|MadSci Network: Astronomy|
I've never heard of a single exposure taking 75 days. The longest single exposure of which I'm aware is a VLA observation of the Hubble Deep Field. Fomalont et al. (1997, Astrophysical Journal, vol. 475, page L5) observed the HDF using the VLA for 50 hours. (I think they have continued their observations and are pushing toward 100 hours.)
(Let me digress briefly with an explanation of astronomical imaging. Astronomers do not look through telescopes because the human eye is not a good recording instrument and the human eye has a limited response to light; the human eye cannot see radio, infrared, ultraviolet, X-ray, or gamma-ray light. No matter how long we stare at an object, we always see the same amount of detail. In contrast, astronomical instruments "add up" the light that we receive from distant objects. The result is that the longer an astronomical instrument observes an object, the better the fainter parts of the object can be seen. This technique of adding together images to observe the fainter parts of an object is not so important for a star, since all stars are points of light, but it is important for observing extended objects like galaxies or nebulosities around stars.
Furthermore, most astronomical instruments used today are electronic. The images formed are stored in an electronic format. The result is that one can take images taken at different times and add them together to produce an image that shows even fainter detail. For instance, I'm doing this combining technique for one of the projects on which I'm working. I'm [trying to] combine images taken two years apart so as to produce an image in which fainter objects can be seen.)
Perhaps the documentary you saw was referring to an experiment? It is not unusual for astronomers to observe the same object many times over a long period of time to see how the object changes, like time-lapse photography.
The actual amount of time that an object is observed depends upon the science involved. Scientifically useful images have been made in as short as 30 seconds with the VLA. I'm aware of people using Arecibo for as short as 20 to 40 seconds. I've made scientifically useful images with the VLBA in as short as 15 minutes. The more typical observation with a radio telescope is a few to several hours, though, because most of the radio objects in the sky are extremely faint.
Regarding your comment about the angular resolution of the telescope, the angular resolution does affect the telescope's ability to see things, however, not quite in the way that you describe it. (A quick aside: The angular resolution of a telescope or the human eye is its ability to separate two closely spaced objects. Imagine a friend making a V with her index and middle fingers. If she's standing right next to you, you can tell that she is holding up two fingers. If she's standing at the other end of a football field, your eye's angular resolution is probably not good enough to tell whether she's holding up two fingers or just one.)
For a point source, like a star, a telescope's angular resolution doesn't matter. The only thing that matters is how big the telescope is (its collecting area) so that it can collect as much light as possible. For an extended object, like a galaxy, a telescope's angular resolution becomes closely linked with how long it takes to detect the object. Because the object is extended, there's not as much light coming from each point of it as from a point source with the same total brightness as the extended object. Lower angular resolution telescopes see an extended object as "less extended" (astute readers will have noted that even whether an object can be approximated as a "point" or "extended" source must depend on the telescope's angular resolution). Thus, lower angular resolution telescopes don't need as much observation time to see an extended object as do high angular resolution telescopes.
For reference, various radio telescope facilities:
National Radio Astronomy Observatory, home of the VLA, VLBA, and the Green Bank Telescope
National Astronomy & Ionosphere Center, home of the Arecibo Telescope
Netherlands Foundation for Research in Astronomy/Joint Institute for VLBI in Europe, home of the Westerbork Synthesis Telescope and the European VLBI Network
Australia Telescope National Facility, home of the Australia Telescope, among others
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