# Time Dilation On An Angularly Accelerating Earth

**Classical Mechanics**Level 5

Alice is in a satellite orbiting the Earth in a circular equatorial orbit with a precise atomic clock.

Bob sat in his house with his precise atomic clock.

Charles is sat at infinity and measures the period of the rotation of the Earth to be precisely 86400 seconds.

Originally Alice measures 30 microseconds more than Bob every time Bob measures 24 hours.

If Charles was to decrease the period of the rotation of the Earth about its axis by 1 second per year, how many years would Charles measure until Alice measured more than 1 second more than Bob every time Bob measured 24 hours?