Escape velocity question & planet sizes

Eh, the Jovians could do it if they invented forcefields. So we’ll have to send down some very durable robots to convince them not to.

If they stack enough monoliths, they could have something like a space elevator. They’d better be quick, though.

I’ve often heard there’s something particularly important about escape velocity in the context of launching rockets. One thing that is important is that if you were going to instantly accelerate the rocket and then let it coast all the way up to infinity, escape velocity is the required velocity to start at – but rockets never launch this way. The rocket does have to keep burning fuel until it reaches the local escape velocity upward, so if the idea is to burn for a while and then stop, escape velocity at the top of the burn is significant. But this still doesn’t make escape velocity at the surface significant.

What I do think is important is that you want to launch with high g forces to minimize fuel consumption, because as the g force is made lower and lower approaching 1, the amount of fuel required becomes infinite (a rocket could work fairly hard to just hover above the launch pad for hours, burning a lot of fuel for zero progress). In this context, escape velocity is not particularly significant, is it? or orbital velocity?

Or am I missing something?

Right. These are called gravity losses–the amount of extra delta V you need just to counteract gravity. It’s not an insignificant effect; generally 1+ km/s in delta V for an orbital rocket.

As you say, the greater the acceleration, the lower the losses, down to the degenerate case where you’re just hovering forever. Gravity is an acceleration itself, so to minimize the losses, you need to spend less time under its influence.

Though even that is an approximation. Gravity isn’t much reduced in low Earth orbit. But when you’re in orbit, centrifugal forces counteract it. So in a sense, the reason high accelerations reduce gravity losses is because the centrifugal forces ramp up more quickly, and not because you’re somehow escaping gravity.

Orbital and escape velocity are still useful figures, but yes, they only apply in a theoretical sense. Any given rocket will need more delta V than the figures indicate.

And there is a tradeoff between overcoming gravity losses and air resistance. If you accelerate more quickly, you minimize gravity losses, but then you’d be going very fast at low altitude, which means huge aerodynamic drag. If you want to minimize aerodynamic drag, you’d go through the atmosphere slowly, then accelerate fast, but this maximizes gravity losses.

If you look at, for example, the description of the “Oberth Effect”, one way to look at it is that a rocket burn is more efficient the faster the rocket is moving. Therefore, you indeed want to accelerate it as much as possible at launch, so I do not think you are missing anything.

As for the escape velocity, if the escape velocity is sqrt(2GM/r) as above, and the acceleration at the surface is GM/r² , then you can see the relation; obviously the density plays a role. The surface gravity is the parameter that obviously gobbles up your thrust, not the escape velocity directly.

The shape of your trajectory also matters. You can fly straight up to get out of the atmosphere as quickly as possible, then do a hard pitchover to get the lateral velocity you need, but this is also wasteful of delta V. The optimal trajectory ends up being a balance between the extremes.

And there’s the simple problem that engines are heavy and cost money. There’s a limit to where more engines eat more payload than they’d save, if you could even fit them on the bottom of the rocket. Plus, even if you could fit them, they might cost more than the value of whatever additional payload capacity you gained. Engines are likely the single most expensive part of a rocket, so this is unlikely to be a good trade.

Oh, and rockets are designed with a peak acceleration in mind. A Falcon 9 hits around 3-4 gees at main engine cutoff. If you increased that significantly, you’d have to beef up the structure, too, which is also very costly (to payload).

So overall, it is very likely not the case that taking an existing rocket and increasing the acceleration will lead to higher performance. In a spherical cow universe, with no aero drag and zero-mass engines and unobtainium fuselage, sure. But not for real rockets.