Astronomy Answers
Seasons on the Planets

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This page explains how you can calculate when the seasons begin on a planet.

According to the astronomical definition, a new season begins when the planetocentric ecliptic longitude \( λ_\text{Sun} \) of the Sun is a multiple of 90°, like so:

Table 1: Seasons: Names

The "name" is an attempt from me to assign names that do not depend on the hemisphere where you are. The "code" is an even shorter label, useful to keep tables narrow.

For example: if the longitude is equal to 0°, then spring begins in the northern hemisphere and autumn in the southern hemisphere. We can call this moment the ascending equinox.

By rearranging some formulas from the calculation pages about the position of the Sun and the equation of Kepler, we find

\begin{align} ν \| = λ_\text{Sun} - Π + 180° \label{eq:ν} \\ \tan\left( \frac{E}{2} \right) \| = \sqrt{\frac{1 - e}{1 + e}} \tan\left( \frac{ν}{2} \right) \label{eq:E} \\ M \| = E - e \sin E \label{eq:M} \\ t \| = \frac{M - M_0}{M_1} \bmod \frac{360°}{M_1} \label{eq:t} \end{align}

where \( ν \) is the true anomaly of the planet, \( Π \) the planetocentric ecliptic longitude of the perihelion, \( e \) the eccentricity of the orbit, \( M_0 \) the mean anomaly at a fixed moment, \( M_1 \) the rate of change of the mean anomaly, and \( t \) the time since the fixed moment. In equation \ref{eq:M} the angles must be measured in radians. If you want to measure them in degrees instead, then replace \( e \) by \( (e × 180°/π) \) in equation \ref{eq:M}.

The reasonably fixed values are shown in the following table, with all angles measured in degrees and all time periods in Earth days. The fixed moment (for \( M_0 \)) is 12:00 UTC on January 1st, 2000 = JD 2451545. I call those values "reasonably fixed" because they vary slowly with time, because the orbits of the planets themselves slowly change.

If you enter these reasonably fixed values into the formulas, then you can calculate when the seasons begin.

If we do this for all seasons and for all planets, then we find for the first begin of the seasons after the beginning of the year 2000:

Table 2: Seasons: Dates

These timestamps are written in an ISO 8601 format: first the date (year - month - day), then a T, and then the time (hour : minute) on a 24-hour clock. These times are listed in the UTC time zone. The corresponding Julian Day Numbers are:

Table 3: Seasons: JD

We find the following lengths of the seasons (measured in Earth days):

Table 4: Seasons: Lengths

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Last updated: 2021-07-19