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Kinetic Energy
Why visiting alien spaceships are impossible

Basaed on Sid Deutsch's article "Why Visiting Alien Spaceships are Impossible" in Skeptical Briefs, June 2008, page 4, with much additional material gathered from Couper & Henbest's Encyclopedia of Space (Dorling Kindersley, London 2003), Kaufmann & Freedman's Universe 5th edition (Freeman, New York 1999), Swinerd's How Spacecraft Fly (Springer, New York 2008), Millis and Davis's Frontiers of Propulsion Science (American Institute of Aeronautics and Astronautics 2009), and Wikipedia (June 2009). Sid Deutsch is a professor of engineering retired from the Polytechnic University in Brooklyn, New York.

Unintelligently designed to increase air resistance

Believers in UFOs should get acquainted with E = 0.5mv². The E stands for kinetic energy, the energy required to get a stationary spaceship (or anything else) of mass m moving at velocity v. When v approaches 20% light speed, the required E increases to roughly 0.5mv² + 0.375mv⁴/c², where c is the speed of light 3 x 10⁸ metres per second (beyond 20% light speed the E given by this equation is increasingly too small). Specifically, the kinetic energy required to reach 10% or 50% of light speed is increased by 0.8% or 26% over that indicated by E = 0.5mv², so the increase can be ignored for speeds up to one-tenth light speed. At 100% light speed the increase is infinite, which is why light speed cannot be exceeded.

As we shall see, kinetic energy explains why visiting alien spaceships are impossible, or at least (even if not theoretically impossible) not realistically achievable. Just do the sums!

Doing the sums
What might be realistic values of velocity v and mass m? The distances in outer space are unimaginably vast -- 4.2 light-years to the nearest star Proxima Centauri (a light-year is 1.0 x 10¹⁶ metres), 10 light=years on average to the 30 closest stars such as Sirius and Procyon, 350 light-years on average to the 20 brightest stars such as Canopus and Betelgeuse, maybe a 1000 million light-years to the other side of the universe. So speeds of at least a fraction of light speed would be needed.

Suppose the spaceship travelled at one-tenth light speed. Its velocity v would be 30,000,000 metres per second, enough to get it from London to Sydney in 1/20th of a second. If it came from the nearest stars 10 light-years away, the journey to Earth would take a century. If it came from one of the brightest stars the journey might take fifty centuries. Beyond this we could be talking thousands or millions of centuries. ETs would need either suspended animation or much patience.

What might be a realistic value for mass m? The Mars Surface Module, in which a human crew could live for 260 days, will weigh around 150,000 kg -- and that's just for existing on Mars. To get the crew to Mars and then back to Earth will each require another spacecraft of around 150,000 kg (this is with crew and spacecraft starting from Earth orbit), making the total around 450,000 kg, same as the international space station. So an alien spaceship assembled in orbit around its home planet might have to weigh at least 500,000 kg, including fuel, if its inhabitants (even tiny ones) are to survive journeys of many years or centuries. Even this weight is only a quarter of what a NASA space shuttle weighs at takeoff, so it is nothing if not optimistic.

Relevant quantities
Kinetic energy in joules = 0.5 x mass in kg x (velocity in metres per second)². Work at the rate of 1 joule per second = 1 watt. Sun's radiation near Earth is about 1.4 x 10³ watts per square metre. One watt of radiation absorbed by one square metre produces a radiation pressure of 3.4 x 10^-10 kg, twice this if the radiation is reflected in the opposite direction. Pressure from the impact of particles in the solar wind is negligible (about 1/5000th of the sun's radiation pressure). An acceleration of 1 g increases the speed every second by 9.8 metres per second.

Substituting the numbers
Substituting the numbers, the kinetic energy of a 500,000-kg spaceship travelling at one-tenth light speed is E = 0.5 x 500,000 x 30,000,000² = about 2 x 10²⁰ joules. For comparison, the entire generating capacity of the United States power system is about 10¹² watts = 10¹² joules per second, which is still tiny compared to the Sun's 4 x 10²⁶ watts. If by some magic we could harness the USA's output to our spaceship, it would take 2 x 10²⁰/10¹² = 2 x 10⁸ seconds to bring it up to speed, or more than six years. And magic would indeed be needed, because thrust is what moves spaceships, not energy. A spaceship in a forest fire would be receiving lots of energy but, in the absence of magic, no thrust.

