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Sun-Earth Distance

 You may use the keys y, m, d, h to increase the year, month, day, or hour, or shift key and y, m, d, h to decrease the year, month, day, or hour. Click into the applet area first ! Click the applet area first. Then: enter decimal degree values for Latitude (southern negative) into the text field of the applet, enter decimal degree values for Longitude (western negative) into the text field of the applet, then press the button "Apply input" Latitude 51.51, Longitude 13.41 is Berlin/Germany. Select from the "Details" menu to get a data table or different diagrams.

The applet is computing the apparent distance of the Earth from the Sun (kilometers and Astronomical Units) using the 409 most important of 997 terms of the VSOP87 planetary theory. In 1850 to 2050, the mean absolute error of the Sun-Earth distance
, compared with MICA, is 1.9·10-7 AU = 28 km, using the conversion 1 AU = 149,597,870 km (details below).
The times of perihelion and aphelion are accurate within about 0.5 hour, and the right ascension and the declination (using fewer terms) are accurate within about 1''.

Select "Anomalistic" from the "Details" menu:

The anomalistic period of the Earth is the time that elapses between two passages at its perihelion. There are large deviations of the interval between perihelion passages (anomalistic period), caused by the Moon deforming the path of the Earth's center (Meeus).

more details below

Select "Data Table" from the "Details" menu:

Perihelion 2011 occurs on Jan 3 at 19 UT (0.9833412 AU).

Geocentric perihelion distance 2010 - 2026
computed by MICA (Multiyear Interactive Computer Almanac by US Naval Observatory)

 2010 - 2026 Distance / AU Distance / km Mean 0.983,299,155 147.099,459 Minimum 0.983,243,565 147,091,143 Maximum 0.983,341,273 147,105,760 Max. - Min. 0,000,097,708 14,617 (Max-Min)/Mean 0.010 % Stand. Dev. 0.000,026,692 3.993 Stand. Dev. 0.0029 %

The small perihelion distance of the Earth in 2020 and 2021 is due to the conjunctions of Jupiter with the Sun (2019 Dec 27, 2021 Jan 29).

Perihelion occurs between Jan 2  and Jan 05 (mean date is Jan 4.0):

 2010 - 2026 Anomalistic Year / days Mean 365.294 Minimum 363.167 Maximum 367.625 Max. - Min. 4.458 (Max-Min)/Mean 1.22 % Stand. Dev. 1.636 Stand. Dev. 0.45 %

The ecliptical longitude of the perihelion is advancing by about 3.3° from 1900 to 2100, making one complete cycle in 22,000 to 26,000 years
:

 2000 - 2050 excentricity Mean 0.0166988 Minimum 0.0166584 Maximum 0.0167521 Max. - Min. 0.000094 (Max-Min)/Mean 0.56 % Stand. Dev. 0.000021 Stand. Dev. 0.13 %

The eccentricity of the Earth's orbit 1900 - 2100 according to Meeus (Astronomical Algorithms, Willmann-Bell) is decreasing by 0.000,042 per century (0.0167,086 in 2000).

In 29,450 there will be a minimum of 0.002281:

More details about long-period variation of the Earth's eccentricity

Select "Difference" from the "Details" menu:
Showing the second differences
dn of daily distances rn:
dn = (rn+1 - rn) - (
rn - rn-1) = rn+1 - 2rn + rn-1
which is an approximation of the second derivative of the r(t) function. It is about zero near the equinoxes where the orbit is almost circular (dn=0).

The local minima of dn occur at (near) New Moon.

Select "Orbit" from the "Details" menu:

An eccenticity of 0.0167 and a radius of 380 pix yields a difference between perihelion and aphelion distance of 12 pix.

Marks for the date of the month:

This checkboxes is showing the magnified radius (magenta),
concentric gray circles at 0.995 AU, 1 AU, and 1.005 AU

The local radius (cyan) is computed from 3 adjacent points Pn-1, Pn, Pn+1, using rectangular coordinates computed from the radius r and the ecliptical longitude L.
Cyclic variations is due to the Eart's moon. Local minima occur at new moon.

VSOP Theory

VSOP 87D: heliocentric ecliptic spherical coordinates for the equinox of the day
The VSOP theorie is computing the Sun-Earth distance R from the Julian Day JD by the sum of series R0, R1, R2, R3, and R4:

The coefficients Ai of R0 (526 terms) behave like this (in units of AU):

Mean absolute error of R (in units of AU), 1900-2050:

Above: mean error (12 positions per year), and standard deviation:
(1.87 ± 0.80)·10-7 AU, or (28
± 12) km

Perihelion of the Earth:

There are large deviations of the interval between perihelion passages of the Earth (anomalistic period), caused by the Moon deforming the path of the Earth's center with respect to a rigorously elliptical orbit [mean perihelion] (Meeus).

The last time of perihelion in December was in 1898, on December 31 at 21 UT.

The date of the mean perihelion, computed by Meeus' algorithm (Meeus), is increasing by about 1.6 days per century, from December 26-28 near 1600 to January 10-13 near the year 2500.

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Visit my page: The Moon: orbit and phases

 Web Links Geocentric Positions of Major Solar System Objects and Bright Stars (USNO Data Services) VSOP (Wikipedia) Multi-Language VSOP87 Source Code Generator Tool Software MICA, Multiyear Interactive Computer Almanac (1780-2050); US Naval Observatory; Version 2.2.2 Books Meeus, Jean: Mathematical Astronomy Morsels; Willmann-Bell, Richmond, Virginia; Chapter 27: On the passages of Earth in perihelion. Meeus, Jean: Astronomical Algorithms; Willmann-Bell, Richmond, Virginia; Chapter 37: Planets in Perihelion and Aphelion.