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Hohmann Angular Alignment

The Hohmann transfer orbit is an elliptical orbit used to transfer between two circular orbits of different radii in the same plane. The angular alignment is the bearing needed to make the transfer.

The Hohmann angular alignment is roughly proportional to the sum of 1 plus the ratio of the orbital radii of the inner and outer bodies to the 3/2 power.

Formula

QuantityVariable["α", "Angle"] == Pi*(1 - Sqrt[(1 + QuantityVariable[Subscript["r", "1"], "Length"]/QuantityVariable[Subscript["r", "2"], "Length"])^3]/(2*Sqrt[2]))

symbol description physical quantity
α Hohmann angular alignment "Angle"
r1 orbital radius of inner body "Length"
r2 orbital radius of outer body "Length"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Hohmann Angular Alignment"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Hohmann Angular Alignment"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject["Hohmann Angular Alignment"], {QuantityVariable[ \!\(\*SubscriptBox[\("r"\), \("1"\)]\),"Length"] -> Quantity[1, "AstronomicalUnit"]}]
Out[3]=

Source Metadata

  • Creator:
  • Date: 1925

Publisher Information