There is more. After the first second the kinetic energy of the 500,000-kg ship would be 10¹² joules, which when equated to 0.5 x 500,000 x v² gives v = 2000 metres per second. Which means that during the first second the ship is accelerating at 2000 / 9.8 = 204 g. A 50-kg super model would weigh in at ten tonnes before being squashed flat.

Finding the energy
Producing 10¹² joules per second = 3 x 10¹⁹ joules per year requires the equivalent every year of burning 700,000,000,000 kg of kerosine or fissioning 500,000 kg of uranium (all of it, not just the part that is fissioned in a reactor before reprocessing) or fusing 150,000 kg of hydrogen as deuterium. Fitting six yearsworth twice over into a 500,000-kg spaceship would be a challenge.

For comparison, 10¹² joules per second is equivalent to pushing more than 3000 NASA space shuttles, each with a takeoff weight of 2,000,000 kg, simultaneously into orbit. It would get a typical heavy payload of 20,000 kg into orbit in two-thirds of a second at an acceleration of 3500 g. If applied to an average 1000-kg car, it would do 0-60 mph in 0.000,0004 seconds, be close to light speed in five minutes, and be past Mars in another ten, always assuming it could survive the acceleration and wasn't destroyed by hitting a speck of dust. Yes, that sort of power corrupts absolutely. But what if less power is applied for longer periods? Would that get around the problem?

Life in the slow lane
Regardless of whether the spaceship is propelled by chemical rockets or by more efficient ion drives and nuclear thermal drives, both of which might reduce the fuel load by 90%, or by laser beams required to somehow lock on targets too far away to be seen quickly enough, if the spaceship is to reach velocity v then it has to acquire 0.5mv² of energy from somewhere. If ETs in suspended animation don't care how long their journey takes, the v's can be smaller and the energy required can be less daunting. For example, if the spaceship travelled at the same speed as the Voyager probe when it left the solar system (16,000 metres per second), it could travel ten light-years in about 2,000 centuries -- a mere nothing compared with the 2,000,000 centuries since the age of dinosaurs.

Contrary to what we might expect, tiny accelerations permanently applied can have surprisingly big results. For example a permanent acceleration and then deceleration of 10^-6 g (meaning an average person would weigh little more than a postage stamp) would reach stars 10 or 100 light-years away in about 65 or 200 centuries at a maximum of 1/300th or 1/100th light speed. The thrust of 0.5 kg needed by our 500,000-kg spaceship could be obtained from the sun's radiation pressure near the Earth by a reflector 0.5 sq km in area, roughly 60 football fields. But to maintain thrust the reflector would need to quadruple in area (and therefore weight) each time the distance from the sun doubled, meaning 60,000 football fields when level with Pluto, and indefinitely more in deep space.

Alternatively the spaceship could start as close to its home star as would be possible without frying the reflector, tack sideways to maximise the starshine and build up speed, then swing by a suitable planet to use the planet's speed to slingshot itself out of the system. In this way a 500,000-kg spaceship with 1000 sq metres of reflector for every kg of mass (60,000 football fields) could leave our solar system at about 140,000 metres per second, enough to reach Proxima Centauri in 95 centuries. To merely escape from the solar system would need 600 square metres of reflector for every kg of mass, which just for the reflector is equivalent to a film of plastic about 1/10,000 mm thick, less if a payload is to be carried, but even this would be so fragile that it could not be assembled except in the weightlessness of space.

Star trekking?
What about warp drives, where the spaceship expands space-time behind it and contracts space-time ahead of it, effectively bringing the destination closer? And wormholes, where travel through higher dimensions provides a short cut through ordinary space-time? Both ideas have been explored by theoretical physicists, and both seem to require more energy than an entire planet could provide, plus matter with negative mass that may not even exist except in a Hollywood movie.

Running on empty
The problem of course is that a ship running on sunshine is useless when the lights go out. And even when the lights are on, the thrust is very very tiny. For example, take an everyday 2-watt flashlight of mass 0.4 kg, switch it on, and leave it in space. The radiation pressure will be 2 x 3.4 x 10^-10 = 7 x 10^-10 kg, so it would accelerate at 7 x 10^-10 / 0.4 = 1/600,000,000 g. After 24 hours it would be speeding at 1.5 millimetres per second after a journey of 65 metres. If its batteries lasted (always a problem), and we ignore gravity effects, it would be at Proxima Centauri after only 700 centuries. Even if its batteries lasted only a month, it would still make the journey in 300,000,000 centuries.

