Search results
Results from the WOW.Com Content Network
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 ...
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.
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 ...
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 = = =.
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]
The derivation is simple. Force is assumed constant, and a = F/m. The mass decreases as fuel is consumed, so you are integrating 1/m, which is ln(m). Tsiolkovsky did this calculation in 1897, according to his notebooks. DonPMitchell 07:42, 26 August 2006 (UTC) In the Special Relativity paragraph, where is the given formula taken from?
which is the Tsiolkovsky rocket equation. If for example 20% of the launch mass is fuel giving a constant v exh {\displaystyle v_{\text{exh}}} of 2100 m/s (a typical value for a hydrazine thruster) the capacity of the reaction control system is Δ v = 2100 ln ( 1 0.8 ) m/s = 460 m/s . {\displaystyle \Delta {v}=2100\ \ln \left({\frac {1}{0.8 ...