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Time of flight (ToF) is the measurement of the time taken by an object, particle or wave (be it acoustic, electromagnetic, etc.) to travel a distance through a medium. This information can then be used to measure velocity or path length, or as a way to learn about the particle or medium's properties (such as composition or flow rate).
The equation = + (+) = is of the form + + =, and such an equation can be transformed into an equation solvable by the function (see an example of such a transformation here). Some algebra shows that the total time of flight, in closed form, is given as [ 10 ]
but t = T = time of flight = The first solution corresponds to when the projectile is first launched. The second solution is the useful one for determining the range of the projectile. Plugging this value for (t) into the horizontal equation yields
Compute the time-of-flight from the eccentric anomaly Finding the eccentric anomaly at a given time ( the inverse problem ) is more difficult. Kepler's equation is transcendental in E {\displaystyle E} , meaning it cannot be solved for E {\displaystyle E} algebraically .
The velocity of the charged particle after acceleration will not change since it moves in a field-free time-of-flight tube. The velocity of the particle can be determined in a time-of-flight tube since the length of the path (d) of the flight of the ion is known and the time of the flight of the ion (t) can be measured using a transient digitizer or time to digital converter.
Time of flight - this measures the time taken for a light pulse to travel to the target and back. With the speed of light known, and an accurate measurement of the time taken, the distance can be calculated. Many pulses are fired sequentially and the average response is most commonly used.
A trajectory or flight path is the path that an object with mass in motion follows through space as a function of time. In classical mechanics , a trajectory is defined by Hamiltonian mechanics via canonical coordinates ; hence, a complete trajectory is defined by position and momentum , simultaneously.
The time of flight is related to other variables by Lambert's theorem, which states: The transfer time of a body moving between two points on a conic trajectory is a function only of the sum of the distances of the two points from the origin of the force, the linear distance between the points, and the semimajor axis of the conic.