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Hohmann Transfer Time Using Radii

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 sum of the radii cubed divided by the mass of the obit center.

Formula

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

symbol description physical quantity
tH Hohmann transfer time "Time"
M mass of orbit center "Mass"
r1 orbital radius of inner body "Length"
r2 orbital radius of outer body "Length"

Forms

Examples

Get the resource:

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

Get the formula:

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

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Hohmann Transfer Time Using Radii"], {QuantityVariable[ \!\(\*SubscriptBox[\("t"\), \("H"\)]\),"Time"] -> Quantity[0.5`, "Years"], QuantityVariable[ \!\(\*SubscriptBox[\("r"\), \("2"\)]\),"Length"] -> Quantity[1.52`, "AstronomicalUnit"]}]
Out[3]=

Source Metadata

  • Creator:
  • Date: 1925

Publisher Information