-focus blur, and is the well known measure of minimum acceptable image sharpness (the same 1x CoC limit of minimum acceptable sharpness that determines the Depth of Field range extents, when Depth of Field sharpness is conventionally viewed in a standard 8×10 inch print size). CoC is used here only as a known value to compare a star trail's rotational blur.

  So Rule 412 (as adjusted for crop factor) limits the rotation trail blur to be no more length than the same size as the Depth of Field CoC limit that we think of as the minimum extremes for sharpness in a normal photo due to mis-focus. Depth of Field is computed as mis-focus blur less than 1x CoC is still sharp, but greater than 1x CoC is not. Depth of Field calculations draw a very firm line there, but that boundary is not real critical (no detectable difference just either side of it). So it might be 0.8x CoC or 1.2x CoC, but 2x CoC might be more concern.

• If the sensor had half the number of pixels (like 3000x2000) but the same sensor mm size, then the trail length is the same mm, but half the number of the larger pixels. Note that 5 or 6 pixels out of 6000 is only 0.1%, and will still appear adequately sharp to us (unless we are really critical or viewing it considerably enlarged). Again, 1x CoC is the same DOF blur limit that we still consider to be a sharp print. That same CoC will still be adequate sharpness of the stars. I do suggest that the multiplier of the CoC limit is the better guide of sharpness than length of star trail.
• There is more info below, and more of these comparisons at page bottom.

CoC can be a few pixels in size, but our large megapixels today mean we normally can’t see that in an 8x10 inch viewing. Except however, if you are going to enlarge the viewing size of the image much larger than 8x10 inches, then you may want to look at blur length in pixels, and this calculator computes that too.

Regarding exposure, while there are great numbers of fainter stars, my notion is that f/2.8 at 30 seconds at ISO 3200 is a decent but rather minimal exposure in a dark sky with a short lens (meaning for about a 12 to 20 mm lens). However, 30 seconds with a longer lens will have objectionable star trails. The Exposure Calculator will compute Equivalent exposures of that, or of other values.

This calculator below offers other more specific goal-oriented methods to examine the trailing problem, offering visibility of the situation. It is NOT about proper exposure, but it does compute trail blur with actual sensor and pixel size and lens focal length. We can compute the exposure time that limits the star trail length to a specific length in digital pixels, or to a specific multiple of the Circle Of Confusion (the standard Depth of Field CoC guide of blurriness). Stars actually are point sources, so comparing to this existing standard for blurriness is very reasonable. However (on a fixed mount), any method involves a very big trade-off between enough exposure time for the stars, or less exposure time to reduce the Earth's motion blur.

If interested in the long blur trails to make the circular ring trails around the North Star, that is simply 360 degrees in 24 hours, which is 15 degrees per hour. But say for a circular 6 hours, you can enter time as 6h x 60m x 60s = 21600 seconds to compute 90 degrees (Solar, clock time).

Focal length is the actual real focal length of your lens, NOT any Equivalent Focal Length.

The calculator must know a Rule to use. So the Rule in the goal input field is used, but you can change it there. It will likely change as necessary with the other options. The Rule is entered as the Full Frame value (FF), around 400 to 500, but its cropped value will be automatically updated to match any Crop Factor you choose. (Cropped value is the specified FF Rule / Crop Factor. Or FF value is Cropped value x Crop Factor). Then both Full Frame and Cropped Rule values will be shown (if crop factor is not 1x).

Options 1-4 are four ways to specify camera sensor size.

• Option 1 - Best accuracy is when entering actual exact sensor dimensions (width and height in mm, from camera specifications).
• Option 2 - Or, if you can determine the accurate sensor crop factor, sensor size can be computed. For mixed cases (of still and movie formats in the same camera), please see Issues determining sensor size.
• Option 3 - You can specify both Equivalent Focal Length and its actual matching real Focal Length to compute the sensor size. If any questions about this, please see Issues determining sensor size.
• Option 4 - You may be able to select one of the general sensor descriptions. This is written for pixels, but if selecting a film size, then "Sensor Width in Pixels" will be made blank (not applicable, but CoC is still there). Millimeter results apply to the negative size, NOT to an enlarged print. Or if the film was scanned at 100% size (and not cropped and not resampled), enter it as Option 1, digital of dimensions of the full frame scanned image size (which is shown here for film sizes).

