A rocket is a device for trading mass for speed. The generic (i.e., gravitationally neutral) mathematical model of this is the equation p = qlog(m(i)/m(f)), where p is the increase in speed, q is the rate of loss of mass (that is, of mass ejection, assumed to be constant over the time interval in question), m(i) is the initial mass of the device (that is, of the rocket), and m(f) is the final mass of the device (that is, what mass remains after the mass to be ejected has been in fact ejected). This equation was published in 1903 by Konstantin Tsiolkovsky 23 years before Robert H. Goddard’s first liquid-fuel rocket was launched in 1926.

Notice how that fact that the logarithm of unity is zero neatly captures the fact that if no mass is ejected, then there is no increase in speed.

Here is the Wikipedia article on this equation.

keywords: Mathematics, Physics, ideal rocket equation, Tsiolkovsy rocket equation

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