# How is precession calculated?

May 8, 2016

Precession can be calculated from the longitudinal shift or time interval between two consecutive equinoxes. At the equinox, the location will be on the line of centers of Earth and Sun.

#### Explanation:

About March 21 (vernal equinox), the noon Sun will be right overhead so that the location is on the line of centers of the Earth and the Sun.

This happens twice every year, about March 21 (vernal equinox) and September 23 (autumnal equinox), at one of the two points where the Earth's equator meets the Earth's orbital plane (ecliptic).

Both longitude and time for this event change a little, every year. By calculating how long it takes to go round the equator once, we approximate the precession period called Great Year = 258 centuries, nearly.

The motion of equinox is in sync with the motion of either pole of the Earth, just about a circle, relative to the center of the Earth. Due to multi-period nodding (nutation) of the polar axis, this path is not a perfect circle., .

My reverse calculations for this Great Year = 25800 years reveals that

Annual change in equinox-longitude = $\frac{2 \pi}{25800} = 0.0002435 r a \mathrm{di} a n = {0.01395}^{o} = 50 ' '$, nearly.

The lateral shift on the equator

= (Earth radius) X (longitude change in radian)

=(6738 km)(0.0002435 radian)=1.641 km