  Film sizes should be accurate in the list, but the precise accuracy of the "1/x inch" sensor numbers requires a little more. Did I mention to please see Issues determining sensor size? But ballpark is likely an adequate guess for this Rule number.

Aspect Ratio computes Sensor Size and CoC and Megapixels, but it does not affect the “Rule” numbers. Aspect Ratio is already known for goal 1 Rule or goal 4 film, but is unknown for goal 2 or 3 or for accuracy of digital in goal 4.

Pixels of Sensor Width is the largest dimension in pixels of the sensor image the camera took (if 6000x4000, then 6000 is the width here, even if you hold it vertical on end). Pixels are only used in calculations in pixels (not used at all in film cases). Only sensor size, focal length and time (and Not pixels) compute other lengths in mm or degrees. Megapixels are shown so you can check that your sensor size dimensions are entered correctly, and megapixels within a few tenths is adequate accuracy. However camera specifications do round off specified values of sensor size in mm, aspect ratio, and focal length, all of those affect exact precision.

This Rule calculation is NOT about exposure time or ISO or aperture. It's only about motion due to 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 30 seconds (you may like the Milky Way exposure to be longer, and manual Bulb shutter can be longer). Since the earth rotates, some trail is inevitable without a tracking mount, and this will be a serious conflict with adequate exposure.

The 500 Rule was for 35 mm film size (may be called FF for Full Frame here), and it did not account for other sensor sizes, and it is NOT about exposure (it is only about tracking motion). 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.

It is necessary to enter the Full Frame Rule here, and then any cropped sensors will also be implemented correctly. The desirable goal will be near a Full Frame 400 rule.

If using a "Rule", it divides Rule by Focal Length to get Seconds. But those seconds won't give the same star 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 to compensate, so it doesn't divide your stated rule. If using "Rule", you must divide that "Rule" by your crop factor first, and the calculator should 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 (they will also show the computed Rule number, and also the 500 Rule result).

Sidereal rate is the default implementation, which is the precise rate of rotation to follow the stars, which is 0.27% different than Solar clock rate. This difference is important over minutes, and magnification (i.e., focal length) increases it tremendously. But if the focal length is short so the magnification is low (for example, full sky Milky Way pictures with 1x crop factor and a wide angle lens), it may have little effect on short fixed mount exposures up to about 25 seconds. Solar days are 24 hours or 86400 seconds for 360 degrees movement of the Sun. Sidereal days are 23 hours, 56 minutes, 4.0916 seconds, or 86164.0905 seconds for 360 degrees movement of the stars (because the Earth moves along its orbit during that day). Adding the Leap Year day makes them agree long term.
Sidereal motion is 15.04107 arcseconds per second of time.

Lunar rate is the Moons motion (eastward retrograde motion, slower than the Earths rotation), loses about 1/2 degree per hour against the stars (27.3 days per lunar revolution).
Lunar motion is 14.685 arcseconds per second of time.

Solar rate is the Suns motion, which is our regular clock time.
Solar motion is 15 arcseconds per second of time.

Stellar 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. The Field of View angle is shown, and can be quite wide for a wide angle lens. Rotation blur is zero precisely at the pole at 90° declination (stars rotate around the pole, which is approximately 0.7° from the North star Polaris). Plus and minus declination compute the same blur numbers, around either pole. Directly above our head is celestial declination equal to our Earth latitude. Technically, star rates right at the horizon are also additionally affected by angular refraction, which varies.

Seconds of time goal entered can be entered as a fraction, like 1/60 or 1/250 second (maybe for Lunar or Solar rates). But stars will like a minimum of at least 20 or 30 seconds (at ISO 3200 and f/2.8)

Degrees computed is the length of the blur trail, in rotational degrees. When extremely small, it might be shown in a format like 1e-7. This -7 means move the decimal point 7 places right, to be 0.0000001 degrees. This might be seen if declination is near the poles, or for a very fast shutter speed.

Results. Seconds is Exposure time (computed by the Rule, it is NOT about correct exposure). Degrees is the star rotation in that time, at selected rate. Trail length is also the motion blur computed in mm, pixels and in terms of CoC, these are measured at the sensor plate.

