Gravitational Time Dilation

General Relativity · 1907

Equation: Δτ = Δt·√(1 − 2GM/(rc²))
Field: General Relativity
Named After: Albert Einstein
Year: 1907

Symbols

Δτ time ticked by a clock at radius r from mass M · Δt time far away · G gravitational constant · c speed of light · the factor under the root hits zero at the event horizon

Significance

Clocks deeper in gravity run slower — predicted from the equivalence principle years before the full theory existed. Not an abstraction: a GPS satellite's clock gains about 46 microseconds a day on this term alone, loses about 7 to its orbital speed, and the receiver in your pocket is corrected for the net 38. Without it, positions would drift kilometres a day.