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A rocket's required mass ratio as a function of effective exhaust velocity ratio. The 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 and can thereby move due to the ...
Once in orbit, a spacecraft may fire rocket engines to make in-plane changes to a different altitude or type of orbit, or to change its orbital plane. These maneuvers require changes in the craft's velocity, and the classical rocket equation is used to calculate the propellant requirements for a given delta-v.
The rocket equation shows that the required amount of propellant dramatically increases with increasing delta-v. Therefore, in modern spacecraft propulsion systems considerable study is put into reducing the total delta-v needed for a given spaceflight, as well as designing spacecraft that are capable of producing larger delta-v.
Because of the exponential nature of the rocket equation the orbital rocket needs to be considerably bigger. Launch to LEO—this not only requires an increase of velocity from 0 to 7.8 km/s, but also typically 1.5–2 km/s for atmospheric drag and gravity drag [citation needed]
The delta-v capacity of a rocket is the theoretical total change in velocity that a rocket can achieve without any external interference (without air drag or gravity or other forces). When v e {\displaystyle v_{e}} is constant, the delta-v that a rocket vehicle can provide can be calculated from the Tsiolkovsky rocket equation : [ 81 ]
Drag coefficients in fluids with Reynolds number approximately 10 4 [1] [2] Shapes are depicted with the same projected frontal area. In fluid dynamics, the drag coefficient (commonly denoted as: , or ) is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water.
Using propulsion, the rocket equation dictates that a large fraction of the spacecraft mass must consist of fuel. This reduces the science payload and/or requires a large and expensive rocket. Provided the target body has an atmosphere, aerobraking can be used to reduce fuel requirements.
This equation can be rewritten in the following equivalent form: = / The fraction on the left-hand side of this equation is the rocket's mass ratio by definition. This equation indicates that a Δv of n {\displaystyle n} times the exhaust velocity requires a mass ratio of e n {\displaystyle e^{n}} .