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Planets orbit around stars, satellites orbit around planets, even stars orbit each other. So the question is: Why don't galaxies orbit each other in general, as it's rarely observed? Is it considered that 'dark energy' is responsible for this phenomenon?

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There are plenty of satellite galaxies orbiting larger galaxies. The question is how long are you willing to wait for an orbit?

The Milky Way has a mass $M$ of something like $6\times10^{11}$ solar masses, or $10^{42}\ \mathrm{kg}$. The small Magellanic Cloud is at a distance $R$ of $2\times10^5$ light years, or $2\times10^{21}\ \mathrm{m}$. A test mass orbiting a mass $M$ at a separation $R$ will have a period of $$ P = 2\pi \sqrt{\frac{R^3}{GM}} = \text{2 billion years}. $$ Such a system could undergo at most $7$ orbits in the entire history of the universe. The universe isn't old enough for the nearest major galaxy to have completed a single orbit around us at its current separation.

Even if you did wait long enough, galaxies aren't particularly good at holding their shape. If you put them in a situation where gravity is strong enough to bend their path into a closed orbit, odds are they will also be tidally torn apart by that same gravity. And we see this all the time, as for example with the Mice Galaxies:

enter image description here

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    $\begingroup$ Beat me... and you even have a picture AND an equation. $\endgroup$ – DilithiumMatrix Nov 14 '15 at 23:34
  • $\begingroup$ That's a 10^9 "billion" or a 10^12 "billion"? (great picture!) $\endgroup$ – Rolazaro Azeveires Nov 15 '15 at 1:06
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    $\begingroup$ @RolazaroAzeveires: in English, always the smaller one. Some older texts use the "long billion", especially British English, but for all official purposes even the UK switched some time in the 1970s. There are still living humans speaking English and using the long billion, but they are sufficiently rare and they diverge from all official definitions/styles, that for any practical purposes they are just wrong :-) Of course, the fact that the French (and other European language) equivalent of the English "trillion" is "billion" can lead to translation errors! $\endgroup$ – Steve Jessop Nov 15 '15 at 11:22
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    $\begingroup$ @SteveJessop It leads to translation errors all the time - especially when the difference isn't "important" (especially in movies - I lost count of all the movies that try to convince us that the Earth is a thousand times older than the universe). Still, the "European" definition of billion makes a lot more sense, and it's commonly used in scientific english (it's a multiple of million, of course). $\endgroup$ – Luaan Nov 16 '15 at 9:04
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    $\begingroup$ @Luaan You mean it's a power of a million since a thousand million (US billion) is by definition a multiple of a million. $\endgroup$ – CJ Dennis Nov 16 '15 at 12:21
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They do! There's an entire class of galaxy, called a 'satellite galaxy' which is defined entirely based on them orbiting a larger galaxy (which would be called a 'central galaxy'). Our own milky-way is known to have many orbiting satellite galaxies, or at least 'dwarf-galaxies'. If dwarf-galaxies aren't enough, the milky-way itself is gravitationally bound to the andromeda galaxy, and they are effectively orbitting eachother. Because of the tremendous size-scales, however, the orbital period is billions of years --- in many cases, far longer than the age of the universe, so that a pair like the milky-way---andromeda 'local group' actually hasn't completed a single complete-orbit in the history of the universe. That's why we can definitely never (even hope to) see galaxies orbit in real-time.

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  • $\begingroup$ Can we apply Newton's laws to galaxies? "the velocities of stars in galaxies were observed to be larger than expected based on Newtonian mechanics."Source $\endgroup$ – Energizer777 Nov 14 '15 at 23:42
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    $\begingroup$ @Energizer777 yes, absolutely. The problem which motivated MOND has been solved by 'Dark Matter' which, on galactic scales, is well described by Newtonian Gravity. $\endgroup$ – DilithiumMatrix Nov 14 '15 at 23:46
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    $\begingroup$ The dark matter has not been experimentally observed and the MOND model is much younger than the dark matter theory. $\endgroup$ – Energizer777 Nov 15 '15 at 0:02
  • $\begingroup$ @Energizer777 if you want to address MOND, that's fine -- but it should be done in its own question, instead of here. See, however, physics.stackexchange.com/a/5778/8521, physics.stackexchange.com/q/6561, physics.stackexchange.com/q/123661 $\endgroup$ – DilithiumMatrix Nov 15 '15 at 0:44
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    $\begingroup$ @Source: that is exactly what led to the theory of dark matter. We assume Newtonian dynamics holds and use the observed velocities to determine the mass inside (at smaller distance from the galactic center). We discover that the mass inside stars is higher than we can account for by the observed light, hence the theory of dark matter. $\endgroup$ – Ross Millikan Nov 17 '15 at 6:06
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galaxy come in many different sizes: some of the small-er ones do rotate ["orbit"] around the edge of a large galaxy ... one can also visualize galaxy-clusters, in which the entire cluster rotates .....

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