# rocket equation

The rocket equation is the fundamental equation of rocketry. First derived by Konstantin Tsiolkovsky in 1895 for straight-line rocket motion with constant exhaust velocity, it is also valid for elliptical trajectories with only initial and final impulses. The rocket equation, which can be obtained from Newton's laws of motion, shows why high effective exhaust velocity has historically been a crucial factor in rocket design: the payload ratio depends strongly upon the effective exhaust velocity. In its simplest form the rocket equation can be written as:

*v* = *v _{e}* ln(

*m*/

_{i}*m*)

_{f}

where *v* is the maximum velocity of the rocket in gravity-free, drag-free
flight, *v _{e}* is the effective exhaust velocity, ln is the
natural logarithm,

*m*is the initial or total rocket mass, and

_{i}*m*is the final or empty rocket mass (

_{f}*m*/

_{i}*m*is the payload ratio).

_{f}