Astronomy & Celestial Mechanics
the sky, computed
Concept

Polar layered deposits — where it appears

Stacks of ice and dust layers kilometres thick at both poles of Mars, laid down over millions of years. Their banding is read as a record of past climate driven by changes in the planet's tilt and orbit.

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

Mars's tilt over fifty million years, and a steadier twin. The obliquity of a Mars-like planet against time over 50 million years, integrated from 25 degrees with its orbital plane wobbling in five secular modes. With Mars's precession constant, 8.26 arcseconds a year, the axis wanders between 1 and 70 degrees, lingering near some values and lurching between them. The same planet precessing 6 times faster — about the Earth's rate, which the Moon's pull makes possible — stays between 23.2 and 30.8 degrees, because its precession is too fast to resonate with any of the orbital-plane frequencies. The orbital perturbations are illustrative, of the size Mars's own are; the chaos is computed from them.

A past that can only be given as odds

Mars's axis is tilted by twenty-five degrees today, and nothing holds it there. Its slow precession falls among the frequencies at which its orbital plane wobbles, the resonances overlap, and the tilt wanders chaotically between nearly zero and sixty degrees. Two calculations that start a hair apart part company within a few tens of millions of years — so Mars's obliquity a billion years ago is not a number anybody will compute. What can be computed is how much of its history the planet spent at each tilt, and that distribution is a prediction the ice at its poles can test.

sky · Obliquity The summer sunshine at Mars's north pole over the last million years. The sunshine reaching Mars's north pole at the summer solstice, relative to its average, over the last 1,000 thousand years (blue), from a forcing built from the main periods of Mars's recent orbit: the tilt varying by about 3.5 degrees in 120,000 years and 1 degree in 99,000, the eccentricity by 0.03 in 95,000 years and 0.02 in 2.4 million, and the perihelion going round the seasons once in 51,000 years. The part due to the tilt alone is dashed. The sunshine swings by a factor of 2.06 between its extremes: the tilt sets a slow swell with a period of 120,000 years, and the precession, whose strength the eccentricity sets, cuts a faster ripple of 51,000 years into it, strongest when the orbit is most eccentric. These two periods, and their ratio of 2.35, are what a record of the sunshine should carry.

Layers that keep the rhythm and lose the dates

Mars's polar caps are stacks of ice and dust laid down while the planet's tilt and orbit changed the summer sunshine, and the question is whether they can be read as a record of that sunshine. They can — for the rhythm. Even when the ice accumulates faster under weak sunshine than under strong, the cycles of the tilt and the precession survive in the depth of the stack in their correct proportion. What does not survive is the date of any one layer.

sky · Obliquity

Named alongside it

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

InsolationObliquityChaotic obliquityEccentricityLyapunov timeMilankovitch cyclesOrbital tuningPeriodogramPrecessionPrecession constantResonance overlapSecular resonance

All concepts