# How is the tilt of the earth determined mathematically?

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.