This file contains notes to the Energy Page.
Kenneth Phillips, Guide to the Sun (CUP, 1992), p.39, 83, 314-18. Measurements made from the ACRIM instrument on the Solar Maximum Mission satellite (1980-89) and the ERB detector on Nimbus 7 (launched 1978).
I understand that the Solar Irradiance is the total amount of solar power in the form of electromagnetic radiation of all wavelengths falling on the disk of the Earth. Of this total, some will be reflected back out into space, some absorbed by air, ground and sea and later re-radiated at a longer wavelength, and some absorbed by the biological system where it does biological work before being re-radiated at a longer wavelength as waste heat.
A. C. Phillips, The Physics of Stars (2nd ed., Wiley, 1994, 1999), p.34 gives the solar luminosity as 3.862 x 1026 W
Note that the actual total energy budget of planet Earth is different, because the concept of an Earthpower makes no attempt to take into account the energy generated within the Earth herself through radioactive decay -- the energy which drives volcanoes, earthquakes and continental drift. The point of the term "Earthpower" is simply to have a convenient, easily visualised measure for large amounts of power. Or, we might say: the Earth's true energy budget consists of the Radiant Earthpower (from the Sun) plus the Internal Earthpower (from within).
John S. Lewis, Mining the Sky (Helix Books, Addison-Wesley, 1996), p.210-11 gives global power consumption as 8,500 GW, in rough agreement.
How long might an interstellar voyage take?
Suppose that the aim was to colonise a new planetary system. The explorers setting out would not want to run too great a risk of being overtaken by a later expedition before they arrived at their goal. Let us imagine that a ship could be built which would make the crossing to a certain star in 1000 years. Assuming a civilisation similar to our own, it would seem likely that well within 500 years a faster ship could be built that would make the trip in half the time. Under such conditions the 1000-year ship would probably not be built.
Might a 100-year ship be launched? That depends again on whether it was anticipated that within 50 years a faster ship could be built which would make the voyage in 50 years or less -- and that economic and political conditions would still be favourable for starship-building at that future date. Obviously this will be a matter for judgement at the time, and the prospective interstellar voyagers will have to go by their best guess of what the future might hold.
Even so, I can imagine several reasons why slow interstellar voyages (lasting centuries or millennia) might be undertaken.
Firstly, a group of people might experience political repression from a regime which controls an entire planetary system. If they had the resources to propel a space habitat into a slow journey to a neighbouring system, they might undertake that voyage in order to free their descendants from repression and start again. Of course they would be subject to the danger that the regime they are fleeing might detect their departure and send a faster ship to chase after them, or might attempt to colonise the target system in any case. On the other hand, experience on Earth has shown that repressive regimes tend to be bad at high technology, suggesting that on the one hand our escapees might well succeed in their bid for freedom, but on the other that they might not need to escape at all if the government they detest loses power through its own internal inefficiencies.
Secondly, an organisation within a rich society might anticipate imminent social and economic decline, perhaps through the threat of war or the growing popularity of an anti-technology ideology. If they did not expect the ideology of progress to recover before they had made the crossing and if there was nowhere for them to hide within their home planetary system, they might venture on a slow transfer to another system.
Again, a planetary system might be threatened with natural calamity. In their novel Encounter with Tiber (Hodder and Stoughton, 1996), Buzz Aldrin and John Barnes force their fictional inhabitants of the Alpha Centauri system onto interstellar voyages by means of a swarm of asteroids which render the system too dangerous for them to remain. A serious change in the radiation from the central star would have the same effect, although this would not happen often in the case of main-sequence stars like our Sun, and even less often to red dwarfs (assuming that red dwarfs could host indigenous advanced life, which is moot). Aldrin and Barnes's aliens are able to build fast interstellar spacecraft, but had they not detected the threat until later they might have had to manage with slow ones.
Finally, it is conceivable that a community living in a space colony might for some reason prefer life in interstellar space rather than in a planetary system, and so would undertake slow interstellar crossings for their own sake, stopping only occasionally to replenish their resources, particularly of energy. This could happen if planetary systems tend to rapidly become overpopulated to the point of claustrophobia, hard as this may be for us to imagine now.
Exhaustion of resources is not a likely motivation. The resources of a stellar system are so vast that the wherewithal to build a fast starship is trivial in comparison. Neither can we anticipate any technological barrier to fast ships, depriving the slow ones of competition, since a vehicle cruising at near ten per cent of the vacuum speed of light will clearly become possible with near-future developments in nuclear fusion (see the Daedalus study by the British Interplanetary Society, 1978), providing that extensive space industrialisation takes place.
We may conclude that a fast interstellar passage would be likely to take a few decades. Much longer than that, and technical progress could be expected to overtake a slow starship; much faster, and the gain in time would not be worth the additional cost, since progress would in any case not have had time to create a ship capable of catching up. If we anticipate a lengthened human lifespan by the time such voyages are attempted, this again suggests that the additional expense of cutting down say a 20-year ferry to a 10-year one would not be considered worthwhile. Naturally, this picture is liable to be modified by political, economic and psychological factors which can hardly be guessed at in advance.
