Wolfram Computation Meets Knowledge

Wolfram Formula Repository (Under Development)

Ideal Rocket Equation

The ideal rocket equation describes the motion of vehicles that follow the basic principle of a rocket: a device that can apply acceleration to itself using thrust by expelling part of its mass with high velocity, and can thereby move due to the conservation of momentum.

The final speed equals the initial speed plus the effective exhaust velocity times the natural logarithm of the ratio of the initial mass of the rocket to the final mass.

Formula

QuantityVariable[Subscript["v", "f"], "Speed"] == Log[QuantityVariable[Subscript["m", "i"], "Mass"]/QuantityVariable[Subscript["m", "f"], "Mass"]]*QuantityVariable[Subscript["v", "e"], "Speed"] + QuantityVariable[Subscript["v", "i"], "Speed"]

symbol description physical quantity
vf final speed "Speed"
mf final mass "Mass"
mi initial mass "Mass"
ve effective exhaust velocity "Speed"
vi initial speed "Speed"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Ideal Rocket Equation"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Ideal Rocket Equation"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ResourceObject["Ideal Rocket Equation"], {QuantityVariable[ \!\(\*SubscriptBox[\("m"\), \("i"\)]\),"Mass"] -> Quantity[1000000, "Kilograms"], QuantityVariable[ \!\(\*SubscriptBox[\("v"\), \("i"\)]\),"Speed"] -> Quantity[0, ("Kilometers")/("Seconds")], QuantityVariable[ \!\(\*SubscriptBox[\("v"\), \("e"\)]\),"Speed"] -> Quantity[5, ("Kilometers")/("Seconds")], QuantityVariable[ \!\(\*SubscriptBox[\("m"\), \("f"\)]\),"Mass"] -> Quantity[100000, "Kilograms"]}]
Out[3]=

Source Metadata

  • Creator:
  • Contributor:
  • Date: 1813

Publisher Information