> Although a momentum balance, these variables can be cast as energies. They are the energy expenditure against gravity (often called delta V or the change in rocket velocity), the energy available in your rocket propellant (often called exhaust velocity or specific impulse), and the propellant mass fraction (how much propellant you need compared to the total rocket mass).
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).
That's all true, but it's not the whole story either. The most efficient way to drop into the sun is to shoot a big orbit way out, then when going super slow out halfway to Pluto to burn just a little bit more to slow down to nudge your orbit and now you're headed to to sun.
The most efficient, in terms of minimum propellant, would be to use Sun's radiation and solar wind to slow it down and thus let the Sun pull down the craft. E.g. big mirror at 45 degrees to solar radiation flux. This could take a lot of time, similar to your way.
They kinda forgot donkeys can just eat local grass and other plants, so if you're going thru area where they can graze it's not exactly eating up the wagon load.
The pack animals typically can't eat enough to entirely subsist off of local plants. Plus any time that you have to let the animals graze is time that you aren't marching.
"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.
I first became aware of Tsiolkovsky's equation 55 or so years ago, as an enthusiastic follower of the Apollo program, first venturing into the world of physics and the power of equations. At the time, I immediately wondered what it said about the suitability of various exo-planets (non of which were as yet "visible" or identified) for development of space-faring intelligent life. This wonderful article by Astronaut Pettit does the calculation I struggled with then:
>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?
>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 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.
> 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.
There are still a lot of stars, with little reason to suspect any one has a life capable planet. While you can get a lot of information from spectral observation, most of the universe isn't close enough to observe it. The earth is young enough that even if we assume infinite magnification most of the universe cannot observe it as no light from earth has reached them yet.
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.
You can still imagine a gravity well that even a nuclear powered rocket would be unable to climb out of. Nuclear thermal rocket has greater specific impulse than chemical propellant rocket, but not by that much.
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.
If a planet with ten times the surface gravity of Earth had an intelligent species like humans that had evolved to tolerate acceleration equal to a multiple of their surface gravity for a given time, perhaps that would open up additional launch possibilities such as a rail gun.
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.
> 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.
Why would that be the practical limit for intelligent extraterrestrial life?
> 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.
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).
Don’t all lunar journeys start with a low earth orbit? Couldn’t you launch into LEO a week or two before hand, then do the lunar assist at the proper time, eliminating the delay concerns of launching from the ground (weather etc)
Or will the fuel needed to boost to escape velocity boil off over the wait?
> Don’t all lunar journeys start with a low earth orbit?
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.
Why isn't there more interest in the dirigible launch/landing platform idea? Heck of an engineering feat to construct one of course, but nothing obviously defying the laws of physics and it would get us out of the thicker part of the atmosphere pretty effectively. And a self-landing rocket wouldn't need as much fuel for the return trip because the buoyancy of the landing platform would absorb some of the shock.
It's much easier to go sideways fast at height of 10km. That's why rockets start vertically (go up), and only later in height they tilt to "go sideways".
Which would be circumvented if the energy of the rocket actually came from a external source, like a microwave laser and the rocket only contained the medium.
Why isn’t it possible for a bunch of rockets with a little propellant left already in space to join forces with a rocket (rendezvous with it) to propel it further and faster than it could achieve by launching from earth with no additional assists?
This is SpaceX's plan for Starship (and one of the reasons I think it will take longer than expected[1]). ULA posited an orbital tanker for cryogenic fuels[2] which was most notable for having an internal combustion engine that ran off the fuel it would hold to keep the fuel chilled.
[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...)
You'd need extra docking mechanisms, which would add a lot of complexity and negatively impact payload performance. By launching 2 rockets you're also doubling the launch cost. With today's prices, it's much more reasonable to design staged rockets and compact payloads than it is to use several rockets so that one of them may fly further. SpaceX aims to overcome this with starship, which is designed to be be refilled in orbit, but we have yet to see if and how it works.
I like that he doesn't suggest a stopover in lunar orbit.
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.
SpaceX has a great track record of safety that rests on a very simple precept: the rocket will fly so much that it will get very safe before it gets human-rated.
Compare with the SLS getting one empty flight before they can’t get anything wrong because they’ll kill people.
Here's a random idea. The rocket equation is a problem because the propellant you throw backwards becomes just useless mass, right? What if instead you had two spacecraft, and one accelerated by throwing the other one backward, then the second one changed direction via a gravity assist or something, and caught up with the first one again? Maybe they could even subdivide recursively. Or the ones thrown backward could link up with the next rocket passing the same way, and become reaction mass for it in turn, and so on.
Conservation of energy doesn't torpedo this idea a priori. The "exhaust" mass would steal energy from the massive body/planet in the gravity assist.
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.
