The subject line pretty much says it. Defining the poles is easy; they are given by the axis of the object’s rotation. But one of these poles must be designated the “northern” one, the other the “southern” one. On Earth, this designation is simply based on a convention that goes back thousands of years, but what is it based on on other planets, moons, or asteroids? Is there some kind of rule that assigns these designations to the two poles unambiguously, or did astronomers simply say, at some stage, “For the Moon we’re going to name this pole here the North Pole, and for other objects we’re just going to make something up as we explore them”?
Similarly for east and west. I suppose that, based on the convention we have hear on Earth, the direction that the planet rotates towards would be east, and this definition is also used for extraterrestrial objects. Is that right?
For north there are two different definitions, which do not agree with each other. Both the United States Geological Survey and the International Astronomical Union adopt the policy that any rotational pole that lies north of the Earth’s ecliptic plane is the North pole. This means that for some planets, such as Venus, the direction of rotation is opposite to that of the Earth as seen from their respective north poles. East and west are defined as the right-hand side and left-hand side of a map with north at the top.
Another, and perhaps more sensible convention is that the North Pole can be defined as the pole where the planet or object is observed to rotate in a counterclockwise direction as seen from the pole. That is the definition used for the Earth, and is the convention used in the astronomical display program Celestia. This non-standard (but entirely logical) convention allows the direction of East to be consistently in the direction of sunrise, and maybe we’ll get round to adopting it one day for exoplanets and other objects.
But at present the direction of north is defined by the ecliptic ( which is basically the plane of the Earth’s orbit) and not by the direction of rotation of the object itself.
5 Rotational elements for dwarf planets, minor planets, their satellites, and comets
For planets and satellites, the IAU definition of north pole is the pole that lies above the invariant plane of the Solar System, and the rotation can be either direct or retrograde.
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The choice of a rotational pole for a body in simple rotation with slow precession is straightforward. One can choose the pole that follows either the right-hand rule or the left-hand rule, and the right-hand rule is chosen here. This would be the “positive” pole to avoid confusion with the north-south terminology.
So as eburacum_45 notes, for planets and satellites, north is north of the plane of the Solar System. However, dwarf planets, etc. use the right-hand rule, assuming the body isn’t undergoing some complicated, possibly irregular rotation.
Not quite: Both definitions agree for Venus’ north pole, but the Sun (assuming you can see it through the clouds) still rises in the west on Venus. More precisely, you could say that a distant star rises in the East. Or more precisely yet, a point of defined celestial coordinates rises in the East.
That’s true. And on a tidally locked planet the local star would not rise or set at all (apart from libration effects).
I think we’ll need to adopt the ‘right-hand rule’ for exoplanets at some point in the future, since we won’t want to constantly refer back to the Solar System to find out where ecliptic north is.
Obviously this gets really messy for objects with tumbling motions and far from spherical shapes.
Back to near-spheres with simple rotation:
And last of all, although the OP didn’t mention it …
Once you have poles, the equator of course comes for free so latitude is well-defined from the git-go. But a “prime meridian” must be selected before longitude can be meaningful. And ultimately, just as on Earth, that’s 100% an arbitrary matter of human taste.
Typically the most prominent surface feature is chosen, but on an ice planet or any other planet with an active enough surface that gets difficult. Venus’s prime meridian is based on radar maps of the surface.
The quote defining poles talks about bodies rotating with “slow precession”…
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Obviously there are no fixed “poles”, but the irregular, not-even-close-to-spherical shape could theoretically play into your hand, for example you would know where I meant if I talked about the “pointy end” or the “red spot”.
There’s lots of good information in the link. A bit more past what I quoted:
The choice of a rotational pole for a body in simple rotation with slow precession is straightforward. One can choose the pole that follows either the right-hand rule or the left-hand rule, and the right-hand rule is chosen here. This would be the “positive” pole to avoid confusion with the north-south terminology. Ideally one would like to choose a pole for excited state rotation that reduces to this definition as the rotational energy relaxes to the ground state. For SAM (short-axis mode) rotational states, it is possible to define a body-fixed axis that circulates in a generally complex pattern about the angular momentum vector and this approaches the simple right-hand rule definition as the rotational energy relaxes to the ground state of simple rotation. Presumably the appropriate body-fixed pole is the axis of maximum moment of inertia. However, the definition for a body in a LAM (long-axis mode) rotational state is not so obvious, because there is then complete rotation about the long axis of the body as well as rotation about a short axis. In this case, the pole should be taken as the minimum moment of inertia (the long axis of an ellipsoid) according to the right-hand rule.
In practice, the initial encounter with a small irregular body may not provide enough information to determine the shape, moments of inertia, and rotational dynamics with sufficient accuracy that rotational parameters based on them will stand the test of time. In such cases, the recommended approach to defining rotational parameters and coordinate axes should be based on the same general principles that apply to planets and satellites. If possible, the initial definition of a body-fixed coordinate system should be based on a shape model and estimate of the moments of inertia, with the polar axis chosen as described above. If there is insufficient information to determine the moments of inertia, it may be necessary to define a coordinate system based on the instantaneous axis of rotation at the time of encounter.
So, not only is complex motion a problem, but sometimes you may have to define the pole without sufficient information. You might end up with a pole that has little to do with either the rotational state or the shape of the object.
@DPRK: Nice one. Lots of fun with chaotic motion about the 2nd axis of inertia. See also:
I was trying to remember the name of that two-lobed asteroid or comet NASA did the flyby of a year-ish ago. Or the name of the mission. A sensible notion of geographic coordinates on that mess would be a … mess.
The recent news about the OSIRIS-REx touchdown on Bennu totally pushed those other names out of my brain. Though Bennu isn’t exactly a billiard ball either. More like a 6-sided die or maybe a base-to-base tetrahedron = quasi-regular octahedron.
Huh, I would have thought that it’d be defined as the point closest to Earth.
And yes, that is actually well-defined. Venus’ rotation has a resonance with the Earth, such that whenever the two planets have their closest approach, she always shows us the same face.
I’d speculate that the point of closest approach is difficult to define with enough precision to register everything else to. Whereas once they have a fairly complete radar map of the surface they can pick something obvious and the rest of the registration is easy enough.
Possibly 486958 Arrokoth, which you may remember under its previous name, Ultima Thule
This object seems to be a contact binary asteroid, where two similar-sized objects are nearly, but not quite separate from each other.
I suspect that some modes of tumbling would be so violent that they would periodically split this object up and redistribute the mass into a new shape.
