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keisanHigh-precision calculations for everyday life and work

Time Dilation Due to Gravity

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Calculates time dilation due to gravity.
The calculation uses the Schwarzschild solution.
The default values for the input variables are based on Earth’s data.
\(T={\large\frac{T_0}{\sqrt{1-{\large\frac{2GM}{Rc^2}}}}}\\\)
Input Variables
重力物体の半径 R
km
重力物体の質量 M
kg
万有引力定数 G
Object's time T0
Seconds
Observer’s time T  Seconds
Ratio of escape velocity to the speed of light: v/c  %
The stronger the gravitational field, the slower time passes for an object as observed by an observer.

\(\normalsize \hspace{20px} T={\large\frac{T_0}{\sqrt{1-{\large\frac{2GM}{Rc^2}}}}}\ ={\large\frac{T_0}{\sqrt{1-{\large\frac{2gR}{c^2}}}}}\\ \\ \hspace{30px}c=299792.458km/s\)

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