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The anomalistic year is the time taken for the Earth to complete one revolution with respect to its apsides. The orbit of the Earth is elliptical; the extreme points, called apsides, are the perihelion, where the Earth is closest to the Sun (January 5, 07:48 UT in 2020), and the aphelion, where the Earth is farthest from the Sun (July 4 11:35 UT in 2020). The anomalistic year is usually defined as the time between perihelion passages.
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The anomalistic year is the time span between successive closest approaches to the Sun. This may be calculated in the same manner as the sidereal year, but the mean anomaly is used. and travels in doing so,Jean Meeus, Astronomical Algorithms (Richmond, VA: Willmann-Bell, 1998) 238. The formula by Ramanujan is accurate enough.
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For example, the ancient Egyptians used the heliacal rising of Sirius to predict the flooding of the Nile. A study of temperature records over the past 300 years suggests that the seasonal year is governed by the anomalistic year rather than the tropical year. This suggestion is surprising because the seasons have been thought to be governed by the tilt of the Earth's axis (see Effect of sun angle on climate). The two types of years differ by a mere 4 days over 300 years, so Thompson's result may not be significant.
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However, the result is not unreasonable. The seasons can be considered to be an oscillating system driven by two inputs with slightly different frequencies: the total input of energy from the sun varies with the anomalistic year, while the distribution of this energy between the hemispheres varies with the tropical year. In other physical situations, oscillating systems driven by two similar frequencies can latch onto either one. One point that must be considered is that the oscillation arising from the tilt of the axis is much greater than that arising from the distance of the sun.
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An illustration of what Mars may have looked like during an ice age about 400,000 years ago caused by a large axial tilt As on Earth, the effect of precession causes the north and south celestial poles to move in a very large circle, but on Mars the cycle is 175,000 Earth years rather than 26,000 years as on Earth. As on Earth, there is a second form of precession: the point of perihelion in Mars's orbit changes slowly, causing the anomalistic year to differ from the sidereal year. However, on Mars, this cycle is 83,600 years rather than 112,000 years as on Earth. On both Earth and Mars, these two precessions are in opposite directions, and therefore add, to make the precession cycle between the tropical and anomalistic years 21,000 years on Earth and 56,600 years on Mars.
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