Here's one way to imagine this. A pair of spacecraft above the south pole push off from each other horizontally, in opposite directions. Their trajectories bend around the Earth, and they meet again over the north pole, going partly sideways and partly up. Now they can join and continue traveling up. Or repeat the maneuver and meet again over the south pole, traveling up even faster. Rocket equation sidestepped.
> pair of spacecraft above the south pole push off from each other horizontally, in opposite directions. Their trajectories bend around the Earth, and they meet again over the north pole
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?
(Edit: these two paragraphs assume you want to put your rocket into earth orbit, which I realised you might not be attempting.)
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.
I'm talking about flying away from the Earth. And yeah, it's making a more theoretical point. All it proves is that "recapturing propellant", so to speak, is possible in principle - it's not prohibited by conservation of energy or momentum or whatever. Like sailing against the wind faster than the wind. Given that, there are probably more efficient ways to exploit this.
You'd still need to get your spaceship pair into an orbit (or at least a sharp sub-orbital hop) in order to excecute your plan though. the spaceship pair wouldn't just hang there in space. Also, it's simply not possible to mechanically push the two ships away from each other with sufficient velocity, and I imagine the explosives needed to blast your two ships apart would be better used in a smaller slower controlled explosion, often called a rocket engine.
There isn't a 'hack' for defeating orbital mechanics sadly. It takes expenditure of energy, and significant amounts of it.
I don't imagine using explosives for it. More like one ship is a railgun and the other a projectile. Then when they meet again, they can convert their leftover relative velocity back to electricity, by having the railgun catch the projectile and charge up.
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.
Pulse nuclear rocket! Project Orion (NOT the boondoggle rocket) FTW!
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.
I think nuclear salt-water rockets might be more tenable. They produce consistent thrust, and do not involve sending nuclear weapons into orbit, hence not breaking any treaties.
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.
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.
I wonder how much it would help to have jets built in to the elevator which add support using compressed gas or something being pumped through the elevator from the ground? Then it would directly support the structure and also give the option of reacting to outside disturbances.
What are you thinking of? Yeah, compressing the air at the base will increase its temperature, and then the pressure (and so temperature) will reduce as it gets higher, but it’s still going to be at a higher pressure than the air outside and so can provide support and reaction mass.
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.
Also when it fails expect the lower end to fall and wreck everything in the area underneath. Which with that length will be a lot! The insurance bill would be … astronomical (see what happened in the Foundation TV show for an example).
Modern space elevator designs (starting from Brad Edwards’s NIAC study in the early 2000s) propose something much closer to a tether than a tower, maybe some hundreds of tons in total mass and shaped like a gossamer-thin ribbon. The worst-case failure mode of such a design would be rather anticlimactic.
Unless the ladder is made of superconductive unobtainium, this will not work (resistive losses kill you).
"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.
Would you? A rocket needs to use propellant for the time it stays in the gravity field, i.e. just to "stay still", while clinging to the ladder does not need propellant.
I think in the past, we also used to have a "tyranny of the horse" equation.
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.
Well, the Alcubierre drive [1] uses negative energy, but at this point it is not clear whether this type of propulsion is just a mathematical gimmick.
[1] https://en.wikipedia.org/wiki/Alcubierre_drive
Not only negative energy but insane amounts of it as well. Originally required converting more mass than the entire observable universe. That was lowered in later works. A recent work moreover made a drive using only positive energy.
We do not know if and I bet plenty of people do not believe such negative energy really exists.
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.
>We do not know if and I bet plenty of people do not believe such negative energy really exists.
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.
Sure, but the fuel or batteries or whatever won't have to lift themselves out of the gravity well. The only fuel needed would be for inertial changes. It's a free G of acceleration!
"Just" need to plug in the anti-grav module and efficiency will soar.
How do you figure? With anti-gravity, you would need very little power for propulsion since gravity would not be a factor (or less, depending on how effective your anti-gravity tech is). The question is how much power the anti-gravity requires.
It could also mean: We only have to feed the escape energy of the rocket itself into the rocket while it is on the ground, and without also carrying fuel upwards.
I would assume (with good reason) that the amount of energy needed to generate a counter to the gravitational field would be the same as the amount of energy required in thrust to do the same thing.
Still, having a drive that doesn't need to push stuff out of its back would be very interesting, IMHO - even if it doesn't work out better energy-wise.
Not really. The Alcubierre "drive" is closer to a "shape", a static solution to Einstein's equations. There is no proposed device that actually achieves this shape. The only idea along those lines implies a kind of Alcubierre railroad - you set up a path of negative mass matter (which almost certainly doesn't exist) and then move this with regular means as the ship is approaching, thereby continuing the bubble for the ship.
I wonder what the ideal gravity is. Weak gravity makes rockets harder to control but strong gravity consumes absurd amounts of fuel. Is there a sweet spot?
Lower gravity means less energy is needed to maneuver. There's less room for error, so the pilot must maneuver more precisely.
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.
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.
It is good to be accessible to everybody but, honestly, this seems like a silly omission.