Assuming you are using single mode fiber, the entrance (mode diameter) is small, usually a few microns (extremes can range from 1 to say 30 microns, but 2-8 microns is common for visible SMF).
The only constraint: you have is to get enough light into that small spot. You can do that with a single lens or convex mirror, a microscope, or a telescope, or even by proximity (hold the fiber so very close to a tiny object that enough light reaches the core, works for certain nanoparticle or biological experiments).
Size of target object: So far I can not think of any constraint on the size of the object. Really the question is how bright the object is and how sensitive the instrument is at the other end. If you have a high-dispersion spectrometer, you probably need a lot more light than if you are doing broadband photometry by counting photons with a photomultiplier.
Object is moving: It doesn't matter if the object is moving or fixed, as long as your optical system can move to track it so that the focused image falls on the core of the fiber. That's simply a mechanical and tracking issue not related to the fiber.
The big advantage of using a fiber is now obvious, you can move your telescope, but keep your measurement instrument somewhere else and fixed, and the flexible fiber will guide the light to it.
Further background
The trick is to put a very large telescope between the object and the fiber, and to use a robot to place hundreds or thousands of fibers at the focal plane, each at the exact location of a galaxy or a star you would like to collect. This way you can line up the other ends of the fibers along a single slit of a spectrometer and study the spectra of thousands or even millions of objects over time without having to point the telescope to each object one-at-a-time.
Fibers have some big advantages:
- Multiplicity and configurability (as mentioned above)
- Flexibility (literally) it allows the telescope and the instrument to be mounted separately and not have to be mechanically aligned and stabilized.
- Mechanical stabilization of source for instruments: even if the telescope drifts and the object moves slightly with respect to the entrance of the fiber, the physical location of the fiber exit can remain fixed. So tracking errors don't affect the distribution of intensity within the entrance slit (virtual or real) of the fiber and therefore don't cause instrumental spectral shifts.
above: From the astrophysicist Ángel R. López-Sánchez's enjoyable A 2dF night at the Anglo-Australian Telescope
above:: From AAO's The stellar cluster behind Sirius
above: GIF from the video (with exciting music) A 2dF night at the Anglo-Australian Telescope
And if you like that robot then consider the "magic fingers" at the focal plane of the Dark Energy Spectroscopic Instrument:
DESI’s focal plane is designed to sit high atop the Mayall Telescope and to carry 5,000 robotic positioners, each holding a fiber-optic cable. Each of these fiber-toting robots is automatically positioned to fix on a preset sequence of individual galaxies and quasars so that the fibers can collect their light. The movements of these positioners must be carefully choreographed to avoid bumping into one another. The roundish focal plane, which measures nearly a meter in diameter, consists of 10 pie-shaped wedges that are fit snugly together. Each wedge holds 500 robotic positioners. The focal plane also contains sensors and light sources called field fiducials that help ensure the positioners are in proper alignment.
And also these robotic fibers in Australia's TAIPAN instrument at Siding Spring Observatory in North-Western NSW:
