What are the main problems with beaming light from the Sun to Saturn?

Question

I recently finished reading the Kim Stanley Robinson novel 2312 - set, of course, in the year 2312. Part of the background to the political negotiations and ongoing terraforming in the outer Solar System involves the transfer of energy to Titan, one of Saturn's moons, from the Vulcanoids, a population of asteroids orbiting the Sun. As far as I can tell, this involves focusing light from the Sun on the asteroids into fine beams, which are then transmitted to Titan with high precision. The energy then warms the moon, and plays a role in the ongoing terraformation.

Speculating on the fine details of realistic technology three centuries in the future is maybe too much even for Worldbuilding Stack Exchange, but I'd like the know some of the main hurdles engineers would have to overcome to do this, even starting in the present day.

What are the physical challenges involved in sending beams of light to Titan, and how could they be overcome, using technology from today or perhaps in the near future (the coming decades)? I know that laser attenuation is going to be troublesome, but are there any other issues, and can they be combated?

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As an addendum, I'd certainly enjoy seeing hard-science answers, but they are absolutely not mandatory (hence, the absence of the tag). MichaelK has written an excellent non-hard-science answer that answers the question well, and I'd love to see others like it. However, there may be bonus points for anyone who takes the hard-science plunge.

Answer 1

The problem is that "focused" does not really mean "concentrated"

Everyone that has ever played with a magnifying glass "know" that you can take the light from the Sun and turn it into an infinitely concentrated dot. This is in essence a variant what you are trying to do.

The problem here is two things:

1. The only reason you can get a dot that small is because the magnifying glass is very close to the "target", compared to the distance to the light source.

2. That is not actually an infinitely concentrated dot; it is a focused image of the Sun.

That is not a very small dot of light, that is an image of the Sun. (Image source)

It turns out that you cannot gather up light and make it go in a beam that is more narrow leaving your light gathering device than it was when it came in. The light beam will always be at least as wide, or wider. To explain this in full detail requires a university course in optics, but in short the principle is called The Conservation of Étendue, and if you want some really hard science I encourage you to read on that link. But it is way too advanced — and it will not serve anyone's purpose — to quote that in full here.

So you will forgive me if I focus the answer a bit. Or rather: concentrate it. ;) And if the answer below seems boring or hard to grasp, I recommend xkcd: what if #145.

When you use optics to move light from a light source, and project it somewhere else, the smallest you can make the projected light is when you attain an image of the light source that is in perfect focus. "In focus" in this case does not mean "concentrated to a very small spot", but instead means that you can see every detail of the light source clearly, because it is not blurred. Simple rules of optics dictate that you can not make the projected light any smaller than this.

The next rule of optics say that the perfect way to project a light source some place else is the pinhole "lens". With a pinhole you will always attain a perfectly focused projection, so with a pinhole, you will always attain the smallest projection.

The next rule of optics say that an infinitely small and perfectly flat mirror is like a pinhole, only that it has the added benefit of being able to bounce the projected image in some other direction.

Yet another rule of optics says that every lens — like the magnifying glass above or in the case of the question: your sun beam device — can be approximated by assuming it consists of an infinite number of infinitely small mirrors. The projection from the lens is just all of these images from the mirrors overlaid on each other.

Now comes the kicker:

The size of a perfectly focused image, using a pinhole, is proportional to the original in the same way that the distance between the lens and the image, and the lens and the light source is proportional to each other.

If you divide the size of the image with the size of the original, you get a ratio... say 1 to 10, the image is 10 times smaller.

That ratio is the same as between the distance from the hole to the image, and the distance from the hole to the original. So if the camera is 1 meter deep, then the distance to the tree is 10 meters.

For your project this means that this "lens" of yours — and I say again: all lenses, optics and other such devices can be approximated by an infinite numbers of mirrors, that in turn are like pinholes — must be closer to Titan than to the Sun. Otherwise the projected image of the Sun on Titan will be larger than the Sun itself and therefore weaker in intensity; you gain as near to nothing it makes no odds.

Assuming you want this focusing device of yours to not waste any sunlight by making it fall outside of Titan, the image of the Sun must be smaller than Titan itself. And since the ratio between the size of the Sun and the size of Titan is about 279 : 1, it will not really make any sense to use this scheme of yours until you have gotten your concentrating device so close to Titan that the distance from this device to Titan, divided by the distance from the device to the Sun, is 1 over 279...

... i.e. you are nearly there anyway.

You might as well then put your reflectors in orbit around Titan and harvest the sunlight there. This also means that you do not need to spread it all over Titan but can put it in spots of greater importance.

Answer 2

There are vibration based minimum size limits

Summary: If you are using either a laser or some other focusing mechanism, there is a minimum size limit to such a device, below which it will not be able to accurately deliver its energy at great distances due to vibration.

