# Re constant acceleration in space

1. Jan 19, 2012

### Filby

i was having a discussion with a friend recently and he seemed to think that you cannot accelerate to a speed which is faster than the speed of the accelerating force coming out of the back of the rocket. but i thought it was the case that u could get to very high speeds in space even if you were being propelled quite slowly and the only limiting factor was the amount of fuel u could carry.

i'm sure he's wrong but i can''t think of the killer argument so i joined this forum to see if u clever folks could sort this out for me.
i just need an example where the speed of the fuel being propelled to create acceleration is slower than the maximum speed the vehicle can reach.
thanks.

2. Jan 19, 2012

### Filip Larsen

Welcome to PF!

You are correct, your friend is not. A simple model of rocket acceleration results in the rocket equation [1], which you may find useful to persuade your friend that you are correct. In particular you can show him the graph and point out that you can end up with a delta-V much larger than the exhaust velocity provided the mass ratio (final mass to initial mass) is large enough.

[1] http://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation

3. Jan 19, 2012

### Filby

thanks for the speedy reply . so is it true to say that nearly all, if not all, modern rockets accelerate to a speed higher than the exhaust velocity?

4. Jan 20, 2012

### Filip Larsen

This is not a true statement on its own, as there are many different types of rocket systems designed for various purposes, many not including needing a high delta-V. For instance, having a high delta-V to exhaust velocity ratio for a single stage rocket is not feasible compared to other design options such a multi-staging, so you are much more likely to see a multi-stage rocket over a single stage rocket for the same delta-V budget.

What you could say, though, is that there is nothing in the principle of rocket propulsion that disallow a rocket system to be designed so that it can achieve a delta-V much higher than its exhaust velocity. For instance, the Space Shuttle has an orbital velocity of nearly 8.0 km/s (just like most other objects in low earth orbit) whereas its engines, the Space Shuttle Main Engine (SSME), "only" has an exhaust velocity around 3.5 km/s at launch rising to around 4.4 in vacuum.

5. Jan 20, 2012

### Lsos

As long as the exhaust is being proelled out the back faster than the rocket is moving (in the rocket's frame of reference), then it should accelerate. Keep in mind that from a rocket's frame of reference...the rocket is moving at 0 m/s.

You can point out a simple flaw in your friend's logic to derail his argument. He says you cannot accelerate to a speed faster than the exhaust. A speed RELATIVE TO WHAT? Imagine you're in space...you might be moving at 10 km/s relative to the earth, but maybe 60 km/s relative to the sun. And probably 100s of km/s relative to the galaxy. By your friend's logic, the rocket should never move at all. Hell, it would probably move backwards.

Ask your friend relative to what, and WHY? If he says "relative to the earth", why should the rocket, in deep space, care where it "started" its journey from?