Ptolemy's Sun

Ptolemy based his theory of the Sun on the work of Hipparchus.

The Earth is in the centre of the Universe and consists of the “spheres” of earth, water, air and fire, as described by Aristotle.

The ecliptic is the reference plane and the vernal equinox ϒ is the reference point. Coordinates are described in terms of degrees longitude (relative to ϒ) and latitude relative to the ecliptic. Latitude is by definition always zero for the Sun.

One year is the time for the Sun to return to the same ecliptic longitude - one tropical year. The sidereal year, return to the same point relative to the stars, is not used because it was believed that the “sphere of fixed stars” rotated round Earth one degree per century. This is to account for what we now call "precession of the equinoxes".

• Ptolemy uses Hipparchus’s estimate of the year which is 6 minutes too long due to measurement errors. The 6m has consequences for the accuracy of all his planetary motion models.

The Sun revolves round the Earth once per year. However, its apparent angular velocity varies. We now know this is due to the eccentricity of Earth’s orbit. This effect can be approximated by having the Sun move at uniform speed round a circle with its centre, D, some distance from the centre of the Earth.

• The circle is known as a deferent circle.
• The centre of the deferent circle is called the eccentric. I it needs to be placed 1/24th of the radius of the deferent circle away from Earth in the the direction of the "longitude of apogee", 65.5°, (λa). This angle was assumed to be fixed but we now know it moves very slowly due to the precession of the Earth’s orbit.

The mean Sun λm☉ shows the longitude the Sun would have if it revolved round Earth at a uniform angular rate.

The animation starts at noon on the 1st day of the month of Thoth in the first year of the reign of Babylonian King Nabonassar, (Feb 26th 747BC).