Launch Equation Log

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This equation was independently derived by Konstantin Tsiolkovsky towards the end of the 19th century and is widely known under this name and ideal rocket equation.
Conservation of momentum applied to a rocket was first done by Russian visionary and scientist Konstantin Tsiolkovsky in 1903. All our rockets are governed by Tsiolkovsky's rocket equation. The rocket equation contains three variables. Given any two of these, the third becomes cast in stone.
The Tsiolkovsky rocket equation, 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 can thereby move ...
change in rocket momentum = M (u + Du) — M u = M Du. ... change in exhaust momentum = dm (u — v) — dm u = — dm v. ... change in system momentum = M Du — dm v. ... force on the system = (p — p0) A — M g cos (a) ... M Du — dm v = [(p — p0) A — M g cos (a)] DT. ... M Du = [(p — p0) A] DT + dm v. ... M Du = [(p — p0) A + dot v] DT.
The equation relates the delta-v (the maximum change of velocity of the rocket if no other external forces act) to the effective exhaust velocity and the initial and final mass of a rocket, or other reaction engine. ... is delta-v the maximum change of velocity of the vehicle (with no external forces acting).
Rocket motion is based on Newton's third law, which states that for every action there is an equal and opposite reaction. Hot gases are exhausted through a nozzle of the rocket and produce the action force. The reaction force acting in the opposite direction is called the thrust force.
Acceleration = resultant force divided by mass = 4.51 ÷ 0.050 = 90 meters per second squared (90 m/s2). This means that, every second, the speed of the rocket increases by 90 m/s. This is nine times the normal acceleration due to gravity. The same method can be used for a full-sized rocket such as the Space Shuttle.
Velocity (v) is a vector quantity that measures displacement (or change in position, s) over the change in time (t), represented by the equation v = s/t. Speed (or rate, r) is a scalar quantity that measures the distance traveled (d) over the change in time (t), represented by the equation r = d/t.
A model rocket is launched straight upward. The solid fuel propellant pushes the rocket off the ground at an initial velocity of 200 feet per second.
How fast does a rocket have to travel to get into space? This really depends on what you mean by “into space.” If you just want to get into orbit around the Earth, you need to reach speeds of at least 4.9 miles per second, or about 17,600 miles per hour.
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