Nothing lasts forever
These huge timescales bring their own problems. For example, suppose methods of suspending animation for thousands of centuries were possible, along with ETs willing to endure them on the offchance of finding something interesting at the other end -- and on the offchance that construction materials and control equipment would survive centuries of cosmic ray bombardment, and the decay of any radioisotopes needed for power generation. Even if radio communication was possible, ETs on their home planet could never know the outcome unless they too entered suspended animation for the required thousands of centuries (all wasted if the offchance didn't come good or they missed the wakeup call). They would also need some way of surviving the many years or centuries between sending a radio message and receiving a reply. Such timescales may not be impossible but they do seem unworkable.

But suppose some ETs were willing to have a go, and could persuade their stay-at-home others to channel resources into an expedition with no hope of the stay-at-homes learning anything, as might apply if the home planet was dying and migration of the fittest was the only option. Indeed, the required resources might be so extreme that only a situation like this could justify them. For example when finished the international space station will have cost $US130,000 million without actually going anywhere, and sending men to Mars is likely to cost ten times this, or roughly $US200 for every person on Earth. Unless there is no alternative, interstellar travel seems unlikely to be popular with the masses.

From the Australian skeptic magazine the Skeptic

Travelling vs arriving
But even if ETs gave it the green light, there is still the problem of steering along the way when the lights are out, like playing a pin table in the dark with a ball that takes years to move between pins. And of protecting the spacehip against centuries of impact by space dust and micrometeorites, to say nothing of the man-made debris in near-Earth orbit -- currently hundreds of thousands of chunks bigger than 1 cm, tens of millions if smaller. Colliding with just a one-milligram chunk at one-tenth light speed would release 0.5 x 0.000,001 x 30,000,000² = about 5 x 10⁸ joules of energy, equivalent to being hit by a ten-tonne truck travelling at 1000 kph. So the spaceship would need bumper shields, outer skins with gaps between them that disrupt each impact.

But bumper shields would quickly burn up during atmospheric entry, so a lander with heat shields would be needed. In which case entering the Earth's atmosphere would be a trip of no return unless the lander carried enough brute rocket power for a safe landing and takeoff back into orbit, and once again the numbers are against it, especially if no remnants (like the descent part of the lander) are to be left behind. Alternatively, if entry was designed to be one-way on the offchance that the Earth was suitable and free of fundamentalist hostility (but how could ETs know this without landing?), our satellite surveillance should have noticed the landing party by now.

Abductions?
The last national wave of UFO sightings in the USA occurred in 1973. It was replaced by claims of alien abductions that by 1995 were no longer generating interest. If the several million Americans who claim to have been abducted were really abducted instead of experiencing an everyday waking disorder, then as Carl Sagan famously remarked, "You'd think the neighbours would notice".

Concluding remarks
The above energy calculations show that an alien spaceship sighted by reliable witnesses would have needed something like a six-year shove by the entire US power system. Not just at takeoff but also at arrival after a journey taking centuries. It couldn't be done unless the power needed was reduced, thus increasing the journey time to hundreds or thousands of centuries. Either way, whether based on energy or travel time, the numbers don't allow it. Believers in UFOs will of course claim that alien spaeships come from a superior civilization, so "they can somehow do it." But this would require changing the laws of physics so that E does NOT = 0.5mv², which is not possible.

Nevertheless scientists have for many years been working on the problems of interstellar travel, which essentially boil down to the problems of propulsion. Their latest findings are collected in Frontiers of Propulsion Science, a 739-page anthology of highly technical articles for graduates and engineers edited by M Millis and E Davis (American Institute of Aeronautics and Astronautics 2009, $US129.95, a version for general readers is planned). The specialist authors survey every currently conceivable way to reach the stars including warp drives, gravity control, and faster-then-light travel. They conclude that rockets are fundamentally inadequate. Plausible alternatives may be achievable in 20-50 years, while others such as worm holes and warp bubbles, even if theoretically possible, will be very difficult and may never be achievable.

In the meantime, whenever someone claims to have spotted an alien spaceship, your response should be: "Whatever you saw couldn't realistically be an alien spaceship." At the end of the day, you need to decide which is the more likely -- an alien spaceship or someone making a mistake.

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