Astrometry 101 - How long of exposure can my image frames be?

There is no hard and fast rule other than long enough to get  reasonable SNR on reference stars and your target. Sets of images can be can be easily aligned (process called image registration) and stacked in a number of ways such as add, median combine, averaging. The goal of astrometry is position measurement, not photometry. With photometry, the higher the SNR, the better the result, with 50 highly desired. But such SNRs are not so practical for faint objects. For astrometry, the SNR of the target should be at least 5. You should be able to detect movement of the target with at least two observations to ensure the target is not a star, if performing comet or asteroid astrometry.

A general rule of thumb for exposure length is the time it takes for the moving object to move one pixel.

To determine this you need to know how fast an object is moving across the sky.

pixel scale  = (206.265) * (pixel size in microns) / (focal length in mm)

If your pixel scale is 2.5 arc sec/pixel and your target is moving at 0.01 arc sec/sec, then you can expose for up to (2.5 arc sec/pixel) / (0.01 arc sec/sec) or 250 seconds for one pixel movement.

Depending on light pollution in your area, your images may be background limited. Light pollution causes the same effect  in your images as you see as the sun comes up in the morning, the sky brightens and stars fade and lose SNR. Bright moonlight causes the same stellar extinction phenomenon as the sky background dominates the stellar light signal ad they disappear.

The large aperture survey telescopes may only expose for 30 seconds in order to reach a certain magnitude desired such as magnitude 21. A smaller aperture scope such as a 0.3 meter or 12 inch scope will be limited by the sky or object movement and pixel scale.

To go for fainter comets and asteroids, you can do a number of things:

• use a focal reducer to get closer to optimal pixel scale.
• stack images
• bin camera pixels to increase effective pixel size
• get a larger aperture scope 

To find how fast an object is moving across the sky, sky motion, you can use a number of resources.

Minor Planet and Comet Ephemeris Service: http://www.cfa.harvard.edu/iau/MPEph/MPEph.html

You can select to display motions as:  "/sec   "/min   "/hr   °/day

You can also select to separate R.A. and Decl. sky motions instead of total sky motion to squeeze a little more exposure time depending on whether RA (or x) or Decl. (or y) is more limiting.

A planetarium program such as TheSky6Pro displays sky motion in the info dialog of solar system bodies including the sun, moon, planets, comets, and minor planets.

JPL has an ephemeris service or HORIZONS Web-Interface: http://ssd.jpl.nasa.gov/horizons.cgi

Generally the closer to earth or sun an object is, the faster its sky motion and brightness.

A faint target can also be moving more quickly and you may need a larger image stack or shorter exposures.

Observing known comets and asteroids makes this decision process easier to predict and plan.

There is the possibility that a new or unknown object may show up in your images, with main belt asteroids being the most likely. By using an average sky motion for these objects, you can limit your exposure times based on that, so that an object will not produce a long streak in an image, but a measurable centroid. The larger aperture scopes have a distinct advantage over smaller scopes here because of their immense light gathering power not limited by object motion but by how deep or faint they want to survey. The general idea is to gather three or more images (or sets of images if stacking)  separated by 10 to 15 minutes each so that any moving objects will readily show up when blinking images or when using software detection. Distant objects such as Pluto, Centaurs, Kuiper Belt Objects (KBOs), or TransNeptunian objects (TNOs) may require time separation of an hour or more to detect them. Large aperture survey telescopes have the advantage of stopping down their focal length and flattening the image field so as to image larger portions of the sky and more efficiently survey the sky.

Reference:

IAU Minor Planet Center Guide to Minor Body Astrometry:

http://www.cfa.harvard.edu//iau/info/Astrometry.html