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### Gravitational Time Dilation Equation and Calculator

Gravitational Time Dilation for Object (GPS Satellite) in Orbit Equation and Calculator

Schwarzachild Factor Calculate Time Dilation.

â€‹According to the Theory of Relativity also heat, pressure and magnetic fields slow time.

dt' = sqrt ( 1 - 2 M G / r c^{2} ) dt

or

dt' = ( 1 - 2 M G / r c^{2} )^{(1/2)} dt

and

dt' = dt / sqrt ( 1 - v^{2} / c^{2} )

Gravitational time dilation is proportional to:

Δ = sqrt ( 1 - 2U )

Where:

U = G M / r c^{2}

Therefore:

Δ = ( 1 - 2 G M / R_{p} c^{2} )^{(1/2)} / ( 1 - 2 G M / R_{o} c^{2} )^{(1/2)}

Δ_{t} = Δ · s

Δ_{t} = Time dilation (difference) between Planet and Orbiting Satellite at specified time duration (sec)

Δ = Time Dilation factor

U = Newtonian gravitational potential in dimensionless form, i.e., divided by the square of the speed of light

c = Speed of light 299792458 m/s

M = Mass of the Earth 5.97219 x 10^{24} kg (or some other planet given in kg)

G = Gravitational constant 6.67408 x 10^{-11} ( m^{2}/ kg / s^{2})

R_{p} = Average radius of the Planet (Mass) 6371000 m

R_{o} = Satellite or Object Orbiting earth or Other Planet/Mass 20180 km

s = Some time duration (seconds) 1 earth day = 86,400 seconds

Contributed by:

Dmitry Vakhtin

Viktor T. Toth

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