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As an amateur with limited budget, I'd be interested in taking photos of the night sky, trying to capture more detail than human eye armed with a lens of comparable parameters to what I have in my camera normally could see. I doubt I'd ever get down to details as fine as Jupiter's moons, but I'd hope to see detail of some nebulae I have a hard time seeing through my inexpensive telescope, stars too dim to notice in less-than-perfect conditions etc. I'm interested in taking full-sky images just as well as zooms on specific objects too.

Currently, I have a lower-end SLC camera, with two lenses - good sharpness though lower aperture with 50-120mm focal length, and a wide-angle, high-brightness one (about 12-50mm) currently. Firmware hacks allow me to take photos of arbitrarily long time, and I have the remote to start and stop it without touching the camera, and generally software-wise the camera is quite powerful. One of the lenses (the longer focal length) is of "standard professional" quality level too.

Is this sufficient to get started? If so, what kind of settings should I use? If not, what other kind of entry-level equipment would I need to obtain/build on budget to get started with night sky photography?

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There are several options.

You can do star trail photos with just a tripod. If you have dark skies, Point the camera near the pole star, do a long exposure, and get star trails as the sky appears to rotate around the pole.

If you're in a light polluted area, then you'll find your maximum exposure time is limited by the light pollution - expose for long enough and the light pollution background will saturate one or more colour channels - which could prevent you using a long enough exposure to get long trails.

You can also take pictures of the moon - since it's basically a gray rock in bright sunlight, you don't need a long exposure at all for this. But you do need a long focal length to make the moon big enough to fill a decent part of the frame, and at 150 mm it's likely to be disappointingly small. (You need around 1500mm or so to fill most of an APS sized sensor frame).

You can also do constellation photography with just a tripod. The trick here is to keep the exposure short enough that the rotation of the earth doesn't cause significant star trailing. As a rough rule of thumb, divide 400 by the lens focal length to get the approximate exposure time in seconds (thus varies in practice depending on where you're aiming, and how picky you are about trailing, but should give you a starting point). Thus with a 50mm lens, you can get away with around 8 seconds, around 2-3 seconds with a 150mm lens, and around 33 seconds with a 12mm lens.

You can improve results by stacking several exposures in software - try the free Deep Sky Stacker - which will reduce noise and usually give you a cleaner result.

For longer exposures, you'll need some sort of tracking mount to compensate for the earth's rotation and prevent star trailing. You can either build a barn door tracker, as mentioned in other replies, which rotate a camera platform around a hinge whose axis points at the celestial pole, or look at a commercial solution.

There are several mounts designed for use with cameras, such as Vixen's polarie, Skywatcher's star adventurer mount (or similar from Vixen or Ioptron), or the Astrotrak system (or Kenko's Sky Memo (not sure if this is still available)). Note that with some of these you also need to budget for a couple of tripod heads - one to point the mount at the celestial pole, and one to point the camera.

Or you could look at a motorised german equatiorial mount - which would also let you use a telescope - but to get good long exposure images with a telescope usually requires a good mount, which range from expensive to very expensive - and may also require autoguiding (automatic correction using a second guide camera and software) to apply corrections for long exposures. Long exposure deep sky imaging is more accessible than it was, but is still expensive to do well (and easily capable of soaking up as much money as you want to throw at it.)

Note that popular go-to alt-az mounted are limited for long exposure imaging, as although goto alt-az mounts can track objects - which is fine for visual use - they suffer from an effect called field rotation which makes the field of view gradually rotate, causing star trailing after a while (around 30s or so - it depends on latitude and where you're pointing). German equatorial mounts, with one axis pointed at the celestial pole, don't suffer from this.

For planetary imaging, the planets are bright enough that you can capture video with a webcam (or similar planetary astro camera) and telescope, and then process the video to stack the best frames. This is a different type of imaging to the long exposure deep sky stuff.

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For long exposure pictures you need to have a motorized mount for your camera. The earth's rotation will lead to streaks otherwise. An affordable way to do this is to use a standard tripod with a star tracker on top. There is a variety of products like:

They cost around 400-500 USD and are fairly small. You need to align them to the sky's north pole (using the star Polaris in Ursa Minor), and then they will rotate your camera as the earth rotates during the night.

Also, you may want to start with your 50mm lens first. The greater the focal length, the higher the magnification, and also the more visible the tracking errors and misalignments of the sky tracker and camera system will be. Be prepared to spend quite some time trying to get good results!

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An affordable option is to build a "Barn Door Tracker", essentially two hinged plates connected by a threaded rod, with the hinge axis pointing at the north celestial pole, if you change the separation between the plates at the appropriate rate star trails will be cancelled out. The Springfield Telescope Makers have a long list of links to online instructions on their website . Gary Seronick's is a particularly complete motorized version while Noctilove is an example of a simple motorless design (with a moderate focal length lens, a clock and a steady hand, you can can manually drive the Barn Door Tracker).

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Also keep in mind that building a barn door tracker yourself is going to be exciting, you'll spend time calculating at what speed the motor should be turning, find the proper gears, cut the wood. It's a lot of DIY excitement that I enjoyed myself. However you must keep in mind that:

  • Motorizing it is going to cost your min 100$
  • Using a door hinge is practical, but also imprecise, you must align the north pole to less than a degree while your pieces of wood would be misaligned.
  • You'll need to adjust precisely to motor speed to match earth rotation, this involves precise measurement of the distance between your hinge and the screw that drives your barn door tracker.

Build a mechanically tracker will be challenging, but as I wend though I can give you a couple of clues:

  • The hinge must be as wide as it can practically be, this will reduce the angle error of the hinge itself.
  • The screw must be as far as possible so that your motor turns faster
  • It would be helpful to have a mechanical part on the opposite side of the hinge to take the sideways efforts and reduce the angular error of the hinge, otherwise take a 5-6mm screw, something large that can be rigid. The more heavy duty the better your alignment will be. Steppers are noisy, use at least 1/32th stepping driver or use a full sine wave 3 phases brushless motor to avoid vibrations and noise.
  • Using a belt drive reduces the noise: most of the noise coming out of my stepper seems to come from the spinning axle. Noises and vibration are getting transferred to the gears and then to the board where they resonate. Using a driving belt dampens the vibrations from the stepper.
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