Escape velocity is a constraint due to limited fuel?

[DaveC426913]

TL;DR

Want to make sure I understand this correctly: escape velocity is "only" necessary because we have limited fuel supply, ensuring we have to get to orbital velocity before it runs out.

I'm working on a story, and I want to ensure I have the basics straight. I'm not looking for any speculation, just facts.

It is necessary to achieve escape velocity - not because we can't escape without achieving it - but because we need to achieve it before we run out of fuel, or we will just fall back.

Currently, we need to achieve orbital velocity before we run out of fuel. But if we ease the constraint on fuel limits, we don't need to worry about escape velocity (effectively, though it's still there).

And it's directly tied to our current technology: chemical propulsion, which has an upper limit on specific impulse (somewhere in the high hundreds of seconds), and involves the rocket equation to constrain our options.

By hypothetical contrast, say we manage to get a working fission or fusion drive. They can have a SI of thousands or tens of thousands or even more (depending on who you ask). This means we can get to orbit and beyond long before running out of fuel.

The upshot here is that, with an engine more efficient than chemical (albeit still propulsion-based) one could choose to lift off from Earth and rise at, say, a flat 5000mph or something. In fact, you could fly all the way to the Moon's orbit at 5000mph, if you chose. Granted, you might still not achieve escape velocity so that, if you waited long enough, you would eventually fall back (an object falling from 250,000 miles from stopped would take on the order of 3 days). But since you have plenty of fuel, you are free to jst turn on your drive and go whereever you want from there.

Am I correct?


Imagine a drive that could only do 1g (so the astronauts would experience 2g on lift off). Without a fuel constraint, it could simply accelerate to 5000mph and throttle back till it just balances Earth's g-pull, and spend the rest of the trip out of the system at 5000mph.

(The above is not any actual scenario, I just want to confirm my assumption that "escape velocity" - in a practical fashion - is a consequence of limited fuel.)

 

[Filip Larsen]

The escape speed is the speed an orbiting object needs at a particular distance from the planet it orbits in order for that orbit to be parabolic (i.e. unbounded with zero speed at infinity) instead of elliptic (bounded with some maximum apoapsis distance). This speed (as a function of distance) is equivalent to a particular constant specific orbital energy (J/kg), i.e. the specific energy that includes both the gravitational potential and kinetic energy. Read about the vis-viva equation for details.

Note that the escape speed is independent on "fuel" and also on direction (apart from directions that in practice will make the object impact the planet instead of escaping). The equation that introduces amount of fuel and efficiency of the rocket propulsion is the rocket equation. With that you can calculate how much fuel (or how small a payload ratio) is need for a particular exhaust speed in order to achieve escape from, say, a given circular orbit. Or from ground launch, although this requires more details about launch profile to include effects of gravity and drag losses.

The rocket equation directly shows that a higher exhaust speed will directly lead to a larger delta-V for a particular fixed initial-mass-to-fuel ratio. As you say, Ion thrusters use this to get much more delta-V for a given fuel mass that the same mass of fuel would for chemical propulsion. However, for propulsion systems that needs its energy from a source external to fuel the limit of the technology is here the specific jet power of the engine technology so for constant jet power the thrust goes down as the efficiency goes up, meaning ion thrusts and such are not good for launch where you need 1G+ thrust. Once in orbit efficient thrusters can use micro-G acceleration to slowly raise the orbit over time.

 

[Filip Larsen]

TL;DR: Want to make sure I understand this correctly: escape velocity is "only" necessary because we have limited fuel supply, ensuring we have to get to orbital velocity before it runs out.

Imagine a drive that could only do 1g (so the astronauts would experience 2g on lift off). Without a fuel constraint, it could simply accelerate to 5000mph and throttle back till it just balances Earth's g-pull, and spend the rest of the trip out of the system at 5000mph.

As you mention, thrusting directly against gravity means thrust worth of around 1G (at surface) will be lost per second and this is called gravitational loss. This loss is the main reason launch vehicles turn towards the horizontal as soon as possible. Thrusting outside the lower atmosphere is always done parallel to the current velocity vector, either to speed up or slow down. Thrust perpendicular to the velocity vector does not change your total orbital energy, only orbit shape (eccentricity).

 

[DaveC426913]

The escape speed is the speed an orbiting object needs at a particular distance from the planet it orbits in order for that orbit to be parabolic (i.e. unbounded with zero speed at infinity) instead of elliptic (bounded with some maximum apoapsis distance).

...once you turn off the engine. Correct?

So, if I have plenty of fuel I need not concern myself with what my craft would do were it ever to reach periapsis and start to fall back.

Note that the escape speed is independent on "fuel" and also on direction (apart from directions that in practice will make the object impact the planet instead of escaping). The equation that introduces amount of fuel and efficiency of the rocket propulsion is the rocket equation. With that you can calculate how much fuel (or how small a payload ratio) is need for a particular exhaust speed in order to achieve escape from, say, a given circular orbit. Or from ground launch, although this requires more details about launch profile to include effects of gravity and drag losses.

Right, so it might be an inefficient use of fuel to simply blast straight off from launch and head straight out to lunar distance. But if one didn't care about fuel use (or time), there's no reason not to.


And, just to dot my i's and cross my t's: a propulsion engine with a higher SI directly means a smaller fuel/payload ratio. An x increase in SI means (roughly) a corresponding decrease in required fuel. (I'm certain there's more to it - it's not direct).



I know this scenario seems illogical, I just want to ensure it's technically true. I will start up a new question in the Sci-Fi section when I get to the details.

