Globes around the Sun
The grid that Claudius Ptolemy used to map the earth is a superb instrument. The exact position of any point on the surface can be defined by just two numbers. It has only one arbitrary element: the position of the Prime Meridian. It has only one big drawback: it only works on spheres.
The earth, as most people know, is not quite spherical. A circle drawn around the equator is just about 68 kilometers, or 42 miles, longer than a circle drawn through the poles. Now, the earth is quite a bit larger than that figure, so from a distance it doesn’t seem to matter. Close up, when measuring actual points on the globe, it becomes a bit of a pain.
From a strictly mathematical point of view, it shouldn’t matter; the grid can be applied anyway. The fact that the Earth rotates creates two non-arbitrary points from which your grid can start. Simply draw a line through the earth from its north pole of rotation to its south pole. Find the halfway point between these two poles — the “center of the earth”. Then find the halfway points on all the circles joining the north and south poles on the surface of the planet: this is the Equator. Now, divide each quarter-circle from pole to Equator into ninety degrees and draw a line from the center out to infinity through each degree mark. Where the lines intersect the surface, there are your parallels.
Only if your planet is a little bit out of true, the distances between those parallels are not going to be equal; if the planet is a flattened spheroid, each degree is going to be just a bit larger toward the equator than it is toward the poles. And if you try to make each parallel exactly the same distances apart, they won’t be at the same angles. This is true of the Earth; the length of a degree of latitude varies between 68.7 miles at the equator and 69.4 miles at the poles.
Of course, it’s not just the Earth that’s a spheroid. All of the other planets and a fair number of moons are spheres and spheroids as well. Why are they spherical? The basic answer is gravity. Given enough mass, and sufficient proximity in space, two masses will be attracted to each other. When one object is as big as a planet or moon, the attraction is pretty much one-sided; everything is dominated by the planet or moon’s center of mass. Anything that gets lifted up away from the center — waves, volcanoes, mountains — feels the pull of gravity to go back toward the center again. As gravity pulls equally in all directions from the center, when every atom has fallen as far as it can fall, you get a sphere, all the fallen objects being piled up at an equal distance from the center. Probably most of the spherical shapes were formed early in the history of the Solar System, when the planets were molten; their liquid shapes would naturally form spheres, distorted only by the centrifugal force of their spinning, which would flatten them a bit.
But rigid, non-molten objects may not collapse into spheres. When they are quite small, the pull of gravity can be too weak to counteract their structural integrity. How small?
Of the various natural objects currently circling the Sun, about thirty are known to be spheres or spheroids. The largest tend to be very even and smooth in shape — they do not really have surfaces, only outer gaseous layers whose cloud-tops form their visible outer boundaries. Since they are non-rigid, very massive, and rotating rapidly, these “gas giants” are also quite flattened.
The “oblateness” of a spheroid is measured by dividing the difference between the equatorial radius and the polar radius by the equatorial radius. If there is no difference, then the form is a perfect sphere; if it a positive number, then it is an oblate spheroid, and the larger the number, the flatter it is. Earth’s oblateness is about .0034. Jupiter’s is much greater: .0637. But Saturn, not Jupiter, is the king of oblateness, with a number of .102. If you look at an image of Saturn, you will see that it presents an oval face when viewed from the side; looking down from the poles, however, it is quite round. Uranus and Neptune, being smaller and more dense, are rather less oblate.
Earth is the largest of the rocky planets with a solid exterior. Venus, the next largest, is nearly a perfect sphere. Mars is slightly more oblate than Earth, but not much. Mercury, the next largest planet, is also an almost perfect sphere. Pluto, the smallest planet, has not yet been imaged adequately to make an estimate of its oblateness.
In addition to the planets, there are several planetary moons and at least a handful of asteroids that are large enough to be approximately round. I don’t have oblateness figures for them, but the largest of them are very nearly spherical. These include two that are even slightly larger than Mercury Ganymede, the largest moon of Jupiter, and Titan, Saturn’s biggest moon — though measurements of the latter have to take its very thick atmosphere into account; recent observations by the Cassini spacecraft have shown that the atmosphere actually differs in thickness by latitude. The next largest moons are Callisto, Io, our Moon, Europa, and Triton (the largest moon of Neptune), all of which present a nearly spherical profile, being too small for their rotation to redistribute their mass much.
As we descend in size and mass, however, the chances of a satellite being irregular become larger again; the smallest satellites are just irregular chunks of rock, chipped away by frequent meteor impacts; their mass is not great enough to form them into spheres. Between moons the size of Triton, down to moons the size of Neptune’s second largest satellite, Proteus, there is a liminal zone: moons in this region tend toward sphericity, but they can be deformed by other forces into distorted shapes. Moreover, at their small sizes, surface features often visibly interrupt their shapes, which no longer appear to the observer as neat circles.
Titania, Rhea, and Oberon — the largest of these mid-sized moons — are quite round, but Iapetus, only slightly smaller than Oberon, is not; some unknown trauma far back in its history has severely distorted its shape, flattening it on one side. It is the largest really irregular body in the solar system, not counting the gaseous planets, whose flattening is regular and predictable.
Smaller than Iapetus are Charon, Pluto’s moon, which has not been well-imaged; then Umbriel, Ariel, Dione, and Tethys, all rather similar in size; the larger Kuiper Belt Objects that have been discovered are estimated to be about the same size, but their exact size and shape are unknown.
The next largest object in the solar system is Ceres, the largest asteroid, orbiting between Mars and Jupiter. Images of Ceres are not very precise; it is nearly spherical, but may be slightly irregular. Smaller asteroids like Pallas and Vesta are at best elliptical (Vesta is actually a very squashed spheroid, more so even than Iapetus).
Among the moons, we have the mini-spheres Enceladus, Miranda, and Mimas. Enceladus, for its size, is remarkably round; Miranda, Uranus’ smallest moon, is generally round, but has such variable surface features as to seriously distort it shape. Mimas, the smallest body in the solar system that could be reasonably called round is actually somewhat egg-shaped.
Even larger than Mimas is Neptune’s Proteus, a thoroughly irregularly-shaped moon, with no round lines at all. Below Proteus, shapes are pretty much random, sometimes long and narrow, sometimes oblong, or compact potato-shapes. This includes the immense majority of objects in the solar system — though all together they count for an insignificant portion of its mass.
These facts bear on the question “what is a planet”?, which has especially been asked with regard to the outermost planet, Pluto — which some people would like to reclassify as the largest known Kuiper Belt Object — in effect, a very big asteroid.
It has sometimes been suggested that a planet is a body orbiting the Sun that is “large enough to be round”. But it is evident that the correlation between size and “roundness” is by no means exact, and a substantial body of objects exists in the twilight zone between the clearly spherical or spheroidal, and smaller and definitely irregular objects. A generous definition would require us to include Ceres and several Kuiper Belt Objects as planets. This is not in itself inadmissible — Ceres was considered a planet for many years after its discovery; but reminds us of how arbitrary our classifications are. Each of the nine recognized planets is very different from all the others, and no one definition easily encompasses them, except for this: they are the nine largest bodies orbiting the Sun. Why draw the line at nine, instead of lower or higher? There is no particular reason, but as it has been done, it might as well remain that way. The working definition of a planet might as well be “any body orbiting the Sun which is the size of Pluto or larger.” This tautologously keeps Pluto in the family of planets, but if Pluto is jettisoned, we might as well go on to drop Mercury from the list, or even Mars. But the time we finish, even the Earth might not count as a world.