The tyranny of the rocket equation (2012)
nasa.gov
nasa.gov
It is good to be accessible to everybody but, honestly, this seems like a silly omission.
This is false, and in a meaningful way. Energy and momentum are not the same. Momentum scales linearly with speed, whilst momentum scales quadratically. One case where this difference matters a lot is the Oberth effect, where the fact that Delta V is a measure of speed rather than energy is of key importance.
The Oberth effect states: "the most energy-efficient method for a spacecraft to burn its fuel is at the lowest possible orbital periapsis". Or, more accurately "the use of a reaction engine at higher speeds generates a greater change in mechanical energy than its use at lower speeds". It just turns happens to be that, in orbit, you are going fastest at the lowest point. This effect is a direct result of the scaling differences. Adding 1m/s will always require the same change in momentum, but the faster you are going, the more it will increase your kinetic energy. For a 2kg object, going from 0m/s to 1m/s increases kinetic energy by 1 joules. Going from 1000m/s to 1001m/s increases kinetic energy by 2001 joules. It is key here that, when expending reaction mass at a given exhaust velocity, it will always result in the same change in momentum, whilst resulting in a different change in kinetic energy. Delta-V is just the total speed change that can be achieved by all momentum generated through reaction mass. The rocket equation is about converting this momentum into a speed by compensating for the fact that a rocket gets lighter as it expends reaction mass, to get to Delta-V.
If Delta V was a measure of energy, then it shouldn't matter where you use your delta V, you always get the same kinetic energy back. Luckily Delta V is a measure of momentum, which allows us to exploit the Oberth effect for more efficient orbital changes.
As for exhaust velocity, _if_ your fuel is your energy source, the exhaust velocity and the energy density are indeed related. But consider an ion engine, where the reaction mass is just mass, and the energy comes from solar panels (or another source of energy).
[1] https://maximumeffort.substack.com/p/the-tyranny-of-the-wago...
ACOUP had a good writeup on it https://acoup.blog/2022/07/15/collections-logistics-how-did-...
"Wagons are more promising. A big wagon pulled by two horses can carry perhaps a ton (1000kg) at maximum (in practice many medieval wagons capped out well below this and were pulled by four horses), but now we have two horses and a driver to consider...Their nutrition requirements are too high and so they require feed, at least some 4.5kg of it per day assuming local grass is available along with time to let the horses graze it (during which the wagon is, of course, stopped). The Romans seem to have allocated around 7kg of barley per day per cavalryman for their cavalry"
EDIT: Ah, I did not realize before linking the acoup blog that the article is actually in response to that same article.
>If the radius of our planet were larger, there could be a point at which an Earth escaping rocket could not be built. Let us assume that building a rocket at 96% propellant (4% rocket), currently the limit for just the Shuttle External Tank, is the practical limit for launch vehicle engineering. Let us also choose hydrogen-oxygen, the most energetic chemical propellant known and currently capable of use in a human rated rocket engine. By plugging these numbers into the rocket equation, we can transform the calculated escape velocity into its equivalent planetary radius. That radius would be about 9680 kilometers (Earth is 6670 km). If our planet was 50% larger in diameter, we would not be able to venture into space, at least using rockets for transport.
So, now, to the Fermi paradox: where are they (the intelligent extraterrestrial life we should have met by now)? Stuck, perhaps, in a gravity well?
Why would that be the practical limit for intelligent extraterrestrial life?
Might not be, but it really doesn't matter that much. The problem is that most of the fuel expenditure is going to lift fuel, not rocket or payload. WIth even the most energetic chemical fuels, only 15% of the total takeoff weight is rocket+payload, and improving the weight of the rocket doesn't change that - you just get whatever weight you trim off the rocket materials as potential payload, and the returns diminish quickly.
Chemical rockets aren't the only means of climbing out of a gravity well, though. Nuclear thermal and nuclear pulsed rockets both provide higher efficiency than chemical rockets.
No engine is 100% efficient, so the spacecraft has to deal with quadratically more waste heat as "efficiency" (exhaust speed) rises.
But there are other ways to climb out of any gravity well (except black hole) than a usual mass-reaction rocket, not benefiting buoyancy.
If the atmosphere is transparent enough, a plane or a ballon could carry a small craft high enough, and then it could be propelled by pressure of a strong laser below. Of course, in alien economics and sufficiently deep gravity well, this could be prohibitively expensive.
Why should we have met them by now? Even if they have a planet significantly smaller than earth, they still need to escape their star, and then spend years in space - without any breakdowns or hitting anything. There are only a handful of stars within 5 light years -that is 5 years at the speed of life (relativity gets interesting if you can actually get that fast), but realistically they can't get going that fast with rockets, so we are talking thousands of years to make the trip. Assuming they are very advanced they left when they first detected life on earth - a bit over 100 years ago radio signals from us would have reached them. Even if they are only 5 light years away it is impossible that we met them yet.
