How do I calculate top velocity for a constant mass rocket in a vacuum?

[JacksonMarks]

I'm programming a simple physics engine that works with rockets in space. I haven't done any physics since high school and I'm embarrassingly lost on how to proceed.

What I have is a constant mass (say 50,000kg for example), and a constant thrust (75,000N for example) on the mass. The mass is in a vacuum. For simplicity, there is no gravity working on the mass either.

How do I calculate the mass' top velocity? I seem to be missing something or not taking something into account because as far as I can see, the mass will accelerate infinitely which I know doesn't make sense.

Any and all help would be appreciated.

 

[The_Duck]

Unless some other force acts on the rocket (and ignoring relativity), it will keep going faster and faster! In an atmosphere, drag force would limit the rocket to some maximum speed, because as you go faster the air pushes back on you harder and harder, until it cancels out your thrust. In a vacuum there's no such drag.

 

[JacksonMarks]

Unless some other force acts on the rocket (and ignoring relativity), it will keep going faster and faster! In an atmosphere, drag force would limit the rocket to some maximum speed, because as you go faster the air pushes back on you harder and harder, until it cancels out your thrust. In a vacuum there's no such drag.

If that is true, then why is it considered impossible to travel at the speed of light? Or is that due to the fact that space is in fact not a perfect vacuum?

 

[The_Duck]

This is why I added the caveat about relativity. In special relativity there is an absolute maximum speed which is the speed of light, even in a perfect vacuum. But I doubt you want to include relativistic effects (which would in any case be very small unless your ships will be traveling monstrously fast) in a simple physics engine.

 

[dav2008]

I seem to be missing something or not taking something into account because as far as I can see, the mass will accelerate infinitely which I know doesn't make sense.

You're not taking into account the fact that you don't actually have an infinite supply of fuel so you can't sustain that thrust forever.

You should also probably consider that burning fuel decreases the mass of the rocket

 

[JacksonMarks]

This is why I added the caveat about relativity. In special relativity there is an absolute maximum speed which is the speed of light, even in a perfect vacuum. But I doubt you want to include relativistic effects (which would in any case be very small unless your ships will be traveling monstrously fast) in a simple physics engine.

Ah alright. Thank you very much for your quick responses.

You're not taking into account the fact that you don't actually have an infinite supply of fuel so you can't sustain that thrust forever.

You should also probably consider that burning fuel decreases the mass of the rocket

I'm aware of both those facts but it's not something that is important for my case.

 

[K^2]

But that IS part of why a real rocket can't reach velocities anywhere close to speed of light. If we could build rockets that can sustain constant thrust without loosing mass, we'd be colonizing other stars by now.

Real rocket creates thrust by ejecting mass at some fairly constant speed V_p. If the fueled rocket had mass m_i, and once it ejected all its propellant it has mass m_f, then the final velocity is given by the rocket formula.

V = V_p ln\left(\frac{m_i}{m_f}\right)

If you ignore this in your simulation, you are effectively using infinite V_p, and then you shouldn't be surprised that your top velocity is also infinite.

 

[Jack the Stri]

Also, for an object with mass to reach light speed, you need an infinite amount of energy, feasible with your setup but not in reality.

 

[JacksonMarks]

But that IS part of why a real rocket can't reach velocities anywhere close to speed of light. If we could build rockets that can sustain constant thrust without loosing mass, we'd be colonizing other stars by now.

Real rocket creates thrust by ejecting mass at some fairly constant speed V_p. If the fueled rocket had mass m_i, and once it ejected all its propellant it has mass m_f, then the final velocity is given by the rocket formula.

V = V_p ln\left(\frac{m_i}{m_f}\right)

If you ignore this in your simulation, you are effectively using infinite V_p, and then you shouldn't be surprised that your top velocity is also infinite.

I appreciate that rockets in real life are fuel based and that they must expel mass in order to actually achieve thrust, but this physics engine is just for a simple arcade video game and as a result players are not going to be restricted on fuel.