I will derive the ideal rocket’s flight equation differently than what is shown in “Viva Rocketry! Part 1”

Let

– the mass of the propellant

– the mass of the rocket at time

– the speed of the rocket and at time

– the speed of the ejected propellant, relative to the rocket

– the magnitude of ‘s momentum

– the magnitude of rocket’s momentum

For the propellant:

where is the speed of at (see “A Thought Experiment on Velocities”)

By Newton’s second law,

.

For the rocket:

.

By Newton’s third law,

.

Therefore,

That is,

.

It implies

or,

.

Since

,

,

and

we have

,

the ideal rocket’s flight equation obtained before in “Viva Rocketry! Part 1“.

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