Earths Rotation Period Variation Calculator
Free Earth’s rotation period variation Calculator for geology & geophysics. Enter variables to compute results with formulas and detailed steps.
Reviewed by Daniel Agrici, Founder & Lead Developer
Formula
Future LOD = Current LOD + (Rate x Years / 100)
The length of day (LOD) changes due to multiple geophysical processes. Tidal deceleration adds ~2.3 ms/century. Glacial rebound subtracts ~0.5 ms/century. The cumulative time shift over a period grows quadratically: Shift = 0.5 x Rate x Years^2. Angular velocity omega = 2pi / LOD.
Worked Examples
Example 1: Century-Scale Prediction
Problem:Calculate the length of day and cumulative time shift after 100 years, given tidal deceleration of 2.3 ms/century and glacial rebound effect of -0.5 ms/century.
Solution:Net rate = 2.3 + (-0.5) = 1.8 ms/century\nLOD change = 1.8 ms over 100 years\nFuture LOD = 86400.002 + 0.0018 = 86400.0038 seconds\nCumulative shift = 0.5 x (1.8/100) x 100^2 = 0.5 x 0.018 x 10000\n= 90 ms = 0.09 seconds\nAngular velocity change: negligible but measurable
Result:Future LOD: 86400.003800 s | Cumulative shift: 0.090 s | Rate: 1.80 ms/century
Example 2: Deep Time: 1 Million Years
Problem:Project Earth rotation 1,000,000 years into the future with a net deceleration of 2.0 ms/century.
Solution:Rate per year = 2.0 / 100 = 0.02 ms/year\nLOD change = 0.02 x 1,000,000 = 20,000 ms = 20 seconds\nFuture LOD = 86400 + 20 = 86420 seconds = 24h 0m 20s\nCumulative shift = 0.5 x 0.02 x (1,000,000)^2 = 10^7 seconds\n= ~115.7 days\nFuture days per year: 365.25636 x 86400 / 86420 = 365.17
Result:Day length: 24h 0m 20s | Cumulative shift: ~115.7 days
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy