All celestial bodies I can think of rotate. The sun, the planets, the moon, the galaxies, clusters of galaxies, the supermassive black hole at the center if the Milky Way, accretion discs, etc. It would be very strange if they didn't. They couldn't even exist.
Are there examples of non-rotating bodies? I can find no funamental reason why such an object can't exist. Maybe a planet or two stars that have had a tangential encounter.
As with any claim of possibility, it really comes down to whether we are able to measure it or not. Since we're not talking about quantum mechanics, this is not too difficult to speculate.
All celestial bodies I can think of rotate. The sun, the planets, the moon, the galaxies, clusters of galaxies, the supermassive black hole at the center if the Milky Way, accretion discs, etc. It would be very strange if they didn't. They couldn't even exist.
Indeed! There are lots of reasons to expect any astronomical object in the Universe to be rotating, e.g., because of the angular momentum it will inherit after formation.
Are there examples of non-rotating bodies?
IT is possible that an object is rotating so slowly that is is not possible for us to measure the rotation rate with empirical certainty, and so we may presume that the object is not rotating, and we'd be fine with assuming it is not rotating in our theoretical models of such an object (within that regime). I do not know of such an example, but one can exist in principle.
Here is a list of observed slowly rotating objects, i.e. asteroids and exoplanets. The asteroid with the currently known smallest rotation rate has a period of ~1800 hours, which is about 75 Earth days. As the first figure in that wiki article shows, there is no obvious correlation between diameter and period for exoplanets.
With disk galaxies, it is known that they all, regardless of difference in size, have the approximately same rotation rate.
Long period radio pulsars are rotating slowly compared to other pulsars, with periods of over 5 seconds, and they are very difficult for astronomers to observe. For example, PSR J0250+5854 has the slowest spin period when compared to any known magnetars and X-ray dim isolated neutron stars.
I can find no fundamental reason why such an object can't exist. Maybe a planet or two stars that have had a tangential encounter.
A simple answer (perhaps) is conservation of angular momentum: the progenitor's angular momentum before the object forms is not destroyed.
There are many objects in the universe. By chance, some will happen to have zero angular momentum. It is a meaningful question, because "all motion is relative" applies to linear motion, not acceleration or rotation.
If an object is changing rotation, slowing down and eventually spinning the other way, at some point it will have a rotation of exactly zero.
Very old black holes will shed angular momentum in the Hawking radiation, so they will naturally become non-rotating ... eventually (but not yet).
But there are objects that are very carefully given non-rotating status: scientific instruments. I suspect that Gravity Probe B was non-rotating (the whole thing, not the gyros held within), and an instrument that studies the CMB will point steadily while making an exposure.
I take back the "relative motion" part, slightly: GP-B was not rotating in the sense of there being no centrifugal forces on it, but it measured (very tiny) rotation anyway due to two GR effects. So what you mean by non-rotating can vary. All observers agree that there's no centrifugal forces; that is, no acceleration due to rotation. But it will change orientation relative to the CMB or another such object that's no in a close orbit, anyway, because space is not flat.
Yes, there is one and only one!
The universe itself is not rotating about an axis; it is isotropic, which is actually a stronger property (meaning all degrees of freedom are equal in magnitude). For example, in addition to non-rotation, it is not stretching in one dimension more than another.
If it were to be rotating, the cosmic microwave background measurements would show spiral effects, which are not present.
You asked for an object in the universe. Whether the universe is in the universe, and whether it is an object, I leave up to the philosophers ;-)
Although you mentioned celestial objects, the actual question didn't specificy that the object had to be a celestial object, so please forgive my pedantry in sharing this very cool, fairly recent research with you!
https://www.imperial.ac.uk/news/174667/scientists-confirm-universe-direction/
"Not rotating" is equivalent to "zero angular momentum". In classical mechanics, angular momentum is a continuum, and so the distribution is a continuous probability distribution where, even if zero is the mode, the probability mass for any single value is zero.
In quantum mechanics, eigenvalues of the angular momentum operation are all half-integer multiples of $\hbar$. Since this gives a finite number of possible values, the probability of zero is finite, but the range of possible angular momentum is so huge compared to $\hbar$ that the probability of it being exactly zero is essentially nil for a particular object. For instance, the angular momentum of the Earth about its axis is somewhere around 75 orders of magnitude larger than $\hbar$.
The probability of an angular momentum randomly selected from a range between zero and the earth's angular momentum being zero is similar to the chances of randomly choosing a molecule of air out a room four times and getting the same one each time. In an infinite universe, we can expect some objects to have zero angular momentum, but the observable universe does not have enough planet-sized objects to expect one of them to have zero angular momentum.
If we go to a molecular level, not only is the range of possible values smaller, but the number of molecules available is larger, so at that scale, there are quite a few with zero angular momentum (again, ignoring mixed states).
A nonrotating body would need to have zero angular momentum. Not very little, not SubUltraMicroscopicallyInfinitestimal, but zero.
The chance of finding a celestial body that does not rotate at all, is about the same as finding a yardstick that is exactly one yard long. Not even one planck length more or less.
Would you consider a planet that rotates once every 10 million seconds to be nonrotating? If so, look to Venus. Which, by the way, is the most non-rotating natural celestial solid body I could find.
Nonetheless, it is still rotating.
How about something that (controlled) rotates less than about 5 milli-arcseconds over a year? For that, look to the Kepler Space Telescope. (when it was still in use, and nonrotating only while commanded to do so).
Nonetheless, it was still rotating.
Attaining absolute non-rotation is as difficult as attaining absolute zero temperature. You can get close. Very very close. But it is unreachable.
Because scalar fields (like the one hypothesized to drive most--but not all--versions of cosmic inflation) don't rotate, the idea that the universe (or the local "Universe", in some versions of a multiverse) doesn't rotate has become very popular, but there have been some indications (like a recent sky survey, described at https://arxiv.org/pdf/2101.04068.pdf, by Lior Shamir) to the contrary. However, non-rotating objects must exist instantaneously in some rare gravitational situations, such as rarely perfect collisions of previously-rotating objects of identical mass & volume.
For a version of cosmic inflation that actually requires rotation of each of the local universes in its multiverse, check out Nikodem Poplawski's torsion-based cosmological model, described in many 2010-2021 papers whose preprints can be found by his name on Cornell University's free Arxiv website. It's well-known but not widely-accepted, mainly because its provision of a (tiny) spatial extent for fermions requires Einstein-Cartan Theory, developed by Einstein and the mathematician Cartan in 1929, a few years after the discovery of particulate spin: Although it reduces to General Relativity in vacuum, ECT is more complicated and uses notation still unfamiliar to many physicists. (Also, Poplawski's model implies a multiverse eternal to the past as well as to the future, and such "past eternality" is contrary to creationistic beliefs widely-accepted in the most populous English-speaking country, so that familiarity with ECT is not necessarily an advantage in many of its ecclesiastical and state-run universities.)
