गुरुत्वीय काल विस्तारण कैलकुलेटर — सूत्र
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.
हल किया गया उदाहरण
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