16 Sept. 2007
SETI League
PriUPS Project

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Fun With Mirrors - Part 4

The Factor Mirror Drive

Believe it or not, this is finally a blogitem about mirrors.  Will it be fun?  Certainly so if you spend time considering spacecraft propulsion.  Perhaps not if you're still concerned about painting your driveway.

But First, a Bit of Housekeeping

I have not been as indolent as it would appear from the gap between today and Part 3.  I've been in and out of computer hell as happens too often.  But I have both resurrected my little PC that I use to make podcasts out of these blogitems, and also posted my earlier blogitems on Google's "Blogspot" service, which has a cooperative arrangement with Odiogo.  This effort has almost brought to completion the creation of my podcasts for older 2006 blogitems.  There are a tiny handful left that I want to read myself because I fear the computer voice won't be able to make enough sense of them given their formatting.  Additionally, I am caught up to "yesterday" and may well even finish "today" by the time this item is published.  Whew!

The Solar Sail

You may remember reading about an unusual spacecraft that was recently launched.  It was sponsored by The Planetary Society and was called Cosmos 1.  What was unusual was its method of propulsionit was to use a "solar sail" to adjust and raise its orbit.  Although it failed to reach orbit due to launch problems, it is widely agreed that the theory is sound.  The sun emits radiationphotonswhich carry energy.  In the previous three blogitems, I talked about the heating effect of these photons.  They warm the earth.  But there is a lesser known true photon fact:  They also carry momentum.  When a photon hits something solid and is absorbed, it also absorbs the momentum of that photon, which tends to push it in the same direction the photon was going.  If the photon is reflected by something solid, such as a mirror, the photon gives it a double push!  If enough photons hit a very light mirror, such as the one borne by the Cosmos 1, the push is significant enough to impart measurable velocity to the mirror.  And, if the mirror is attached to a spacecraft, it, too, is accelerated. 

The great problem with rockets is that they require energy and mass to go fast.  Chemical rockets, barely adequate for exploring the solar system, solve the problem by using an enormous amount of fuel, which contains mass and chemical energy, to propel a relatively tiny payload.  The advantage of the solar sail is that the spacecraft needs no fuel.  It is literally powered by sunbeams.  Unfortunately, with any mirror-sail that can be built with current technology, the limited area for intercepting and reflecting solar photons isn't enough to produce much acceleration.  Can we do better?

The Mirror Space Drive

I think so.  Solar photons contain a lot of energy.  Again from the past few days' calculations, we calculated that just the energy absorbed by one year of CO2 emissions, itself a tiny percentage of the total from CO2, and orders of magnitude less than the total for other causes, was over a terawatt-year.  That's a lot of energy!  Can we use the enormously potent solar photons to propel a solar sail more efficiently?  Let's try a thought experiment:

Put a mirror on the moon.  Let's make it a big mirror, with a variable focus.  Maybe a rotating pool of mercury with a variable spin rate, or maybe just some movable panels of Mylar.  Now, let's take our solar sail space ship and aim the reflected solar photons at this mirror, which will return them to the ship, which will return them to moon, and so forth.  What do we accomplish by this?  In effect we are amplifying the sunlight.  Instead of each photon bouncing off the sail, imparting a tiny bit of momentum, and returning to empty space, we are reusing the photon.  What amplification factor can we get?  Ten?  100?  More?  It would depend on how clean the mirrors are, how carefully they are aimed, how much leakage there is, how efficient they are, etc.  This isn't an engineering study, just a concept, but certainly the answer is "many!"

Anything that multiplies the efficiency of a space drive by "many" times has got to be good. 

Note to Science Fiction Writers

I haven't seen this concept written up anywhere.  In particular, the Wikipedia article doesn't mention using mirrors to increase a solar sail's acceleration.  But I haven't read everything.  If I stole this from you, albeit unknowingly, please email me the name of the book in which it appears, and I shall happily credit you.  If you want to steal it from me, please be sure to call it the "Factor Mirror Drive," which, apart from giving proper credit, sounds pretty neat, if I do say so myself.

Note to Celestial Engineers and Rocket Scientists

Don't spend more than a minute thinking about why this "can't work."  Just as do you, I give full credence to two important conservation laws, energy and momentum.  The Factor Mirror Drive violates neither.  Consider a single photon bouncing between two perfect mirrors fixed to each other.  Theoretically the photon will continue to bounce forever.  No energy is lost by the photon in reflection, and no momentum is imparted to either mirror (or if it is, the other mirror, fixed to the first, counteracts it in the next bounce.)  Therefore, there is no net change of motion of the two-mirror system and the photon will maintain its energy.

Now, remove the constraint that the mirrors be fixed to each other.  When the photon hits one mirror, twice the photon's momentum is imparted to the mirror and it starts to move away from the other mirror.  Likewise another 2-times momentum loss occurs at the other mirror, which also accelerates away from the first.  In each case, the photon loses energy due to doppler (red) shift caused by radiation from an object that's moving away.  In other words, the photon's energy is absorbed by accelerating the mirror masses.

As for practical consideration:  The visible spectrum, where most of the sun's radiation is concentrated, is one octave wide, from 380nm to 750nm.  If the mirror covers just this band, and can keep reflecting 'til a 380nm photon is dopplered down to a 750nm photon, it will allow 50% of the photon's energy to be used to separate the spaceship/moon system, for an efficiency of 25%.  At slow separation speeds, that's a lot of reflections!  At larger separations, implying greater relative velocities, it would be many fewer reflections, but the optical efficiency of the system would suffer at the greater distance.  It would be fun to postulate more nearly perfect mirrors or giant mirrors of planetary dimensions that could boost a spaceship to near light speed.  But right now, I'll just settle for a working Factor Mirror Drive to increase the efficiency of my solar sail.

NP:  "(I'm Always Touched) By Your Presence, Dear" - Blondie

Richard Factor

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