the million dollar solar system
TRANSCRIPT
How long would you allow yourself to be locked up inside a spaceship in order to visit one of the planets of our solar system? And how much would you pay? These are the questions underlying everything else that is discussed in this essay. A few decades from now a team of astronauts will spend about three years on a mission to Mars, probably travelling via Venus and certainly spending 95 percent of those three years locked inside a tin can with nothing out the window to see but starlight, and doing essentially nothing but laundry. The first crew to do this will be motivated by the thought that they will be going somewhere never explored before, and the pleasure that comes from that. But how about the second crew, or the third? Succeeding crews will have the honour of filling the remaining gaps in our knowledge of Mars, but this is going to wear thin after a while. How much further down the line of missions will it be before the desire to explore is trumped by the discomfort and the cost? At what stage in the march of technology – if ever – will planetary exploration become a pleasure trip for people like you and me?
My feeling is that two weeks is about as long as I would want to spend on any vesel between ports of call. Therefore I imagine (rightly or wrongly) that for sustained exploration of the solar system by human explorers, visits to the planets have to be this short. Otherwise planetary exploration will always be something that robots do on our behalf. With this in mind I have come up with a thought experiment about exploring the solar system within that time frame and at a cost low enough for at least some of us to afford: one million dollars. This of course is out of reach for most of us, but I want to show how this price tag scales down when we use the same technology to explore the closer planets. I think you might be surprised, as I was when I first saw the data.
The first thing to note is that this technology that I am referring to will not be anything – not even remotely – similar to what we use in space today. A rocket flying to Pluto in two weeks and stopping on arrival needs to travel at a speed approximately 1.6% of the speed of light. Using the best propellants and rocket engines we have today, this journey would consume more propellant than there is mass in the solar system. I have done the calculations. The amount of fuel is so great that not even my spreadsheet can obtain an answer, and my spreadsheet can handle numbers with more than 300 digits in them (in scientific notation). To give a point of comparison, the number of kilograms of material, of any kind, in our solar system is a number that has at most 31 digits in it. The rocket fuel number is at least 270 digits longer. That doesn’t just mean I’d need to burn the mass of 270 solar systems but something much, much greater: probably more mass than there is in the entire universe.
Well, if a two-week rocket-propelled journey to Pluto is out of the question, how short a journey could a real rocket do to Pluto? Let’s say we consumed just the mass of the solar system getting to Pluto. That journey would take eight months. Eight months. Don’t forget that gravitational assistance from Jupiter is out of the question for the next 200 years, and wouldn’t be that useful anyway because the addition in velocity is trivial compared to the speed required to get there in this much time. Clearly today’s rocket technology won’t allow us to explore the solar system much beyond what we have achieved already. It will get us to Mars and Venus, but only with Herculean effort, Gatesian investment and whole lifetimes of preparation. The rest of the solar system is robot territory until we can come up with something better.
Well, okay, technology has to improve. Let’s say we can crank up the exhaust velocity of a rocket to 60 kilometres per second, which is about fifteen times better than what our best chemical rockets do and is more or less the theoretical limit for engines using ions as propellant. My spreadsheet can at least calculate that number. An ion engine of this kind flying to Pluto in two weeks would need a fuel tank big enough to carry the contents of 10,000 solar systems. That strikes me as being rather extravagant and somewhat counter to our growing sensitivity to the environment. What if we cranked it up to 100 km/s? Still we would need to use an entire dwarf planet as fuel, and there aren’t that many dwarf planets in our solar system to use, on a regular basis.
Well, there has to be some point at which rocket propulsion becomes practical for two week deep space missions. By practical, I imagine that to mean rockets that consume their own weight in fuel across the entire journey. A 100-tonne spaceship therefore would need a 100-tonne fuel tank. The engine which could make this work would have to have an exhaust velocity of 7000 km/s, fully 200 times faster than the engines on today’s best chemical rockets. An engine that can do this can get to Pluto in two weeks, Neptune in ten days, Uranus in seven, Saturn in four, Jupiter in two and Mars in as little as four hours. A trip to the Moon would take less than ten minutes, but the damage wreaked upon the Earth by firing megatonnes of matter into it at a speed a thousand times faster than the impact speed of most meteorites might make this a rather unpopular business venture. Just saying...
Somehow I don’t think rocket fuel will ever become so cheap that people would want to squander it in this way, so let me switch this investigation round a little and consider journeys to the planets that each take fourteen days (each way), and see what happens to the fuel bill then. Under those conditions, a two-week trip to Neptune uses 70% as much fuel as a two week trip to Pluto, a trip to Uranus uses 40% as much, a trip to Saturn uses 20% as much, and a trip to Jupiter uses 10% as much. Destinations closer than Jupiter get harder to discuss because at this close range the fuel bill depends on whether we take the shortest route or cut across the solar system. If we took the shortest route to Mars, the journey would need 3% of the fuel used to get to Pluto. So if the journey to Pluto cost a million dollars in fuel (never mind the accommodation costs) then the journey to Mars costs $26,000. A trip to our Moon costs $46 and a trip across the Atlantic or Pacific or Indian Oceans would cost about $2.30.