 

[DaveC426913]

Thrust perpendicular to the velocity vector does not change your total orbital energy, only orbit shape (eccentricity).

Right. But I only care about orbits if I plan to turn my engine off.
With sufficient fuel, orbital/fuel optimization becomes less of an issue.

i.e. I can just rocket out to 100,000 miles, "stop"* for a while and then turn "right" and blast my way to somewhere else.

*technically, I am in a parabolic orbit, but why do I care with no worries about fuel?

(Again I know this seems illogical, but I'm trying to decouple space travel from the constraints of our technology).

 

[Filip Larsen]

...once you turn off the engine. Correct?

Yes, when free falling from that point on.

You can say that when a rocket it thrusting (in directions along the current velocity vector) it will be increasing its orbit energy and once that energy pass zero (bound orbits usually defined with negative energy) the rocket can be said to have achieved escape. If it stops thrusting at that point it will (ignoring the effects of other massive objects) coast to infinity relative to the planet. If it thrust a bit more after achieving escape speed it will coast to infinity with speed to spare (called the hyperbolic excess speed).

 

[DaveC426913]

Thanks guys. I'll transfer my subsequent questions over to the sci-fi forum.

 

[Bandersnatch]

Am I correct?

To answer this directly - sure. If you don't have to worry about fuel. You could even walk out of a gravity well at a snails' pace, if you had a really long ladder. Escape velocity is for when you have to give your rocket one good push at some point in your launch - typically at the start - and be done with it.

With arbitrarily efficient engines you can ignore most of orbital mechanics, and just fly wherever in a straight line, at whatever speed.

 

[Filip Larsen]

I can just rocket out to 100,000 miles, "stop"* for a while and then turn "right" and blast my way to somewhere else

Yes, the more efficient (higher exhaust speed) and powerful (higher jet power) your rocket has the more you can "ignore" gravitational loss and orbital mechanics. If rockets in your story can thrust with 1G for hours on end then orbital mechanics probably becomes less of an issue. However, there are limits to this for rockets, see mass annihilation rocket.

This theoretical maximum means that the theoretical maximum delta-V you can get from a (photon) rocket of given mass ratio is given by the rocket equation where the exhaust speed is set to the speed of light. Delta-V for small mass ratios is almost linear in fuel spent, so if a sci-fi photon rocket has 10% of mass as fuel then it can achieve a delta-V of around 10% c or 30'000 km/s. Probably enough for most stories. However, the other limit is power. Accelerating at 1G that would mean engine for such a photon rocket has a "throughput" of 3 GW per kg of total mass. If engines mass is 10% of initial total mass then that mean engine must handle at least 30GW per kg. Cue magic materials technology.

 

[Janus]

While a higher exhaust speed is more efficent in terms of fuel usage, there is a drawback in terms of energy usuage. Doubling the exhaust speed doubles the final velocity you can achieve with the same fuel reserve, but it requires 4 times as much energy to achieve. And while doubling the exhaust velocity also doubles the thrust per kg of fuel burned, it again requires 4 times the energy. While a fusion rocket solves this in terms of energy concentration, it's not very practical for a ground based launch. That much higher exhaust velocity also means a much more energetic/hotter exhaust. Meaning a fusion rocket launched from the ground is likely to leave a molten launch pad behind.

 

[DaveC426913]

Thanks.

Ideally, I want a minimal acceleration so that the otherwise short interplanetary trip takes days or weeks rather than hours.

I'll get to the more practical aspects in my subsequent sci-fi thread.

 

[Ken Fabian]

Fusion still appears to need an abundance of reaction mass - that might colloquially get called 'fuel' .

The fusion engines part seems likely to have a lot of fixed mass, which will require more reaction mass, undercutting some of the gains from high exhaust velocity. There are trade-offs.

If the exhaust velocity is extremely high it becomes (more) dangerous over a longer distance. Launch pads of ordinary materials won't like it and as the rocket rises, will affect wider areas.

Other possibilities include the ground based lasers up the rear. Those still have to utilise reaction mass - something for the lasers to vaporise - but don't have to carry so much fixed mass as reactors/rocket hardware.

For fiction purposes it may be better not to dwell too much on the difficult details or numbers that more realistically aren't going to work.

 

[DaveC426913]

Fusion still appears to need an abundance of reaction mass - that might colloquially get called 'fuel' .

The fusion engines part seems likely to have a lot of fixed mass, which will require more reaction mass, undercutting some of the gains from high exhaust velocity. There are trade-offs.

If the exhaust velocity is extremely high it becomes (more) dangerous over a longer distance. Launch pads of ordinary materials won't like it and as the rocket rises, will affect wider areas.

Other possibilities include the ground based lasers up the rear. Those still have to utilise reaction mass - something for the lasers to vaporise - but don't have to carry so much fixed mass as reactors/rocket hardware.

For fiction purposes it may be better not to dwell too much on the difficult details or numbers that more realistically aren't going to work.

Yes, I am covering that in my other thread in the sci-fi forum. That's where I break away from the facts and get into the more handwavium stuff.

 

[Baluncore]

Escape velocity, as a number, depends on where in the gravity well you specify the calculation begins. We might assume either the surface of the Earth, or an existing orbit. The application of the term escape velocity, implicitly assumes that the available fuel mass has been used before that point, as it would be in the case of a gun.

For departure from the Earth's surface with minimum fuel, take an initial advantage of Earth rotation, launch from near the equator, climb vertically through the densest atmosphere, and then accelerate towards the East, on a trajectory in pursuit of the escape velocity at that altitude.