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“.