Once you look at some alien more than 10 light years we cannot really establish meaningful science communications as our advances mean anything we are interested in we probably figure out already. (we can still exchange culture) At 50-60 light years out, they can't even get a message back to us now that they know we are here. Once you get to a bit over 100 they don't know we are here yet no matter how sensitive their radios are.
In short there is no Fermi paradox: there might or might not be life out there, but they don't even know we are here, and it they couldn't reach us if they did.
All that assumes two things for which there is no strong argument. First, that an extraterrestial intelligence would only be interested in traveling to another planet because it detected signs of intelligent life there. But why would that be? Why wouldn't a "life friendly" planet be almost as interesting? Suitability for life, and likely even the signal of the presence of life, is something you can get from spectral observation.
And second, intelligent life may or may not care a great deal about the time of travel. No reason intelligent "iife" elsewhere should not be self-constructed to be indefinitely patient and repairable.
For example humans accelerating 4g for 2 minutes over a 5,000 mile track would only achieve 10,000mph. The extraterrestrials accelerating 40g for 2 minutes over a 50,000 mile track would achieve a speed of 100,000mph. Here the larger circumference of their planet might also help, or the density of energy they dealt with on a daily basis would influence what type of launch facilities were feasible.
http://svs.gsfc.nasa.gov/vis/a000000/a003300/a003364/
Unfortunately it's not usable for a lot of targets because it closes the window of opportunity too much (a three week window for hitting Mars becomes a handful of days with a Luna assist).
Main source for all this: https://space.stackexchange.com/questions/4027/has-luna-been...
Or will the fuel needed to boost to escape velocity boil off over the wait?
No, at least they don't have to. It's more efficient to boost directly into an orbit that's eccentric enough to bring you close to the moon, if you started from LEO you'd lose a lot of the gains.
> Or will the fuel needed to boost to escape velocity boil off over the wait?
No, but relighting an engine is a relatively high risk procedure, so it only makes sense if the gains are large.
They have used planes in a similar way though: https://en.m.wikipedia.org/wiki/SpaceShipTwo
https://en.wikipedia.org/wiki/Laser_propulsion
It might be dangerous for humans, but for material transport it seems comparable to spinlaunch.
[1] If NASA were to plan a mission that needed on orbit refueling they would not even start building a spacecraft until they had tested out all of the elements of on orbit refueling before hand. SpaceX is "assuming" they can make it work and proceeding with Starship. To date NASA has awarded some contracts (https://spaceflightnow.com/2020/10/16/nasa-selects-companies...)
[2] https://sciences.ucf.edu/class/wp-content/uploads/sites/23/2...
I wonder if a SpaceX SuperHeavy with no Starship mounted could get itself to orbit. Probably its tanks would not start out full, for that.
I have taken to calling Starship the "can". With on-orbit refueling you can send cans to lots of places. First paid for seems to be a can to the moon. AFAICT there is no actual use for Orion or SLS; they could launch the "spam" in a Crew Dragon and transfer it to the can in LEO for trans-lunar, and back again to land in.
Seems like getting the booster and can crew-rated would be a good thing to do early.
Compare with the SLS getting one empty flight before they can’t get anything wrong because they’ll kill people.
If you do this a million million times you might slow the planet down to where it has no more energy to usefully donate, but a one-off maneuver is negligible.
I do think the idea of 'throw a solid mass rather than hot gas', but for a totally different purpose: stealthy change of orbits in space-warfare.
Okay, they’re in polar orbits [1].
> going partly sideways and partly up
Wat? (“Up” is ambiguous. Do you mean northward on the first half of their polar orbits? If so, it’s the same as sideways relative to a ground-based observer.)
> they can join and continue traveling up
As in parallel to the pole? “Up” away from the North Pole? How did they accelerate from an orbit to this trajectory?
No matter how you spin it, if you want these two rockets to go in exactly opposite directions and meet up again, The point at which they meet would _not_ be partially sideways and partially "up" (away from the earth). at the point where they meet, they would be going 100% parallel to the ground, and 180degrees from each other (ie, direct head-on collision).
This is ignoring the fact that minimal stable orbital velocity (the minimum speed for your rockets to go 'around' the planet, is about 7.8km/s, or 17 thousand miles per hour. and because they're going in opposite directions, thats 34 thousand miles per hour of effective collision speed.
Now, if you're suggesting instead, a full 'escape' velocity from the earth that allows them to both enter parabolic trajectories, and meet at some arbitrary point in the distance, I hope you've thought of a way to allow your two spacecraft to survive an explosion that launches them from 0 m/s relative to each other to roughly 22km/s relative to each other (49 thousand mph), in some semi-instantaneous event. If we assume this 'push' from each other happens over 10seconds (this is generous), that's gaining 2.2km/s/s, which is 224G for 10 seconds.