A cruising speed in the region of 40,000 km per second (13% of light speed) seems reasonable. This is equivalent to travelling the circumference of the Earth every second, or the Earth--Sun distance every hour. Mind-boggling as such a velocity may seem, it still takes about 38 years to reach Alpha Centauri, with acceleration and deceleration phases at the beginning and end of the journey of a couple of years each and an unpowered cruise of some 34 years.
In all discussions of spacecraft driven by high-thrust rocket propulsion there are two crucial figures: the exhaust velocity ve, which reflects the energy content of the fuel used, and the delta-V, or total change in velocity desired for a particular mission before the rocket is discarded or refuelled. These affect the mass ratio R, which is the starting mass of the complete vehicle divided by its final mass when the fuel has all been used up (or: the mass of fuel required to drive each tonne of spacecraft is equal to R-1). These are related by the rocket equation:
delta-V = ve times the natural log of R
When ve is less than about half the desired delta-V, small changes in ve produce massive changes in R. Thus if ve is one quarter of the delta-V, R is 55, and therefore 54 tonnes of fuel are needed to propel each tonne of engines, tanks and payload. If ve is reduced or the delta-V increased until their ratio is 5 instead of 4, R now works out at 148, requiring 147 tonnes of fuel to propel each tonne of the spacecraft -- obviously totally impractical. Ideally, the exhaust velocity needs to be at least of the same order of magnitude as the delta-V.
I assume a two-stage starship, in which the first stage boosts the ship onto its unpowered interstellar coast, while the second stage decelerates the ship at the destination star system.
If the cruising speed is set at 40,000 km per second, then the delta-V for each stage will also be 40,000 km per second. Can we actually build a ship with this capability? Clearly we can if we can find a fuel with an exhaust velocity of around ve = 25,000 km per second, or greater. The BIS Daedalus study thought that ve = 10,000 km per second might be achievable with the fusion of deuterium and helium-3 using near-future engineering. A value of twice this does not seem unrealistic and has the advantage of making a fast starship possible, so I assume ve = 25,000 km per second, whence the ratio delta-V / ve = 1.6 and therefore R = 5. (This is very close to the point of maximum energy efficiency.)
If the initial acceleration of the ship is 2% of one Earth gravity, then the transit time to any star equals the distance to that star in light-years plus an extra 0.535 light-year, divided by 0.13. Transit times to some nearby stars will then be:
How much energy does this starship consume? The energy consumed by a rocket is given by the formula: 1/2 the fuel mass times the exhaust velocity squared. If we consider the energy required per tonne of spacecraft (excluding fuel), Es, then this is given by:
Es = 0.5 (R - 1) ve2
That is for a one-stage vehicle. With a two-stage one, a more specific design has to be sketched out. A plausible design has a payload of 19 (in arbitrary mass units), a second stage dry mass of 6 (i.e. tanks and engines), a first stage mass of 36, and second and first stage fuel loads of 100 and 644 respectively. This allows us to calculate a value of 12 x 1015 Joules per kilogram of payload mass for the one-way journey.
How heavy might we make our starship payload? On the one hand it would be nice to have a manned starship (manned, that is, by both men and women, obviously); on the other, we would not want to be too extravagant in this first sketch. 30,000 tonnes is a convenient mass to visualise, being about the weight of a small ocean liner. We may imagine that within this sort of figure there is enough material structure to provide all the life-support systems needed for say a few hundred passengers and crew, given likely advances in engineering strong but lightweight structures in space.
We then arrive at our answer of an energy consumption of 30,000 times 1000 (kilograms per tonne) times 12 x 1015 = 3.6 x 1023 Joules, or 1.0 x 1014 MWh.
Marshall Savage also arrives at exactly this figure (The Millennial Project, p. 327).
We are of course talking about a "conventional" starship, i.e. one powered by rocket propulsion. It would accelerate for a couple of years, cruise in free fall for a few decades at somewhere between 10 and 20 per cent of the speed of light, and then decelerate for a couple more years at its target star.
"Warp drive" is a purely science fiction concept, not a serious engineering one. Astrophysicists who talk about dropping starships into black holes or wormholes in spacetime to speed them to their destinations are speculating!
The most plausible power source for a rocket-propelled starship would be the Martin--Bond nuclear pulse engine, based on the fusion of deuterium with helium-3. Such an engine has been sketched in considerable technical detail in the report on Project Daedalus, published in 1978 by the British Interplanetary Society. It was thought feasible to send the Daedalus probe on a fifty-year one-way flyby trip past Barnard's Star, at a range of 5.97 light-years.
The Daedalus design would need improvement before it became suitable for a ship capable of decelerating at its destination. Firstly, the cruising speed of 12.2% of the vacuum speed of light would be halved to a relatively slow 6.1%, pushing up the transfer time to even the nearest stars to close to a century. Secondly, the main nuclear reaction which powers the ship, of deuterium with helium-3, is triggered by a small core of deuterium and tritium, which is easier to ignite. Since tritium is radioactive with a half-life of only 12 years or so, after several decades of cruise this fuel would become useless and the ship would be unable to fire its engine to decelerate.
The use of antimatter to store solar energy remains a tantalising possibility. The problems of manufacture, storage and use in any kind of engine seem likely to be extremely difficult to solve.
Whether either fusion engines or antimatter engines or both will ever become economical is a question which can only be answered by getting out there and trying to build them!
Text last revised 18 May 2003 / 34th Apollo Anniversary Year