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Kepler's First Law

Kepler's laws of planetary motion are three scientific laws describing the motion of planets around the Sun. The first law states that the orbit of a planet is an ellipse with the Sun at one of the two foci.

The orbital radius increases as the semimajor axis increases, and varies based on phase and eccentricity of the orbit.

Formula

QuantityVariable["r", "Radius"] == (QuantityVariable["a", "Length"]*(1 - QuantityVariable["e", "Unitless"]^2))/(1 + Cos[QuantityVariable["θ", "Angle"]]*QuantityVariable["e", "Unitless"])

symbol description physical quantity
r radius "Radius"
a semimajor axis "Length"
θ phase "Angle"
e eccentricity "Unitless"

Forms

Examples

Get the resource:

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

Get the formula:

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

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Kepler's First Law"], {QuantityVariable["r","Radius"] -> Quantity[1.49597887`*^8, "Kilometers"], QuantityVariable["a","Length"] -> Quantity[1.49597887`*^8, "Kilometers"]}]
Out[3]=

Source Metadata

  • Creator:
  • Date: 1609

Publisher Information