UV index and UV dose: varying Sun-Earth distance
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UV radiation

UV index
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Varying Sun-Earth distance

Because the Earth follows an elliptic orbit around the Sun, the Sun-Earth distance and this has to be accounted for in the UV index and UV dose calculation. With D_0 the average distance, the correction factor is:
         f(D) = ( D / D_0 ) ^2
This factor is computed with Kepler's first law from the date of the measurement and from the perihelion date and the eccentricity of the Earths orbit for the measurement year (the perihelion is the point in the Earths orbit where it is closest to the Sun).

The latter two are determined from a table of the Earth perihelion data for the years 1901-2100 (the source is discussed below), where the eccentricity is 1 minus the distance at perihelion -- see the two graphs below. The value of f(D) varies between about 1.034 on 3 Jan. and about 0.967 on 3 July.

We assume that the correction factor f(D) has no error, i.e. that the perihelion of the Earths orbit is known very well.

The perihelion date and the eccentricity of the Earths orbit for the measurement year in the period 1901 to 2100 (red) and the average over that period (blue).
[ download figures as PDF ]

Data source

The Earth perihelion data for the years 1900-2100 was found on the website Cococubed - School of Earth and Space Exploration Arizona State University maintained by Francis Timmes. The datafile was published in 2016, downloaded and adapted slightly for the TEMIS UV processing: a file header was added, the day&month string was adapted from "02jan" to "02 jan", and columns with the fractional day and the eccentricity were added (shown in the above graphs) -- download the datafile.

Meanwhile, the data at Cococubed has been updated to include more years; see: perihelion datafile; a link to this files is given at the Cococubed Ephemeris page (search for "perihelion").


last modified: 3 December 2020
data product contact: Jos van Geffen & Michiel van Weele & Ronald van der A
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