Navigation on Haumea

Haumea is one of the solar system's largest dwarf planets, almost as wide as Pluto. It is rapidly spinning, [resulting in a highly irregular shape.](https://en.wikipedia.org/wiki/Haumea#/media/File:Haumea.svg)

Haumea spins once every 3.9 hours, causing it to bulge at the equator, like many objects do--the Earth, Jupiter, Saturn, Uranus, Neptune, and other Kuiper Belt Objects also bulge at the equator and have flattened poles. But Haumea has something extra. Most planets with bulges have an oblate spheroid shape. That means they are just a flattened sphere, all points on the equator have the same radius from the center, but the poles are closer together than the equatorial antipodes. Haumea's a triaxial ellipsoid, meaning all cross sections are ellipses and not circles. Cut the planet along its equator and you get an ellipse. [Picture here](http://mathworld.wolfram.com/images/eps-gif/OblateSpheroid_700.gif)



This gives it the fantastic and rare property of having two sets of geographically significant poles. (This is also true with tidally locked planets and planets which are sideways *prolate* shapes.) The main poles are North/South, the rotational poles. But there's also a West/East pole, collectively referred to as the Long Poles because they are along the long axis of the object and the replace longitude. (You could just use longitude as normal, setting the prime meridian as one of the "poles," but that's not as cool. And some of this applies to tidally locked worlds too--people on a non-magnetic tidally locked planet, for instance, won't use North/South at all, but instead will use Sunwards/Nightwards. Add a magnetic field and you once again get two sets of meaningful poles--and compasses will be discovered after solar navigation.)

This has some interesting implications for navigation. [Figure 1](https://imgur.com/xt2MGpk).

On Earth, when you go west, you can keep going west forever. If you go North, you will eventually encounter the North pole and start going South, before you encounter the South pole and start going north again. The bottom of figure one shows two antipodal observers on an Earthlike planet. They are both looking north, and both agree that west is to the left and east is to the right. On Haumea, with West and East poles, they disagree. The "top" person says west is to his right, the "bottom" person says west is to his left. If you travel west long enough, you'll cross the west pole and start going east, until you cross the east pole and start going west.

I'd like to add a third set of "poles" which are used as reference points, not actual poles for measuring angles from. These are the equidistant points, essentially the point where the West/East hemisphere boundary crosses the North/South hemisphere boundary (the latter is called the equator, usually.) I'll call these Bill and Bob. Bill and Bob are the points on the equator directly between North and South.

To find your position on superHaumea, you need to gather some information. You know what direction the planet is spinning, Spinwise, because you can easily see either the stars or the sun move across the sky within a few seconds or minutes of observing. You can also find your latitude--found during the night by watching for the point in the sky that the stars are pivoting around (or if you know of a pole star or pole pointer asterism), you can measure the altitude of that point and that will be your latitude. You can also know what your apparent gravity is.

Some explanation. On a rapidly spinning planet, two things affect your apparent gravity. Your centrifugal force experienced and your true gravity. At the spinpoles, you are closest to the core of the planet and so you are experiencing the highest true gravity, and the equator you are further from the core and experience a lower true gravity. This is more complicated than just the inverse square law, because the planet will not have all the mass concentrated in the center, it will be internally differentiated, with a heavy core and a less heavy mantle, etc. If it isn't internally differentiated, then the true gravity will be the same over the entire surface. Planets are pretty much always internally differentiated. The centrifugal force is based upon your distance from the axis of rotation, the line going between the north and south poles. This is the radius of the circle, essentially. At the spin-poles, you are being spun around a circle with radius near zero, so the centrifugal acceleration is very low. At the equator of an oblate planet the centrifugal force is the highest. For oblate planets, the apparent gravity is related only to the latitude. For triaxial ellipsoids like our super-haumea, you also have both things varying along the equator, so apparent gravity is lowest at the west/east poles, but can get fairly high at Bill and Bob, and higher still at the Spin Poles.

By using a scale with a known mass on it (not a balance scale, obviously), you can find your apparent gravity at any point on the surface. This tool will be as important as a compass, though more difficult to construct and use. It will include level bubble tubes to ensure the measurement is being taken straight up. Use at sea will be difficult in strong waves, but to be fair, so is taking a latitude measurement. To make use of the measurement, you need either a good mathematician or a map with iso-gravity lines or something similar.

