I Is the classical ideal rocket thrust equation correct?

[ObeseKangaroo]

TL;DR Summary

Is classical ideal rocket thrust equation correct?

Hello!
I have recently found this fascinating article: https://zenodo.org/record/3596173#.YJ1ttV0o99B
The author claims that classical equation for rocket thrust in incorrect because F is not equal to ma for a changing mass.
Neither my professors nor me can see any errors.
Do you think this article is correct?

 

[ObeseKangaroo]

I realize that if we move into the frame which has speed υ, the same speed as the rocket has in this very moment, F would in fact equal ma. But what about other frames? The force should be invariant when it comes to inertial reference frames.

 

[vanhees71]

How can a self-contradictory paper be correct? The usual rocket equation is correct, and you have to take into account the full momentum balance of the body of the rocket and (!) the exhausted fuel (per unit time). Look at the moment $t$.
$$\mathrm{d} p = \mathrm{d} t F = \mathrm{d} (m v) - \mathrm{d} t \dot{m} (v-v_{\text{rel}}),$$
where $F$ is the total force on the rocket (body of the rocket + the fuel still contained in it=total mass $m=m(t)$ at time $t$). The first term is the change of the rocket's momentum during time increment $\mathrm{d} t$ and the 2nd term is the momentum transported away from the fuel, where $v_{\text{rel}}$ is the exhausted fuel's speed relative to the rocket. So finally you have
$$m \dot{v} + \dot{m} v_{\text{rel}}=F.$$
Close to Earth you can set $F=-m g$.

The solution of this linear equation is found by first solving for the homogeneous equation,
$$m \dot{v}+\dot{m} v_{\text{rel}}=0.$$
For $v_{\text{rel}}=\text{const}$ the solution can be written, independently of the specific time dependence of $m$:
$$\dot{v} =-v_{\text{rel}} \ln (m/m_0) \; \Rightarrow \; v=v_0 + \ln(m_0/m),$$
where $v_0$ is the velocity of the rocket at $t=0$ (with total mass of body + fuel $m_0$).

For the solution of the equation including the gravitational force of the Earth you finally get
$$v(t)=v_0-g t + \ln \left (\frac{m_0}{m} \right).$$

 

[Drakkith]

On mobile, so forgive my short post.

The paper seems to be dependent entirely on the supposed fact that people aren't taking the changing mass of the rocket into account. Which is absurd.

Equation 2 on page one is: -vrel*dm/dt=ma
Which is just f=ma, obviously.
The claim is that since the mass term on the right is changing over time this isn't Newton's 2nd law on the rocket. Which is ridiculous. The author simply doesn't understand that this equation is true at any instantaneous moment.

Further into the paper the author claims that thrust eventually reaches zero and then goes negative, decelerating the rocket. Yet the author also appears to agree that rockets in real life work correctly, so I have no idea how they think the thrust could become negative and also think rockets actually work.

A conundrum of unexplained contradictions.