The sky, computed.
Nothing in this subject can be picked up, weighed, or visited. Every number in it was inferred — from an angle, a brightness, or something that repeats — and the inference is nearly always geometric. This is a collection of essays about how that is done, one idea at a time, illustrated to the point where the argument becomes visible.
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19 essays
The orbit is an ellipse, and the Sun is not in the middle of it
Kepler's first law is usually drawn wrong. The interesting content is not the ellipse — it is the focus, and the fact that one of the two is empty.
OrbitsEqual areas in equal times, which is angular momentum in disguise
Kepler's second law is a statement about the area a radius line sweeps. It looks like an odd thing to have noticed, and it turns out to be a conservation law arriving eighty years early.
OrbitsThe law that links period to size, and weighs everything
Kepler found that the square of the period goes as the cube of the orbit. Newton found the constant of proportionality, and that constant is a mass — which is how every mass in astronomy has been obtained since.
OrbitsEvery orbit one force allows, and the number that picks between them
Circle, ellipse, parabola, hyperbola. A single inverse-square force permits exactly these four, and one number decides which — including whether the body ever comes back.
GravitationNeither body is still, and the wobble is how planets are found
A planet does not orbit its star. Both orbit a point between them, and the star's share of that motion is small, measurable, and the reason thousands of planets are known.
GravitationThe tide is a difference, which is why there are two of them
The Moon pulls the ocean toward it. That explains one bulge. The second one, on the far side, is the whole of the physics — and it comes from subtracting.
GravitationFive places that keep station, in a problem with no solution
Three bodies under gravity cannot be solved. Restrict the problem slightly and five exact answers fall out anyway — three of them roots of a quintic, two of them perfect equilateral triangles.
The observed skyThe sphere that is not there, and why it is still the right model
The stars are at wildly different distances and the celestial sphere is a fiction. It is also the most useful fiction in observational astronomy, because for pointing at things, distance is exactly the information to throw away.
The observed skyThe Sun's path, and the tilt that makes the seasons
Summer is not when the Earth is closest to the Sun — that happens in January. It is when the Sun climbs higher and stays up longer, and both come from a 23.4° tilt.
The observed skyPhases are not shadows, and eclipses are
Half the Moon is lit at every instant of every month. The phase is which part of the lit half faces the Earth — and confusing that with a shadow is the commonest error in astronomy.
StarlightThe triangle that reaches the stars, and stops
Parallax is the only distance measurement in astronomy that assumes nothing. It is also the only one with a hard ceiling, and everything beyond that ceiling rests on it.
StarlightA scale that runs backwards, multiplies, and works
Brighter stars have smaller magnitudes, and five steps is a factor of a hundred. A scale invented by eye in the second century BC turned out to be logarithmic, because eyes are.
StarlightColour is a thermometer, and it reads across the galaxy
A star's colour gives its surface temperature, from two brightness measurements and no other information. It is the cheapest useful measurement in astronomy.
StarsThe diagram that sorted the stars, by plotting two things against each other
Plot brightness against colour for a few thousand stars and they do not scatter. They fall on a narrow band with two islands off it, and explaining that structure is most of stellar astronomy.
StarsMass decides everything, by a power of three and a half
Two stars of the same mass are almost the same star. Double the mass and the output multiplies by eleven — which is why a modest range of masses produces a colossal range of stars.
StarsWhy the biggest stars die first, and take the galaxy with them
A star thirty times the Sun's mass has thirty times the fuel and burns it forty thousand times faster. It lasts a few million years, and everything heavier than iron exists because of it.
SpaceflightThe cheapest way between two orbits, and why it is so slow
Two burns and a long coast is the least fuel that will move a spacecraft between two circular orbits. It is also, for anything beyond the Moon, an unreasonably long wait.
SpaceflightThe speed that does not come back, and the √2 that separates it
Escape speed is exactly the square root of two times circular speed, at every distance from every body. Being in orbit is already 71% of the way to leaving.
SpaceflightStealing speed from a planet, which does not notice
A flyby cannot change a spacecraft's speed relative to the planet. It changes its direction — and adding the planet's own motion back turns that into free velocity.
Threads running through
themes, not chapters
Everything is a conic
One force law, four curves, and the discovery that a comet and a planet differ only in how fast they were going.
Measuring the unreachable
Nothing in this subject can be picked up, weighed or visited. Every number in it was inferred from an angle or a brightness.
Two bodies, and no more
The two-body problem is solved exactly and the three-body problem is not solved at all. Almost everything since has been about living with that.
The sky as a clock
Periods that repeat to the second, used to build calendars, find longitude, and detect planets nobody can see.
Light is the only messenger
One thin stream of photons carries distance, temperature, composition, motion and age — and everything visible is already old.
Small perturbations, large consequences
The corrections that were supposed to be negligible: Neptune found in the residuals, Mercury's extra arcseconds, and orbits that are stable only for a while.
Scales that defeat intuition
Distances, times and densities so far outside experience that the only reliable instrument is arithmetic.