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Hohmann Total Delta-V

The Hohmann transfer orbit is an elliptical orbit used to transfer between two circular orbits of different radii in the same plane. The total delta-v is the change in velocity needed to enter and exit the elliptical orbit.

The Hohmann total delta-v increases with the square root of the mass of the orbit center. As the radius of the inner and outer orbit increases, the delta-v decreases.

Formula

QuantityVariable[Row[{"Δ", Subscript["v", "total"]}], "Speed"] == Sqrt[(Quantity[1, "GravitationalConstant"]*QuantityVariable["M", "Mass"])/QuantityVariable[Subscript["r", "2"], "Length"]]*(1 - Sqrt[2]*Sqrt[QuantityVariable[Subscript["r", "1"], "Length"]/(QuantityVariable[Subscript["r", "1"], "Length"] + QuantityVariable[Subscript["r", "2"], "Length"])]) + Sqrt[(Quantity[1, "GravitationalConstant"]*QuantityVariable["M", "Mass"])/QuantityVariable[Subscript["r", "1"], "Length"]]*(-1 + Sqrt[2]*Sqrt[QuantityVariable[Subscript["r", "2"], "Length"]/(QuantityVariable[Subscript["r", "1"], "Length"] + QuantityVariable[Subscript["r", "2"], "Length"])])

symbol description physical quantity
Δvtotal Hohmann total Δv "Speed"
M mass of orbit center "Mass"
r2 orbital radius of outer body "Length"
r1 orbital radius of inner body "Length"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Hohmann Total Delta-V"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Hohmann Total Delta-V"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ResourceObject["Hohmann Total Delta-V"], {QuantityVariable[ \!\(\*SubscriptBox[\("r"\), \("1"\)]\),"Length"] -> Quantity[1, "AstronomicalUnit"], QuantityVariable[ \!\(\*SubscriptBox[\("r"\), \("2"\)]\),"Length"] -> Quantity[1.52`, "AstronomicalUnit"]}]
Out[3]=

Source Metadata

  • Creator:
  • Date: 1925

Publisher Information