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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 ...
Snap, [6] or jounce, [2] is the fourth derivative of the position vector with respect to time, or the rate of change of the jerk with respect to time. [4] Equivalently, it is the second derivative of acceleration or the third derivative of velocity, and is defined by any of the following equivalent expressions: = ȷ = = =.
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.
Figure 1: Approximation of a finite thrust maneuver with an impulsive change in velocity. An impulsive maneuver is the mathematical model of a maneuver as an instantaneous change in the spacecraft's velocity (magnitude and/or direction) [3] as illustrated in figure 1. It is the limit case of a burn to generate a particular amount of delta-v, as ...
A variety of other rocket propulsion methods, such as ion thrusters, give much higher specific impulse but with much lower thrust; for example the Hall-effect thruster on the SMART-1 satellite has a specific impulse of 1,640 s (16.1 km/s) but a maximum thrust of only 68 mN (0.015 lbf). [45]
Tsiolkovsky calculated, using the Tsiolkovsky equation, [16]: 1 that the horizontal speed required for a minimal orbit around the Earth is 8,000 m/s (5 miles per second) and that this could be achieved by means of a multistage rocket fueled by liquid oxygen and liquid hydrogen. In the article "Exploration of Outer Space by Means of Rocket ...
At 30% c, the difference between relativistic mass and rest mass is only about 5%, while at 50% it is 15%, (at 0.75c the difference is over 50%); so above such speeds special relativity is needed to accurately describe motion, while below this range Newtonian physics and the Tsiolkovsky rocket equation usually give sufficient accuracy.
A space vehicle's flight is determined by application of Newton's second law of motion: =, where F is the vector sum of all forces exerted on the vehicle, m is its current mass, and a is the acceleration vector, the instantaneous rate of change of velocity (v), which in turn is the instantaneous rate of change of displacement.