Wikipedia defines thrust as $$T=v\frac{dm}{dt}$$

Is this something fundamental or can this be derived ?

I was not able to find it on the internet so I thought of asking if here .If proof questions are not allowed a link would be very helpful.

Thank you .


1 Answer 1


Thrust ($T$) is the force one receives by "expelling" some mass $dm$.

We start by conservation of momentum for a mass $m$ travelling in one dimension at speed $v$ which expels a smaller mass $dm$ and changes thus its velocity by $dv$. The expelled mass travels at speed $-c$ with respect to the moving mass, so that it has a speed $(-c+v)$ in the observer's frame of reference.

We have $$m v = (m - dm)(v+dv)+dm (-c+v)$$ which becomes

$$m v = mv +mdv -dmv -dmdv -dmc + dm v$$

and simplifies to

$$ 0 = mdv-dmdv -dm c $$ we neglect $dmdv$ as is the product of two small quantities and are left with

$$mdv = c dm$$

we divide everything by $dt$ and get

$$m {dv \over dt} = c {dm \over dt}$$

Finally, using Newton's second law, $$m {dv \over dt}=ma_T=T$$ is a force and indeed it is the force that "accelerated" the mass forward by a quantity $dv$ due to mass expulsion, which is indeed the thrust, so

$$T= c {dm \over dt}$$


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.