1. I hear the example of a theoretical rocket's acceleration slowing due to a mass gain at high fractions of c all the time, but I think I'm missing something. If a rocket (with its propellant) is moving at such speeds that a significant mass gain would occur, wouldn't it accelerate at the same rate because the propellant has also gained mass in proportion to the rest of the rocket?

I may be interpreting the example wrong, or maybe I'm just mixed up, but this has been bugging me and any help would be much appreciated, thanks.

2.

3. So if the propellant gains mass doesn't it take more energy to accelerate to the same exhaust speed?

4. Originally Posted by Wyatt Happ
I hear the example of a theoretical rocket's acceleration slowing due to a mass gain at high fractions of c
Relativistic mass increase is a misleading concept that has led to much confusion; modern textbooks have thus largely abandoned that notion. It is better to think of the total energy of the rocket, which is a combination of its rest mass and its momentum :

What happens is that as the rocket gains speed, it is only the momentum part that increases, leading to a gain in total energy, thus requiring greater force to accelerate further; the rest mass on the other hand is an invariant quantity, and never changes for any observer. Keeping these notions separate avoids much unnecessary confusion.

5. Originally Posted by Dywyddyr
So if the propellant gains mass doesn't it take more energy to accelerate to the same exhaust speed?
The propellant is the energy, so as the propellant increases so would the energy thus increasing its speed?

6. Originally Posted by The Huntsman
Originally Posted by Dywyddyr
So if the propellant gains mass doesn't it take more energy to accelerate to the same exhaust speed?
The propellant is the energy, so as the propellant increases so would the energy thus increasing its speed?
Combustion of the propellant provides the energy, would "mass increase" while maintaining the same chemical structure provide extra energy?
There isn't more mass, just what there is becomes "heavier".

7. Originally Posted by Dywyddyr
Originally Posted by The Huntsman
Originally Posted by Dywyddyr
So if the propellant gains mass doesn't it take more energy to accelerate to the same exhaust speed?
The propellant is the energy, so as the propellant increases so would the energy thus increasing its speed?
Combustion of the propellant provides the energy, would "mass increase" while maintaining the same chemical structure provide extra energy?
There isn't more mass, just what there is becomes "heavier".
So the actual atoms of this rocket are gaining more mass? Like an oxygen atom suddenly having the mass of gold?

8. Originally Posted by The Huntsman
So the actual atoms of this rocket are gaining more mass? Like an oxygen atom suddenly having the mass of gold?
Not really, that's why I made a point of using quote marks around "mass" and "heavier" etc.
Like Markus pointed out it's not actually an increase in [rest] mass.
But I made my argument the way I did to highlight the error in the basic assumption.

9. Originally Posted by The Huntsman
So the actual atoms of this rocket are gaining more mass? Like an oxygen atom suddenly having the mass of gold?
No, that is exactly the type of fallacy one falls into when speaking about "relativistic mass increase". Mass does not actually increase; the only thing that increases is the total energy of the system as a whole.

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