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Hohmann Transfer Time Using Semimajor Axis

The Hohmann transfer orbit is an elliptical orbit used to transfer between two circular orbits of different radii in the same plane. The transfer time is the time it takes to complete the transit along the orbit.

The Hohmann transfer time is proportional to the square root of the semimajor axis cubed divided by the mass of the obit center.

Formula

QuantityVariable[Subscript["t", "H"], "Time"] == (Pi*Sqrt[(Quantity[1, "GravitationalConstant"^(-1)]*QuantityVariable[Subscript["a", "H"], "Length"]^3)/QuantityVariable["M", "Mass"]])/(2*Sqrt[2])

symbol description physical quantity
tH Hohmann transfer time "Time"
M mass of orbit center "Mass"
aH semimajor axis of Hohmann transfer orbit "Length"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Hohmann Transfer Time Using Semimajor Axis"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ ResourceObject["Hohmann Transfer Time Using Semimajor Axis"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Hohmann Transfer Time Using Semimajor Axis"], {QuantityVariable[ \!\(\*SubscriptBox[\("t"\), \("H"\)]\),"Time"] -> Quantity[0.5`, "Years"], QuantityVariable[ \!\(\*SubscriptBox[\("a"\), \("H"\)]\),"Length"] -> Quantity[0.76`, "AstronomicalUnit"]}]
Out[3]=

Source Metadata

  • Creator:
  • Date: 1925

Publisher Information