The modes Seconds and Rule must use the specified seconds, so the blur trail varies accordingly.
The modes Pixels and X CoC must hold at the specified blur length, and so these computed seconds will vary.

Arcseconds per pixel and pixels per degree and can aid stellar angular measurements from the photo image. But note the measurement is limited to spans of "small angles", not more than about 10 degrees (but even 15° is still fairly close). Telescopes and even 200 mm telephotos only see a small angle, but wide angle lenses see much more. The "flat" dimension in mm or pixels (in an image) is the tangent of the angle, and tangent is NOT a linear function for larger angles (but accuracy is OK for angles less than 10 degrees). This method is astronomy's plate scale (stellar arc-seconds per flat plate mm) which measures small angles on flat plates (60 arcseconds per arcminute, 60 arcminutes per arcdegree). This dimensional property works to measure Small angles on any images that are not cropped or resampled, if you can enter the sensor and focal length properties used then. Remember, not exceeding 10 degrees.

For planned future images too. Wikipedia says the Sun's angular size is 31′31″ to 32′33″ (about 0.53 degrees) and the Moon's size is 29′20″ to 34′6″ (0.488 to 0.568 degrees). The distance to the elliptical orbits varies slightly with position, but both diameter sizes are roughly about 0.5 degrees. So this pixels per degree number will tell you what size of those to expect on your sensor and lens. Lens focal lengths are rounded, so it will help to know your lenses actual focal length accurately too. My tests of the calculator for the full moon diameter, with rounded 600 mm and 2000 mm lenses both showed about 0.54 degree, which is within tolerance (at the "largest full moon" periods recently). Here's a Moon perigee and apogee calendar. The expected 0.5 degree size will fill half of that pixels per degree number of pixels. The moon is illuminated by the Sun, the Full moon and is roughly near normal daylight exposure, but exposure varies depending on phase and orbit position. At apogee position, the moon is 14% smaller and about 1/3 EV dimmer than at perigee. A quarter phase moon (side lighted) will need +2 or +3 EV more exposure than Full. The Moon's average reflectivity (albedo) is 12%, so the photo should look middle gray dark, not white.

Circular polar star trails: If using an interval timer with one second spacing, the calculator's one second setting can compute the gap size in pixels between shots (or just use wide angle). Specify the declination of your widest view, because rotation blur is zero at exactly 90° declination at the pole. Note that a camera shutter speed of 30 seconds is actually 32 seconds, so that timer interval needs to be 33 seconds, so that it does not skip shots.

But this calculator is NOT about 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

Milky Way pictures are normally improved with substantial post processing to add dazzle. There are many ideas, see Google: How to Edit Milky Way photos.

Andromeda galaxy, M31
Nikon D800, 70-200 lens at 200 mm
f/2.8 30 sec, ISO 3200
One single exposure
White Balance 4150K +3 Tint
This was Rule 6000 (30 sec × 200 mm) but it was tracked

Using a tracking mount, this is M31 Andromeda with a full frame Nikon D800 and 70-200 mm camera lens, one single exposure at 200mm, f/2.8, 30 seconds at ISO 3200, November. That is EV -2 at ISO 3200, which is Light Value -7 EV (at ISO 100). This is heavily cropped, see a similar full frame image above, with same 200 mm lens, but not rotation was Not tracked then.

Andromeda is the closest and brightest spiral galaxy, 2.5 million light years distant, magnitude 3.4, and in a dark sky, it's faint smudge of the small central core is the furthest thing seen with the naked eye. Or rather I should say detected by eye, it's a tiny vague smudge and takes a dark sky. It is actually a bit more than three degrees size (would appear six times larger in the sky than the full moon), but the faint size is not captured here in only 30 seconds. It seriously needs a longer exposure to have seen more. But what we can perceive with naked eye is that fuzzy little bright center spot. Andromeda is on a collision course with our own Milky Way galaxy (at 70 miles per second), expected in about 4.5 billion years. The frame also shows dwarf galaxies M32 (close top right, mag 8) and M110 (top left, mag 9).

