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Kepler's Third Law

Kepler's laws of planetary motion are three scientific laws describing the motion of planets around the Sun. The third law states that the square of the orbital period of a planet is proportional to the cube of the semimajor axis of its orbit.

The orbital period squared increases as the cube of the semimajor axis, and decreases as the reciprocal of the sum of the masses of the orbiting bodies increases.

Formula

QuantityVariable["T", "Period"]^2 == (Quantity[4*Pi^2, "GravitationalConstant"^(-1)]*QuantityVariable["a", "Length"]^3)/(QuantityVariable[Subscript["m", "1"], "Mass"] + QuantityVariable[Subscript["m", "2"], "Mass"])

symbol description physical quantity
T orbital period "Period"
a semi­major axis "Length"
m1 primary mass "Mass"
m2 secondary mass "Mass"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Kepler's Third Law"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Kepler's Third Law"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ResourceObject["Kepler's Third Law"], {QuantityVariable[ \!\(\*SubscriptBox[\("m"\), \("2"\)]\),"Mass"] -> Quantity[5.9742`*^24, "Kilograms"]}]
Out[3]=

Source Metadata

  • Creator:
  • Date: 1619

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