Eccentricity of the orbit of the Earth

from 1,000,000 BC to 1,000,000 AD

 According to Meeus (More Mathematical Astronomy Morsels, Chapter 33) Bretagnon published in 1984 an algorithm for the eccentricity e valid for a very long period of time: The time T is expressed in thousands of years from the epoch 1850.0. The sums h and k have 19 terms of coefficients Hi, gi, and βi. This method gives good results from 1,000,000 BC to 1,000,000 AD.

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 Year (-1,000,000 .. 1,000,000): Eccentricity e =

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The Earth's orbital eccentricity changes with a period of about 100,000 years in the range of to 0.06: The mean value of the eccentricity is 0,02674, the present value is 0.01670. The perihelon distance dP for an ellipse of semimajor axis a and eccentricity e is: dP = a*(1 - e) dP / a = 1 - e The amount of solar radiation S received by the Earth ( "insolation") is proportional to the square of the inverse: S ~ (a/dP)2

 Year Eccentricity e Perihelion distance dP/a = 1 - e S ~ a2/dP2 Ratio of radiation S / S2000 Deviation from 2000 2,000 0.01671 0.98329 1.03427 1 +/- 0 % -970,000 0.05767 0.94233 1.12614 1.08883 + 9 % 30,000 0.00231 0.99769 1.00463 0.97134 - 3 %

 Year Eccentricity e Aphelion distance dA/a = 1 + e a2/dA2 Ratio of radiation S / S2000 Deviation from 2000 2,000 0.01671 1.01671 0.96740 1 +/- 0 % -970,000 0.05767 1.05767 0.89392 0.92404 - 8 % 30,000 0.00231 1.00231 0.99540 1.02894 + 3 %

 Perihelion For the minimum value of the eccentricity e the amount of solar radiation received by the Earth (insolation) is 3 % less than at present, and for the maximum value of e the radiation is 9 % greater than at present. Aphelion For the minimum value of the eccentricity e the amount of solar radiation received by the Earth (insolation) is 3 % greater than at present, and for the maximum value of e the radiation is 8 % less. The difference of the insolation at perihelion and at aphelion is 7 % at present, and 17 % for the maximum eccentricity.

(c) 2006-2018 J. Giesen

2019, May 17