Okay, I’m an idiot. Just to preface this. But let’s say I’m in space. There’s no wind resistance right? If I accelerate, I’ll maintain that speed. Why can’t I just burn more fuel and go faster?
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The Tsiolkovsky rocket equation.
You can go faster by burning more fuel, but you have to bring more fuel to accelerate the fuel you are going to use to go faster.
Beyond a certain point going a little bit faster means you need to carry exponentially more fuel.
Going fast is easy. Burn fuel, exhaust one way, acceleration the other way.
But going even faster is harder. The faster you go, the harder it is to go even faster, since it takes more energy to go faster than fast.
Eventually, you will reach a point at which you cannot go faster because going any faster would take more energy than you can have, so you eventually stabilize at some high speed.
It takes 4 times as much energy to go 2 times as fast.
Eventually, you will simply run out of energy to go faster – let alone going any faster relative to your current speed to notice any change in speed.
Assuming unlimited fuel, we can still only go so fast based on the engine design and the speed at which the exhaust leaves the rocket engine. The exhaust coming out of the rocket can only go so fast. At some point, the mass of the rocket and the thrust of the engine are going to balance each other out.
To use an example, imagine we are talking about a hose.
If the water is coming out at a slow speed, the hose doesn’t zip around the yard, it just sits there. But if you turn up the water pressure, suddenly the water leaving the hose can push the hose around. That is basically thrust. The amount of thrust is based on the water leaving the hose. The water leaving the hose cannot push the hose backwards faster than the water itself is leaving. To increase the speed of the hose, we have to increase the speed at which the water leaves the hose. If the water leaving the hose is traveling at 10 mph, the hose cannot move faster than that. If we get it up to 20 mph, now the hose can start to whip around.
To use some real world examples, a shuttle engine exhaust is about 4500 m/s. the boosters were 2500 m/s. That is solid rockets vs liquid fuel.
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