The entire frame of this picture is about the same as the Andromeda frame shown above, but it is greatly cropped here to about 40% of full frame height, and resampled to 33% size. It is just one single image (not stacked), but Long Exposure Noise Reduction (normal) was On. It needs much more exposure, but it was my first try with a tracking mount. The general idea today is that it is best to stack several 30 second exposures, instead of trying a longer single exposure.

The editing I did (surely considered very mild by some standards) in Adobe Camera Raw (ACR) was to crop it much tighter, and set white balance by eye to find the small pleasant spot between Temperature too blue or too yellow, and Tint between too green or too magenta (this white balance was 4150K° and +3 Tint, but nearby city lights can have effect). It used the ACR lens profile to correct vignetting (but none of the frame corners are in the view of this crop), and added the Curve's Strong Contrast. Exposure +1, Blacks -80 to darken the sky, Clarity +35 to bring out the galaxy a bit, and Saturation +50 to bring out the colors. There are both some red and some blue stars. And then resampled the crop to 33% size for the web.

An "Equatorial mount" lets the telescope or camera rotate on an axis aligned to be parallel to the Earth's axis. This axis is pointed to the pole near Polaris, the North Star, so it rotates same as Earth on its axis. This lets one simple rotation motion stay locked on a star (instead of a complicated X and Y motion that requires a computer to perform it precisely, like a regular camera tripod which is called an alt-azimuth mount). On this equatorial axis, a motor can keep turning the camera back at near the same slow rate the Earth turns forward (actually at the Sidereal rate for the stars), so that the camera is locked onto the same spot in the sky with no relative motion.

For this purpose, there are a few motorized star tracking camera mounts available (ballpark cost around $500 US, from iOptron, Vixen, etc, at Amazon, B&H, etc). The iOptron SkyGuider Pro I used has a small fixed telescope literally built into the hollow polar axis to align the mount on Polaris, easy to use, with an illuminated scale marking the offset amount and direction from Polaris. Then tonight's current direction to set it too is obtained from a smart phone app showing current month/day/hour location to properly align the mount (see page 15 of the user manual). This is extremely handy. Using the South Pole is a similar situation. This "Full package" system includes all but include the tripod or the ball mount to mount and aim the camera.

Polaris: Setup out in the field first carefully aims the polar axis of the mount at the North pole near Polaris (RA: 2h 31m 48.7s, dec: +89° 15' 51"). Polaris is actually about 3/4 degree from the pole, perhaps 44 minutes. This separation is near about 1.5 times the full moons diameter (so in a telescope, it's further than you might imagine). The direction of Polaris around the North pole rotates during the night, and over the course of a year. If the mount’s rotation axis is aligned on that correct spot, then the mount’s rotation around the pole will track accurately for long periods of time. If misaligned a bit, then it will skew a bit during that time.

Using this tracking mount, the small image is a 127x78 pixel 100% crop from this same image (greater enlargement, slightly left of galaxy center) showing round stars without trails (but without tracking, 200 mm at 30 seconds would otherwise compute a 6000 Rule, and 55 pixels of trail at declination 41° degrees).

But there is another very popular and inexpensive DIY idea for a suitable tracker for a camera, and if serious about it, you may want to investigate an easy-to-build barn door hinge tracker for the camera. Do look deep into that Google list, because there are many versions of this shown. The hinge axis is aimed at Polaris, the North Star, so the stars revolve around it. The accuracy of that aim will affect the tracking precision. 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 (360° per minute). It can get fancy, some versions add a small One RPM motor and gears, but if no motor, this drive screw can be manually turned, for example as 1/4 turn every 15 seconds, which would then compute motion blur as just 15 seconds (still suitable for wide lenses, but allowing a much longer overall exposure). Don't shake the camera doing the adjusting. The straight line screw travel won't be adequate tracking accuracy over many minutes, but it is very popular and very suitable for a few minutes, if polar aligned fairly well.

Stars and Rules

If 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. Pixel values shown are for 24 megapixels (the 6000 pixel width), which will vary with your own megapixels. These are Sidereal numbers.

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

A Rule adjusted for Crop Factor leaves those two results unchanged, but changes time and all the others. The short time may not be usable.

Changing only megapixels in same sensor width changes trail in pixels, but not degrees or mm, so the image xCoC looks the same (half the pixels of width, in half of the width, looks the same).

Changes are shown as the columns progress downward.