If you know your measured gravity and you know your latitude, you can narrow down to four points on the world that you could possibly be at. There are many possible locations for a given gravity, many for a given latitude, but only four for both. Finding this requires either a slide rule or a good mathematician.

Then you can narrow down to just two of the four points by seeing whether the gravity increases as you go spinwards or decreases as you go spinwards. [Figure 2](https://i.imgur.com/oqXvShx.jpg). Figure two depicts a diagram looking at the North hemisphere of superHaumea, with the four possible points on the surface labelled.

If gravity is increasing as you go spinwards, you know you're going towards Bill or Bob, if it's decreasing as you're going spinwards, you know you're going towards a Long Pole.

Now having narrowed down your position to two points. Say gravity decreases as you're going spinwards. You should now either be going towards the West pole or the North pole. (Take only the points diagonally across from one another on the rectangle created by the four points from earlier.)

Now from here, I'd like to point out that I have absolutely no idea how to differentiated between whether you're on the Bill hemisphere or the Bob hemisphere, near the West pole or the East pole. The only way that could work is if there are naked-eye satellites, either put there artificially or that formed there naturally (I'll come back to that) that you could see only from one side but not the other. This sounds like a problem at first glance, until you compare that to the Earth and other earthlike planets.

On Earth, sailors were getting lost during long deep sea voyages all the time. There was no way of measuring longitude for sure. Some folks suggested that you could try to measure the positions of the galilean moons of Jupiter against a known catalogue of their positions, essentially as a way of keeping time consistently. The answer ended up coming from the invention of good clocks. Subtracting the observed position of the Sun at local noon from the time your clock, calibrated at your home port, allows you to know as precisely as your solar observations and the precision of the timekeeping, what your longitude is relative to your home port. Another solution, which takes a lot of extra time and resources, is to sail to your destination latitude, which is very easy to find, and sail west or east until you reach your destination. This is obviously not ideal if you're trying to get somewhere fast and efficiently, nor if you don't know your current longitude relative to your destination. It is worthless for exploration.

But on superHaumea, you *do know which of the two points you're at*. Unless you've been drifting at sea for months or years and no one has bothered to keep any kind of records of where you've been, and everyone has terrible memory, you will generally know at the very least whether you're on the Bill hemisphere or the Bob hemisphere. (Or West/East hemisphere.) Even if somehow you don't know what hemisphere you're in already, you can still make informed decisions with only two possible points. If your maps tell you that three weeks spinwise will bring you home if you're on the Bill hemisphere, then you can sail spinwise to get either home or at the very least, find out that you're on the Bob hemisphere instead.

**Other, astronomical ways of finding your position**

If the superHaumea is more of a superIo, a large moon in a low orbit around a gas giant, then it will still have a high rotation rate (because of the short orbital period and the fact that it's tidally locked), causing it to be oblate, AND it will definitely have a tidal bulge that creates long poles. In that case, you can measure the altitude of the center of the gas giant to find your eastLatitude, which you can use to find your longitude. This can be done even on mostly spherical tidally locked planets/moons. But you ALSO have the advantage of being able to find your longitude on the far side of the moon, using the above method, and discarding the one of two possible points in which you should be able to see the parent planet. This also works if the planet is a version of rocheworld, two similar mass planets orbiting each other extremely closely, however in that case the curvature of the spheroid will be asymetrical anyway, evidence even if it's cloudy that you're on the near side.

Haumea and similar bodies also have another trick up their sleeve: close satellites. On oblate and spherical worlds, close-in equatorial satellite orbits are stable unless they are interacting with other large bodies like a close-in sun or other moons. For Haumea-shaped triaxial ellipsoid planets, the changing shape of the gravitational field as the planet rotates causes most orbits to be chaotic and unstable. But there are islands of stability in the simple integer ratio orbits, orbits whose periods are simple first-order ratios (denominator-numerator = 1, using integers less than about 9 or so) are stable. This would include 3:2 resonance, which appears to be where Haumea's rings are orbiting, and the 1:1 resonance, which is the same as haumea-syncronous orbit. If a satellite is parked in a 1:1 orbit, then you can tell which hemisphere you're in based upon where the satellite is in its orbit. There may be multiple of these moons, however they will all be roughly over the same hemisphere, because there can only be at most 3 stable natural satellites per orbit. One large satellite, one in the large moon's L4 lagrange point, and one in the large moon's L5 lagrange point. Alternatively you can have two large or small moons in eachother's mutual L4/L5 lagrange point. The lagrange points are all 60 degrees apart, so for 3 satellites there's only 120 degrees between the two most distant.

