Why isn't a day the same as a spin?

A planet's "day" gets used for two different things: how long it takes to spin around once, and how long until the Sun rises again. Usually those are close enough that nobody notices they're different numbers. On Mercury and Venus, they really aren't.

Watch two clocks pick a planet

Left: the plain spin, measured against the distant stars. Right: the same globe, but sunlight is fixed in place -- watch the marked point cross into the light. That crossing is a sunrise, and it happens once per solar day, not once per spin.

Why they're not the same the classic diagram

The angle in this diagram is exaggerated so it's visible at all -- like the horizon page's curve, the geometry is real but the scale isn't.

Try it yourself an orange and a lamp

Be the planet

Stick a toothpick in an orange (or just hold a ball) to mark "your town," and put a lamp on a table in a dark room to be the Sun. Stand a couple of steps away holding the orange, and spin it once all the way around, marking with your eye some fixed point in the room -- a corner, a picture -- so you know when the spin is really done.

Now take a step

This time, spin the orange once while also stepping sideways around the lamp, the way a planet orbits while it spins. When the orange has turned exactly one full spin (lined up with that same corner or picture again), check the toothpick: it's not pointing at the lamp anymore. You have to keep turning a little further before your town faces the Sun again -- exactly the gap the diagram above is drawing.

The faster you walk around the lamp compared to how fast you spin the orange, the bigger that extra turn gets. Walk a full lap for every spin or two and you've basically built Mercury.

How it works for anyone who wants the formula

Over one full spin (measured against the stars), a planet also sweeps a bit of its orbit -- that stolen time is what the Sun needs to be back in the same spot. The exact relationship:

1 / solar day = 1 / spin − 1 / year

Plug in Mercury's numbers (spin 58.65 days, year 87.97 days) and you get a solar day of 175.9 days -- almost exactly three spins. Venus is the oddity: it spins backwards, and its spin (243.0 days) is even longer than its year (224.7 days), so the same formula gives a solar day of 117 days -- shorter than the spin it came from, because the backwards rotation and the orbit are working together instead of against each other.

Planet Spin (sidereal) Solar day
Mercury58.65 days175.9 days
Venus243.0 days (retrograde)116.8 days (retrograde)
Earth23.93 hours24.00 hours
Mars24.62 hours24.66 hours

For the gas giants the difference is a rounding error -- their years are so enormous compared to their few-hour spins that the "stolen time" per spin is a fraction of a second.

The same trick, one step up

Every number on this page came from picking something to measure against — the distant stars gave one answer for a day, the Sun gave another, and neither is the wrong one. That habit does not stop at days.

Ask whether the Moon goes round the Earth and the same thing happens: from here it plainly does, once a month, and from the Sun it plainly does not — it sweeps a smooth near-circle round the Sun and never once turns back. Does the Moon go round the Earth? →