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Gravitational Time Dilation Using Gravity

Gravitational time dilation is a form of time dilation, an actual difference of elapsed time between two events as measured by observers situated at varying distances from a gravitating mass. The higher the gravitational potential (the farther the clock is from the source of gravitation), the faster time passes.

The time seen by a stationary observer equals the time in rest frame divided by the square root of 1 minus twice the ratio of the gravitational acceleration times the radius from the center of the massive object to the speed of light squared.

Formula

QuantityVariable["t", "Time"] == QuantityVariable[Subscript["t", "0"], "Time"]/Sqrt[1 + Quantity[-2, "SpeedOfLight"^(-2)]*QuantityVariable["g", "GravitationalAcceleration"]*QuantityVariable["r", "Radius"]]

symbol description physical quantity
t time seen by stationary observer "Time"
g gravitational acceleration "GravitationalAcceleration"
r radius "Radius"
t0 time in rest frame "Time"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Gravitational Time Dilation Using Gravity"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ ResourceObject["Gravitational Time Dilation Using Gravity"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Gravitational Time Dilation Using Gravity"], {QuantityVariable[ "t","Time"] -> Quantity[1, "Seconds"], QuantityVariable["r","Radius"] -> Quantity[12, "Kilometers"], QuantityVariable[ \!\(\*SubscriptBox[\("t"\), \("0"\)]\),"Time"] -> Quantity[1, "Seconds"]}]
Out[3]=

Source Metadata

  • Creator:
  • Date: 1907

Publisher Information