Editing Specific impulse (section)

===Specific impulse as effective exhaust velocity===
{{Refimprove section|date=August 2019}}
Because of the geocentric factor of ''g''<sub>0</sub> in the equation for specific impulse, many prefer an alternative definition. The specific impulse of a rocket can be defined in terms of thrust per unit mass flow of propellant. This is an equally valid (and in some ways somewhat simpler) way of defining the effectiveness of a rocket propellant. For a rocket, the specific impulse defined in this way is simply the effective exhaust velocity relative to the rocket, ''v''<sub>e</sub>. "In actual rocket nozzles, the exhaust velocity is not really uniform over the entire exit cross section and such velocity profiles are difficult to measure accurately. A uniform axial velocity, ''v''<sub>e</sub>, is assumed for all calculations which employ one-dimensional problem descriptions. This effective exhaust velocity represents an average or mass equivalent velocity at which propellant is being ejected from the rocket vehicle."<ref>{{cite book|author=George P. Sutton & Oscar Biblarz|title=Rocket Propulsion Elements|url=https://books.google.com/books?id=2qehDQAAQBAJ|year=2016|publisher=John Wiley & Sons| isbn=978-1-118-75388-0|page=27}}</ref> The two definitions of specific impulse are proportional to one another, and related to each other by:
<math display="block">v_\text{e} = g_0 \cdot I_\text{sp},</math>
where
*<math>I_\text{sp}</math> is the specific impulse in seconds,
*<math>v_\text{e}</math> is the specific impulse measured in [[metre per second|m/s]], which is the same as the effective exhaust velocity measured in m/s (or ft/s if g is in ft/s<sup>2</sup>),
*<math>g_0</math> is the [[standard gravity]], 9.80665 m/s<sup>2</sup> (in [[United States customary units]] 32.174 ft/s<sup>2</sup>).

This equation is also valid for air-breathing jet engines, but is rarely used in practice.

(Note that different symbols are sometimes used; for example, ''c'' is also sometimes seen for exhaust velocity. While the symbol <math>I_\text{sp}</math> might logically be used for specific impulse in units of (N·s{{sup|3}})/(m·kg); to avoid confusion, it is desirable to reserve this for specific impulse measured in seconds.)

It is related to the [[thrust]], or forward force on the rocket by the equation:<ref>{{cite book|author=Thomas A. Ward | title=Aerospace Propulsion Systems|url=https://books.google.com/books?id=KEPgEgX2BEEC&pg=PA68|year=2010|publisher=John Wiley & Sons |isbn=978-0-470-82497-9|page=68}}</ref>
<math display="block">F_\text{thrust} = v_\text{e} \cdot \dot m,</math>
where <math>\dot m</math> is the propellant mass flow rate, which is the rate of decrease of the vehicle's mass.

A rocket must carry all its propellant with it, so the mass of the unburned propellant must be accelerated along with the rocket itself. Minimizing the mass of propellant required to achieve a given change in velocity is crucial to building effective rockets. The [[Tsiolkovsky rocket equation]] shows that for a rocket with a given empty mass and a given amount of propellant, the total change in [[velocity]] it can accomplish is proportional to the effective exhaust velocity. 

A spacecraft without propulsion follows an orbit determined by its trajectory and any gravitational field. Deviations from the corresponding velocity pattern (these are called [[delta v|Δ''v'']]) are achieved by sending exhaust mass in the direction opposite to that of the desired velocity change.