免费引力时间膨胀计算器
计算引力场中的时间膨胀效应。
Time at Infinity
1.000000000696042 s
Time at Infinity vs Proper Time (at surface)
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).
- 012GM/(rc^2) = 2 * 6.674e-11 * 5.972e24 / (6.371e6 * 8.988e16)
- 02= 7.972e14 / 5.726e23 = 1.392e-9
- 03sqrt(1 - 1.392e-9) = 1 - 6.96e-10
- 04t_far = 1 / (1 - 6.96e-10) = 1 + 6.96e-10 s
- 05Difference: 0.696 ns per second
常见问题
How does this affect GPS?
GPS satellite clocks are in weaker gravity and run about 45 microseconds per day faster. Without correction, GPS positions would drift by about 10 km per day.
What happens at a black hole?
As r approaches the Schwarzschild radius (2GM/c^2), the time dilation becomes infinite. Time appears to stop at the event horizon as seen from outside.
Has gravitational time dilation been measured?
Yes. The Pound-Rebka experiment (1959) measured the gravitational redshift over just 22.5 metres. Modern atomic clocks can detect differences over a height of 1 metre.
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