There isn't a 'hack' for defeating orbital mechanics sadly. It takes expenditure of energy, and significant amounts of it.
Or the two ships could be a spinning pair tied by a cable, and then the cable is severed. To make a fast spinning pair, start two spinning pairs in parallel planes and opposite directions, and make them accelerate against each other electrically.
There are probably objections to those too, like size of railguns and strength of cables, and then engineering can find answers to that, and so on.
I honestly wonder if they could do more bomb design wiht modern simulation/supercomputers that will have near-zero bad isotopes / fallout.
The #1 reason I think we should have a moon base is that we can use it as a launch site for a Project Orion craft that would economically move a couple million tons around the solar system. You have a million ton ship that can get to Jupiter in a month, that means practical asteroid mining.
Their thrust is lower, but the complexity is lower aswell. No weird damping system to 'absorb' the explosion, and crucially, much less radiation. You are dumping the reaction products away from you, rather than shooting the reaction products at yourself as with Orion. Hence you need much less radiation shielding.
On the moon it's just about doable with current technology and realistic levels of mass.
Paging Larry Niven...
A ring with a diameter matching your skyhook's length might seem to need 22/7 times the mass lofted to orbit, but the stresses on it are much less complicated, so it may be lighter than that. You may imagine one rolling around Earth, dipping to 100 km and flinging off whatever grabs on at up to 10 mi/s.
BTW, I calculated that the tensile strength of the material of any rotating ring, whether girdling the sun like Niven's, or just orbiting the regular way like a Halo or Culture "orbital", must be enough to support against its inside surface "gravity" a full radius's length of the material.
So, a ring rotating to provide 1G and taking 24hrs to do it (so days are the right length), would have to be about 2M km in radius. It would therefore need to be made out of something that could support a 2M km long constant-thickness cable against 1G, or more than 100x as strong as what you would need for an earthly space elevator.
A ring of 100 km radius rotating so that its tangential velocity matches earth orbital velocity less earth's rotation, 7.5 km/s, accelerates anything that latches onto it at 560 m/s^2, or 55 G. One at 1000 km radius would pull 5.2G, a little less strenuous for puny humans; they would need to endure it for a few minutes until flung off. That one would need to be made of stuff that could hold up 5200 km of itself, which might be just within range of what we can make.
Methods for dodging satellites are left as an exercise for the reader.
Will be interested if you have any studies on it.
http://hopsblog-hop.blogspot.com/2016/08/lunar-sky-hook.html
https://hopsblog-hop.blogspot.com/2016/04/liftport-lunar-tet...
There's also a wikipedia article:
"Real" versions of this scheme would use laser power beaming. Of course, a "real" version of the scheme would also need hefty rockets on the passenger vehicle to keep them from dying if the vehicle fell off the ladder (or if the ladder broke). The rockets are needed to either slow the vehicle before atmospheric entry (so the deceleration is not fatal) or thrust sideways to put the passenger pod into elliptical orbit that just misses the atmosphere. The delta-V needed at the worst case altitude is non-negligible.
The catch is that nobody can actually build a ladder strong enough. Space elevators from Earth require sci-fi materials.
You might even be able to take advantage of this by chilling the compressed air before it goes into the beanstalk, so that it absorbs heat from the surrounding air on the way up. Or have separate pipes with one carrying methane to burn as fuel. Lots of options to evaluate.
Yes, we've ruled out aluminum and wood. But don't give up! Got any single-crystal graphene? That might work!
If you needed a horse to pull a wagon some distance over terrain unsuitable for grazing, you needed to carry a significant amount of fodder for the horse.
The longer the distance, the more fodder you needed and thus the more load for the horse. If you were so heavy, you needed 2 horses, then you needed even more fodder.
This was a huge limit to ground transportation in the past.
"Just" need to plug in the anti-grav module and efficiency will soar.
This is essentially a case of "draw the rest of the owl".
Besides, all warp bubble metrics so far are inertial; meaning the ship is unable to accelerate, so they're a gimmick nowadays. I have hopes we find something workable though.
Plenty of people believe that mental problems are all caused by disembodied souls unleashed by Xenu of the Galactic Confederation when he blew them up with A-bombs in Hawaii, back when Earth was called Teegeeack.
What "plenty of people" believe is not important.
Maybe this isn't a problem outside all the little simulators I've tried. Computer control exists, after all. Maybe these simulators all suck and I'm wrong. All I know is when I tried pilot the ship near a low gravity planet, the slightest mistake would put me in an escape trajectory. So I developed this intuition that I need to be much more careful in lower gravity, like a space version of a therapeutic index.
https://www.orionsarm.com/eg-article/484746e824a3a
Doesn't need super advanced technology, can be build incrementally, avoids most catastrophic failure modes and allows you to settle essentially any random rock in space.