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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 ...
In the relativistic case, the equation is still valid if is the acceleration in the rocket's reference frame and is the rocket's proper time because at velocity 0 the relationship between force and acceleration is the same as in the classical case. Solving this equation for the ratio of initial mass to final mass gives
Konstantin Tsiolkovsky wrote about using rotation to create an artificial gravity in space in 1903. [1] Herman Potočnik introduced a spinning wheel station with a 30-meter diameter in his Problem der Befahrung des Weltraums (The Problem of Space Travel). He even suggested it be placed in a geostationary orbit. [2]
Rocket mass ratios versus final velocity calculated from the rocket equation. The Tsiolkovsky rocket equation, or ideal rocket equation, can be useful for analysis of maneuvers by vehicles using rocket propulsion. [2] A rocket applies acceleration to itself (a thrust) by expelling part of its mass at high speed
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.
All acceleration requires an exchange of momentum, which can be thought of as the "unit of movement". Momentum is related to mass and velocity, as given by the formula P = mv, where P is the momentum, m the mass, and v the velocity. The velocity of a body is easily changeable, but in most cases the mass is not, which makes it important.
where the quantities in these equations are: is the velocity > is the flight path angle is the altitude; is the atmospheric density; is the ballistic coefficient; is the gravitational acceleration
Classical mechanics utilises many equations—as well as other mathematical concepts—which relate various physical quantities to one another. These include differential equations, manifolds, Lie groups, and ergodic theory. [4] This article gives a summary of the most important of these.