Your Coordinates

Module 02

Your odometer

PLATE № 02 — PATH LENGTH
SIMPSON INTEGRATION · REAL EPHEMERIDES
EPOCH · —

About this instrument

The Earth spins, orbits the Sun, and rides with the Sun around the galaxy. None of it stops. But there is no single answer to how far you have gone: it depends entirely on what you measure against, and the honest number changes by a factor of a thousand.

Amsterdam, Netherlands

Every one of these numbers is a distance measured against something. Change what you measure against and the answer changes — by a factor of a thousand.

Distance travelled
—
kilometres, and rising as you read

measured against the Sun

This is the largest frame in which every digit is exact. Your rotation and Earth's orbit both come from real ephemerides, so nothing here is assumed. The frames below are just as honest, but two of them rest on a measured constant rather than a computed one.

Earth is not travelling at a constant speed

Earth runs fastest in early January, at its closest to the Sun, and slowest in early July. That is a spread of about a kilometre per second across the year. Your birthday, 15 JUN 1990, is marked.

The same journey, measured differently

Not stages of one trip. Four separate answers to the same question, each complete in itself.

against the centre of the Earthexact
—
speed now 0.000 km/s

Rotation alone. At the equator this is 1,674 km/h; at the poles it is nothing at all. Computed from your latitude, not assumed.

against the Sunexact
—
speed now 0.000 km/s

Your rotation added to Earth's orbit as vectors, not as numbers. At midnight the two work together and you are moving faster than at noon — and Earth itself runs from 29.3 to 30.3 km/s depending on where it is in its ellipse.

against the centre of the galaxymeasured
—
speed now 0.000 km/s

The Sun circles the galactic centre once every 225 million years. Its speed is the least certain number here: published values run from 220 to 250 km/s, and we use 247.

against the microwave backgroundmeasured
—
speed now 0.000 km/s

The closest thing to being still that the universe offers: the frame in which the afterglow of the Big Bang looks the same in every direction. This already includes the galactic orbit — it does not get added on top.

Where the usual figure goes wrong

Most versions of this calculation add the speeds together. Both steps of that are wrong, and here is what it costs.

Adding speeds that point different ways

Walk down the aisle of an aeroplane. You are doing 5 km/h relative to the cabin and the plane is doing 800 relative to the ground — but you are only doing 805 if you walk towards the nose. Walk towards the tail and you are doing 795. Speeds have directions, so they have to be combined as arrows, not as numbers. Right now your spin is partly working against Earth's orbit rather than adding to it.

spin plus orbit, added as numbers
— + — = — km/s
the two combined as arrows
— km/s
overstated by
—

Counting the same motion twice

Your speed against the microwave background already contains the trip around the galaxy — it is the same journey, seen from further out. Adding the two is like adding your speed relative to the plane's cabin to your speed relative to the ground, and calling the result your real speed. The number that comes out describes nothing at all.

against the galactic centre
— km/s
against the microwave background
— km/s
the two added together
— km/s

a number that does not describe anything

The working out

Amsterdam, Netherlands

Why you cannot add up speeds — the reference frames explained →

Values used, and where they come from

Rotation and orbit: computed per instant from astronomy-engine (MIT), not from a fixed figure. Earth's own state vector, and yours from your latitude.

Sun around the galactic centre: 247 km/s. Genuinely uncertain — published values run from 220 to 250 km/s, so treat this figure as good to about ten per cent.

Sun against the microwave background: 369.82 km/s towards galactic longitude 264.021°, latitude 48.253° (Planck 2018 dipole). This is the Sun's motion, not the Local Group's 620 km/s.

Galactic to equatorial conversion checked against the known position of the galactic centre and pole.