That there is pretty much the point of this essay. New technology is never applied to just one thing. A rocket system capable of reaching Pluto in a hurry is capable of turning our planet into a beehive buzzing with transcontinental aircraft. What will life be like when we can hop on a sky-bus and be in London for breakfast, Tokyo for lunch and Sydney for a sunset barbie? We are already carting thousands of people around the world daily even though today’s air tickets are expensive. What will it be like when airfare costs less than the meal we buy upon arrival?
Well, this is all speculation based on the assumption that rockets will get faster and more efficient, which they can only do if we discover new materials and new processes for pushing material ever faster out of rockets. If we are speculating about future technologies then we should not limit ourselves to inertial means of propulsion, but instead allow for the possibility that the technology that gets humans to the planets is non-inertial. What would such a thing look like? I have no idea, but our experience of the last three hundred years tells us that, whatever it is, it will require the consumption of energy, and we can calculate how much energy is needed. This is a fairly simple calculation. Consider the gravitational potential energy of the Earth and (say) Pluto; that’s the potential energy states imposed on these planets by the Sun’s gravitational pull. Then consider the kinetic energy for each planet as it moves around the Sun. The difference in kinetic energies added to the difference in potential energies is the amount of work done by the spaceship.
(This does not take into consideration the energy required to get the spaceship out of Earth’s own gravitational well and into Pluto’s gravitational well, which I’m assuming are minor compared to the energy required to travel between planets.) This is the best that we can possibly aim for. No energy is wasted if we travel around the solar system with a technology like this. It implies we can give motion to a spaceship in one direction without wasting energy giving motion to rocket fuel in the other direction. Thermodynamics suggests we can never get this efficient with energy use. But what if we could? What would planetary exploration look like then?
I have calculated these values for a selection of planets in our solar system, and tabulated the answers below. The values are the work which must be done, measured in Giga-Joules, necessary to get a 100-tonne spaceship from Earth to each planet. Mercury 70,200 Venus 16,900 Mars 15,300 Asteroids 28,000 Jupiter 35,900 Saturn 39,800 Uranus 42,100 Neptune 42,900 Pluto 43,300
It is interesting to see that more work must be done to send a spacecraft to Mercury than to Pluto. This is understandable if we see ourselves lowering the spacecraft down into a steep gravity well in the case of Mercury, and pushing a spacecraft over increasingly flat ground in the case of Pluto. If I pretend that the Pluto journey takes two weeks, then the averaged energy consumed per second is 35,800 Kilowatts. Therefore this magical engine, whatever it is, requires at least this much power to operate. Where does all this power come from? If it’s directly from the Sun, in the form of solar panels, then the collecting area has to be as big as a square 200 metres along each side; not impossible but certainly challenging. It assumes absolutely no inefficiency in the energy conversion. Inertial effects on a solar panel this big would be enormous. But then, we’re talking about non-inertial transportation, so maybe this won’t be a problem after all. A nuclear reactor taken off one of today’s marine vessels could handle this power output quite easily.
Be that as it may, an engine that can apply this much power to moving itself around the solar system can get to Pluto in fourteen days and Mars in about five. What kind of future would this technology imply? Well, it means that energy can be turned into motion without pushing against anything. Presumably this means cars that don’t turn wheels, aeroplanes that don’t turn turbines or propellers, things that defy Newton’s law of action and reaction. If we can break that law, then we can break pretty much anything. The sad news is that this law is even older than the law of conservation of energy and (like the latter) has never been observed to fail. So I think that this magical device for exploring the solar system will never be invented. And where does that leave us with regard to exploring the solar system? Unfortunately, back home in front of our TVs, watching robots do it on our behalf. It could happen.
There is one known exception to all of this, however: nuclear pulse engines. These are devices that detonate a series of nuclear bombs beneath the pusher plate at the rear end of a spaceship. The recoil of the explosion pushes the spaceship in the direction you want to travel. The effect is equivalent to a conventional rocket engine with an exhaust velocity as high as 10,000 km/s. That’s higher than what was needed for the two week Pluto mission. So the journey is possible, in theory. We just have to turn the production of nuclear weapons into an assembly line process, churning these things out like hamburgers and storing them in a huge warehouse in space somewhere. If a flight to Pluto cost a million dollars and uses (shall we say) a thousand nuclear explosives, then folks like you and me would be able to buy nuclear weapons for less than a thousand dollars each. That scares me a little. I’ve never been particularly fond of the nuclear pulse concept, largely for the reason I have just given, but I see now that it is the only way we will ever have of taking humanity out into the solar system, unless something truly revolutionary comes along to tip over everything we thought we understood about space travel. That kind of revolution would make Einstein’s revolutionary thinking look quite tame.
It could simply be that we all stay home and get to know the solar system by looking through telescopes instead. It’s not the cop-out that it may seem at first. Telescopes in the near future will be deployed in space that are going to be very large, much larger than telescopes that could be built on the surface of the Earth. What then will be our attitude towards exploring the planets in person when we can see through telescopes the ice melting on the surface of a comet, the cracks stretching in the ice-fields of Enceladus, the rocks flying out of volcanoes on Io? Will we still need to go out and scratch our names on the boulders of the outer planets? Sadly and irrationally, I think so! It’s just who we are. -DC, 2015