Astronomy & Celestial Mechanics
the sky, computed
Concept

Leap-year — where it appears

A calendar year with an extra day inserted so that the calendar's average year matches the tropical year. The rule for which years are leap years is a fractional approximation to the year's length beyond a whole number of days.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

A solar day that runs off to infinity as the spin approaches the orbit. The length of the solar day — sunrise to sunrise — in units of the world's own year, against its sidereal rotation period in the same units, with retrograde spin to the left. A world that spins much faster than it orbits has a solar day barely longer than its rotation, which is the Earth's case: its rotation is a few thousandths of its year, and it sits at the foot of the curve just right of zero, too close to the axis to mark. As the spin slows towards the orbital rate the solar day diverges, because the world turns to follow the Sun: at exactly one rotation per orbit the Sun stands still in its sky and there is no day at all. Mercury, turning three times in two of its years, has a solar day of 2.000 years — 176 Earth days. Venus, turning slowly backwards, has one of 116.8 days, 0.52 of its years, with the Sun rising in the west. The definitions of a day and of a year that the Earth keeps far apart come within a factor of two of each other, or exchange places.

A day longer than the year

On the Earth a day and a year are far apart, so a calendar has only to count one in the other. On a world whose spin is not much faster than its orbit, the solar day runs off towards infinity: Mercury's day lasts two of its years, Venus's sun rises in the west twice a year, and a locked moon has a day set by its planet. Every calendar problem met on the Earth returns, and some of them return inverted.

sky · Calendars Four tropical years, one for each season. How long the Earth takes to return to the same season, measured from each point of its orbit, minus the mean tropical year of 365.24219 days, in seconds, against the season point (the Sun's longitude). The perihelion drifts relative to the equinox, so between two returns of the same season the planet must cover slightly less than a full orbit in true anomaly, and that shortfall takes longest where the planet moves slowest. Measured from the March equinox the year is longer than the mean by 12 seconds; from the June solstice, 50 shorter; from the December solstice, 49 longer. The full range is ±51 seconds. The Gregorian calendar's average year, 365.2425 days (dashed), is 27 seconds longer than the mean and 15 seconds from the year counted from the March equinox, the one it was built to hold.

A year that depends on the season counting it

The tropical year is quoted to eight decimal places, and it is not one number. Counted from the June solstice it is fifty seconds shorter than counted from the December solstice, because the Earth's perihelion moves through the seasons and the planet covers the last of each year's shortfall at whatever speed it happens to be moving there. The Gregorian calendar was fitted to the year counted from the March equinox, which is why its average year is the length it is — and that year is itself drifting. On Mars the spread is fourteen minutes, and a calendar's leap rule can be more precise than the year it is meant to hold.

sky · Calendars

Named alongside it

The objects these essays reach for when they reach for this one.

Continued fractionClimatic precessionEquinoxGregorian calendarLength of dayMarsPerihelionRetrograde rotationSidereal daySolar daySolsticeSpin orbit resonance

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