# rocket equation Definition and Topics - 20 Discussions

The Tsiolkovsky rocket equation, classical rocket equation, or ideal rocket equation is a mathematical equation that 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 can thereby move due to the conservation of momentum.

Δ
v
=

v

e

ln

m

0

m

f

=

I

sp

g

0

ln

m

0

m

f

{\displaystyle \Delta v=v_{\text{e}}\ln {\frac {m_{0}}{m_{f}}}=I_{\text{sp}}g_{0}\ln {\frac {m_{0}}{m_{f}}}}
where:

Δ
v

{\displaystyle \Delta v\ }
is delta-v – the maximum change of velocity of the vehicle (with no external forces acting).

m

0

{\displaystyle m_{0}}
is the initial total mass, including propellant, a.k.a. wet mass.

m

f

{\displaystyle m_{f}}
is the final total mass without propellant, a.k.a. dry mass.

v

e

=

I

sp

g

0

{\displaystyle v_{\text{e}}=I_{\text{sp}}g_{0}}
is the effective exhaust velocity, where:

I

sp

{\displaystyle I_{\text{sp}}}
is the specific impulse in dimension of time.

g

0

{\displaystyle g_{0}}
is standard gravity.

ln

{\displaystyle \ln }
is the natural logarithm function.

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