Gravitational Time Dilation
Δt_surface/Δt_far = √(1 − 2GM/Rc²) — clocks run slower deeper in a gravity well.
Time Dilation Results
Time ratio (surface / far away)0.999999999
Time ratio0.9999999993
rs / R (compactness)1.39215e-9
Slower vs. ∞ (μs/day)60.141 μs/day
Slower vs. ∞ (s/year)0.0219665 s/yr
Slower vs. ∞ (ms/year)21.9665 ms/yr
A ratio of 0.9999... means clocks at this location tick slightly slower than clocks infinitely far from all gravity. GPS satellites must correct for both gravitational and velocity time dilation.
Comparison:
| Location | Ratio | μs/day slower |
|---|---|---|
| Earth surface | 0.9999999993 | 60.14 |
| ISS orbit | 0.9999999993 | 56.52 |
| Moon surface | 1 | 2.711 |
| Mars surface | 0.9999999999 | 12.15 |
| Sun surface | 0.999997877 | 183400 |
| Neutron star (ex) | 0.7642994946 | 20360000000 |