Words

38 words, each in a sentence or two, with the chapter that uses it.

action: A total added up along a path: the motion in it minus the pull, summed over the whole trip. Nature's paths make it as small as possible, which is how the figure-eight orbit was proved to exist without solving anything. — The ones that come back around
angular momentum: How much spin a system has, counted around a chosen point. It never changes, which is why three bodies with any spin at all can never all meet at one place. — Ten things that never change
barycentre: The balance point of a group of bodies. For two bodies alone it either sits still or coasts in a straight line forever, whatever the two get up to. — Two is easy
central configuration: An arrangement of bodies that can spin without changing shape. For three bodies there are five: three straight lines and two triangles. — The two ways three rocks can hold a shape
chaos: Nearby starts drifting apart at an exponential rate. Not randomness — the same start always gives the same path — but it puts an expiry date on any prediction. — A hair's difference, and a different sky
conic section: Circle, ellipse, parabola, hyperbola: the shapes you get by slicing a cone, and exactly the shapes a two-body orbit can take. — Two is easy
conserved quantity: Something about a system that never changes as it moves — energy, momentum, spin. Each one found is one unknown removed. Three bodies have ten and, by Bruns' theorem, no more of the usable kind. — Ten things that never change
double precision: The sixteen-or-so digits a computer normally carries. Enough for most work, and in a chaotic triple the error in the last digit grows to swamp the first one. — So you step it
eccentricity: How stretched an orbit is. Zero is a circle, near one is a long cigar, one or more and the body leaves and does not return. — Two is easy
ejection: The usual ending for three bodies thrown together: one leaves for good and the other two are left in a tighter pair. — What usually happens
energy: Motion plus pull, added up. Negative means bound together, positive means the system will come apart. It cannot change, which makes it the audit on any computed orbit. — Ten things that never change
ephemeris: A table of where the bodies will be, at stated times. What astronomers actually want, and what stepping the equations produces. — So you step it
figure-eight orbit: Three equal weights chasing one another around a single figure-eight track, with no overall spin. Found by computer in 1993, proved to exist in 2000. — The ones that come back around
gravitational constant: G, the number that sets how strong gravity is: 6.674 30 × 10⁻¹¹ in metres, kilograms and seconds. The least precisely known of the fundamental constants. — Everything pulls on everything
hierarchical triple: A close pair with a distant third body. The stable way to arrange three bodies, and the arrangement of the Sun, the Earth and the Moon. — What usually happens
Hill sphere: How far a planet's grip reaches before the Sun wins. About 1.5 million km for the Earth; the Moon orbits at a quarter of that. — Two big, one small
homoclinic tangle: The infinitely folded crossing pattern Poincaré found in 1890 and declined to draw. The first sight of chaos in mathematics. — A hair's difference, and a different sky
inverse square: A quantity that falls off as the square of the distance. Twice as far, a quarter as strong. Gravity and light both do it, for the same geometric reason. — Everything pulls on everything
Jacobi constant: The one quantity a light third body cannot change in the rotating frame. It fixes which regions the body is shut out of. — Two big, one small
KAM theorem: Kolmogorov, Arnold and Moser: in a system close to a solvable one, most orbits keep their shape under small disturbances and the rest go chaotic. Named for all three, proved over nine years. — A hair's difference, and a different sky
Kozai–Lidov mechanism: A distant third body tilted more than about 39 degrees trades its tilt for stretch in the inner orbit, cycling it between round and elongated. — What usually happens
Lagrange point: One of five places where a light body can keep station with two heavy ones. L1, L2 and L3 sit on the line through the pair and need correcting; L4 and L5 sit at the triangle corners and hold. — Two big, one small
leapfrog: The stepping method that kicks by half a step, drifts a whole step, then kicks again. Cheap, symplectic, and it does not leak energy. Every animation on this site runs it. — So you step it
Lyapunov time: How long it takes a small error to grow by a factor of about three. The shelf life of a prediction: about five million years for the inner solar system. — A hair's difference, and a different sky
n-body problem: The same question for any number of bodies. Two is solved, three is this site, and a hundred billion is a galaxy — which is oddly easier to describe than three. — What it is not
periodic orbit: A motion that returns to its exact starting positions and speeds and then repeats. Two bodies always do it; three bodies do it only for special starts, of which thousands are now known. — The ones that come back around
perturbation: Treating a hard problem as an easy one plus a small correction. How the Moon's motion was worked out for two centuries, and how a spacecraft's path is planned. — Two big, one small
Poincaré section: Instead of watching the whole path, mark the spot every time it crosses a chosen plane. Order shows up as curves and loops; chaos shows up as a scatter of dots. — A hair's difference, and a different sky
reduced mass: The single weight that makes a two-body problem behave like one body: the product of the two divided by their sum. — Two is easy
regularisation: Changing variables so that a collision, where the equations divide by zero, turns into something a calculation can pass through. Levi-Civita, 1903. — So you step it
restricted three-body problem: The case where the third body is too light to pull back. Two heavy bodies on a known orbit, one speck along for the ride, and enough structure left to draw. — Two big, one small
shape sphere: Throw away a triangle's size and which way it points, and what is left — its shape — is a point on a sphere. Collisions sit on the equator; the equilateral triangles are the poles. — The ones that come back around
singularity: A moment past which a solution stops existing. For three bodies it is always a collision; with five bodies, Xia built one with no collision in it. — Crashes, and the kind of trouble that is not a crash
softening: Adding a small constant under the distance in the equations so a close pass cannot blow up the arithmetic. A deliberate lie, used where the close passes are not the point. — So you step it
symplectic: A property of a stepping method: it preserves the geometry of the equations, so energy wobbles instead of drifting. The reason leapfrog beats the obvious method. — So you step it
Trojan: A body sitting near a planet's L4 or L5 point. Jupiter has over ten thousand catalogued; the Earth has a couple. — Two big, one small
two-body problem: Two bodies under gravity. Solved in closed form: an ellipse or its relatives, repeating forever. The only gravitational case with a napkin answer. — Two is easy
zero-velocity curve: The fence drawn by Jacobi's constant: the boundary of where a light body could go if it stopped. It cannot cross, and the gates open in a fixed order as the constant falls. — Two big, one small