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When a spacecraft approaches its target (whatever is it a moon or a planet), how do they take photographs about it? Do they take as much as possible, or just in certain situations? What does it depends on?
Also, is it the same during a stay in the atmosphere/on the surface?
When a probe approaches a small body like a comet or asteroid, they only get a chance to take a few high-res pictures, because what they make are mosaics. That means that the pictures are actually stitched together from tens of smaller pictures. After a few of these, the perspective and distance will have changed so much, that they can no longer stitch the images together seamlessly. If they inaccurately estimate the relative position of the object to the spacecraft, they may not get the frame they wanted. So they have to either do the math right, or they have to have instruments on board so the probe can decide what the perfect frame is.
The speed of taking a single images varies wildly. It all depends on how dim the object is and how big the imaging sensor is. If the objects is bright, it takes only a fraction of a second to gather enough photons for a usable image. On the other hand, the Hubble space telescope can take weeks to picture distant galaxies.
The next limit is the transmission speed. The probe has some internal storage, but eventually it will have to phone home to unload the scientific paydirt. If it is close to earth, that can happen as fast as it can take pictures. If it is in outer space, it can take a very long. The Voyager probes transmit signals at only 160 bits per second.
So if a probe flies by an object quickly, or is very far from earth, it needs to be picky.
Orbiting probes have more time for transmission, but here also, pictures are often carefully planned in order to get the most out of the probe's lifetime.
I thought that the HRSC instrument on the Mars Express orbiter scanned the Martian surface continually in a line underneath the orbiter, but I was unable to find a source to back this up. Maybe I misremembered. In any case, it pictured more than 60% of the Martian surface, you can't say it's very selective about what it wants to see.
Rovers like Curiosity have an array of cameras on board. Some take a continuous video stream for navigation, others take mosaic pictures as described above. The picturing time can be anywhere from instantaneous to seconds. Curiosity once took 12 seconds to take a picture of nearby Ceres and Vesta. Pictures like this are "made to order", but Curiosity also carries artificial intelligence to decide if anything in its surroundings is "out of place" and needs investigating.
There is no single answer to this question because there are many variables involved.
Limiting factors.
Several factors come into play when designing a mission.
The orbit of the vehicle.
A flyby mission offers very limited opportunities to observe the target object. For a vehicle in a bound orbit, the opportunities are limited by the vehicle's lifetime. The very different natures of flyby versus bound orbits dictate very different strategies in how a mission is designed and performed.
Communications and onboard storage.
How fast data can be downlinked while communication is enabled, how often and for how long communication is enabled, and storage capacity to save data between downlinks all limit the kind of pictures and number of pictures that can be taken.
How the "camera" works.
Note the quotes. Don't think of a camera as only something that takes a picture comprising N*M pixels in one swell foop. There are a number of other ways to take a "picture".
Some "cameras" take but a single pixel at a time. The scanning radiometers fall into this category. A number of the Earth-observing weather satellites use this technique. A rotating mirror focuses light from a specific angle onto a very narrow field of view sensor, which captures the data as one pixel (or one set of pixels, one per wavelength). The mirror rotates a bit, typically cross-track, and the sensor captures that data. In short order, the sensor will have generated individual pixels that represent a swath of data. It starts over, capturing another swath of data. In the meanwhile, the satellite has moved. The combination of mirror rotating and satellite motion lets the "camera" form a continuous image.
Other cameras collect a row of pixels at one time, typically across-track. This is how the HiRISE camera on the Mars Reconnaissance Orbiter works. It takes an N pixels × 1 pixel snapshot of what's immediately below, waits a bit, and takes another N×1 picture. As is the case with the scanning radiometer approach, this continuous scanning process eventually builds up a nice big image.
Yet other cameras work more or less like a digital camera you can buy off the shelf. They take an N pixels by M pixels snapshot of what's in the field of view, wait some time, and take another. The upside of this approach is that all of the pixels in a single image represent the same point in time. A downside is that it's much harder to stitch images together to form a composite.
