How is the tilt of the earth determined mathematically?

1 Answer
Dec 25, 2015

The obliquity, or axial tilt angle, is can be calculated by a power series based on observation.


There is a mathematical formula which can be used to determine the Earth's obliquity. It is #ε = 84381.448 - 46.815T -0.00059T^2 + 0.001813T^3#
Where the angles are in arc seconds #84381.448/3600 = 23.439°# which was the obliquity at the J2000 epoch on 2000-01-01 12:00:00. T is the number of Julian Centuries days since the J2000 epoch, which is the number of days before or after J2000 divided by 36525.

Hence the obliquity is decreasing at a rate of about 46.814 arc seconds every 36525 days.