引力时间膨胀计算器 — 公式
Gravitational Time Dilation
General relativity predicts that clocks run slower in stronger gravitational fields.
Formula
t_far = t_near / sqrt(1 - 2GM / (rc^2))
where the Schwarzschild factor 2GM/(rc^2) is the ratio of the Schwarzschild radius to r.
On Earth's surface, clocks run about 0.7 nanoseconds per second slower than clocks far from any gravity.
计算示例
On Earth's surface (M = 5.972e24 kg, r = 6.371e6 m).
- 2GM/(rc^2) = 2 * 6.674e-11 * 5.972e24 / (6.371e6 * 8.988e16)
- = 7.972e14 / 5.726e23 = 1.392e-9
- sqrt(1 - 1.392e-9) = 1 - 6.96e-10
- t_far = 1 / (1 - 6.96e-10) = 1 + 6.96e-10 s
- Difference: 0.696 ns per second