Very small moons might not gravitationally interact enough to make eachother unstable, but in theory over time they will migrate slowly back and forward and eventually collide or fall into the trojan points. If all of the moons are the same mass, you could fit 7 or more moons equidistant from each other along one orbit, but that situation can not form naturally. And unless you can tell the difference between the moons, it's unhelpful for navigation.

There may be an effective way to tell your longitude based upon satellites in orbits in the other resonances, but I don't know how. Finding latitude based on a geosyncronous satellite works on all planets, but Haumea-shaped worlds are the only ones where you'd be likely to find 1:1 orbits without the satellites being big and/or close enough to tidally lock to the planet--that is, the rotation of superHaumea is not really affected strongly by its 1:1 moons, it's just that 1:1 orbit is one of the only places where moons can be, whereas for oblate and spherical planets you only find moons in 1:1 orbits if the moon made the planet rotate at the same rate that the moon orbits due to a mutual tidal lock.

Now for the fun part. Imagine what sailing on a planet like superHaumea would be like. Strong winds driven by the quick rotation, powerful storms wound up into tiny and numerous weather systems, gravity varying over the surface, perhaps even vast waves near the long poles as gravity can't hold the waves down. Atmospheric pressure varying vastly over the surface as pressure is proportional to air weight, and if the air mass is the same the pressure will change. (Or perhaps the pressure will try to maintain constant, and the air mass over the equator and the long poles will be greater, resulting in super tall diffuse atmospheres over those regions?)  There is no slope as the gravity changes. Being in hydrostatic equilibrium (which the oceans at least DEFINITELY will be) means that even though gravity changes, the surface will always be level (except for the obvious mountains and hills and things). Will the inhabitants sleep for two hours at a time during the night and stay up for two hours of the day? Or will they sleep for two days in a row and wake for two days in a row? Do they sleep related to the day/night cycle at all?

This is all related to a few other interesting things.

* Derelth: my first attempt at building a rapidly spinning planet, now a lot of what I've talked about in that post is found to be incorrect! [Read here](https://www.reddit.com/r/worldbuilding/comments/4a2toe/derelth_the_oblate_planet/). If there's any interest (or maybe if there isn't) I might reinvent Derelth *as* superHaumea, fleshing out the ideas better.
* Mission of Gravity: The 1957 novel by Hal Clement is *THE* book on this kind of spinning planet. Featuring alien sailors navigating their very alien hypermassive oblate homeworld "Mesklin", with 700 G at the poles and only 3 G at the equator, spinning once every 18 minutes. In addition to being one of the *best* pieces of hard science fiction worldbuilding, it's also a thrilling adventure that is well worth your time, go read it! [Amazon](https://www.amazon.com/Heavy-Planet-Classic-Mesklin-Stories/dp/076530368X)
* Whirligig World: The essay written by Hal Clement describing how he built Mesklin, goes into some good detail and has a few lovely insights on what it is to be a hard sci-fi worldbuilder. (Available in *Heavy Planet: The Classic Mesklin Stories*)
* Whirligig World: My Kerbal Space Program planet mod that I've now been developing for over a year, in which you play the spaceflight simulator game KSP, but instead of an earth-like homeworld and solar system, you are in an alien binary star solar system, starting on the super-earth, 28 minute period, airless planet Mesbin. [Find here](https://forum.kerbalspaceprogram.com/index.php?/topic/166563-06-october282018-whirligig-world-planetary-system-an-absurd-homeworld-in-an-alien-solar-system-151145131/)
* Haumea: The third object to be discovered which is now formally recognized as a dwarf planet. The basis for this post. [Wikipedia](https://en.wikipedia.org/wiki/Haumea).

If you have any questions be sure to comment them, I fear that I may not have explained some of what I meant correctly.