Assertion: A laser mounted on ISS could not accurately hit an object the size of Titan at the distance from the Vulcanoids to Saturn due to the vibration of ISS.

Vibration measurements

For the International Space Station, we can get estimated vibration from Figure 1 of this paper. Vibration is graphed as frequency in hertz versus acceleration in root mean square micro-g's.

Vibration can be modeled with simple spring dynamics, so that the position of a sinusoidally moving spring is give by $$x(t) = A\sin(2\pi f t)$$ where A is amplitude, f is frequency and t is time. We are given root mean square acceleration, and we wish to find amplitude. Acceleration is the second time derivative of position $$a(t) = -A(2\pi f)^2\sin(2\pi f t)$$ and the root means square acceleration is the magnitude of the acceleration sine function over the square root of 2, expressed as $$a_{rms} = \frac{A (2\pi f)^2}{\sqrt{2}}.$$ We can solve this last equation for $A$ in terms of $a_{rms}$ and $f$, both given to us in Figure 1. I measured the various points on that figure, and got a maximum vibration amplitude of about 4 mm at about 1 Hz.

Projecting this vibration to Titan

Using basic trigonometry (right triangles, basically), we can determine the effects of this vibration on a distant target. If a laser pointer of length $l$ were vibrating at 4mm, and it were pointed at an object of radius $r$ at a distance of $d$ away, vibrations would cause the object to be missed entirely if $$\frac{4\text{mm}}{l} \gt \frac{r}{d}.$$

Since we are dealing with Titan, we can use the radius of Titan as $r = 2576000 \text{ m}$ and the distance between the Vulcanoids and Titan, about $d = 1.346e12\text{ m}$ at minimum (roughly 10% more at maximum). Plugging in $r$ and $d$ with our given 4 mm of vibration, we find that our laser pointer must be about 2 km long for the amplitude of the vibrations to be less than the radius of our target.

Alternately, we can say that if the focus were 100 m long, roughly the length of the ISS, then the maximum allowed amplitude of vibrations in the ISS would be 0.2 mm. Either way, it is clear that ISS is too small and vibrates too much to reliably hit Titan at 9 AU distance.

Mitigating factors

Since it is left open-ended in the question what the actual mechanism of power delivery over this great distance is, these vibration limits answer the question of "what are the main problems."

The first and most obvious mitigating factor is to simply make the focusing mechanism very large. If the focusing mechanism were built into one of the Vulcanoid asteroids, that would help alot.

The second obvious mitigating factor is to create vibration buffering mounts for any heavy equipment in the station. Modern industrial equipment is tuned to be remarkably vibration free: the GE LM2500 marine gas turbine engine alarms at 0.1 mm vibration amplitude; Wartsila's W20 (20 cylinder) marine diesel generates about 0.25mm vibration on the block during normal operations.

Still, even with very low vibration levels, the inaccuracy of the beam at such a distance is notable. If the projection of vibration on the target is a significant percentage of the target's radius, the delivery system may not be adequate for the purposes of whoever is paying to have this energy delivered.

Sunlight delivered this way, for example, wouldn't be very useful for growing plants. Lasers aimed at a power station on Titan wouldn't be of much use either. The magnitude of the vibration problem depends a lot on the uses of the delivered energy.

Answer 3

There is a fairly brute force means of achieving these ends, and you can "handwave" a bit to say Robinson is describing parts of this device.

What you want is an Artificial Laser Star. Using the ionized plasma of the solar photosphere as the lasing medium, it is possible to build laser emitters of immense power and beam energy to Saturn (or well out into the Oort cloud, for that matter). Indeed, something like this could be used to launch laser lightsail driven starships much like Robert L Forward suggested.

One version of the Artificial Laser Star involves a series of mirrors orbiting the sun. A laser is fired into the platoon and bounces around the sun in a ring between the mirrors. As the ring passes through the ionized plasma of the photosphere, a population inversion occurs and more laser light is generated, with the ring acting as the "cavity" of the laser and the mirrors as the resonating mirrors. When the beam is of the appropriate power, one of more of the mirrors is "half silvered" (probably by manipulating the reflective index of the material) and the beam is emitted into space.

Now the biggest issue here isn't creating the beam or using "Vulcanoids" as the mounts for the mirrors and control devices, but rather how to keep a continuing beam aimed at Saturn (or more specifically, Titan). In order to do this and prevent incinerating spaceships and planets which might pass through the beam path, the beam should be emitted above the plane of the ecliptic, and at one or more mirrors in highly eliptic orbits around the sun. These mirrors then redirect the beam back to another series of mirrors (probably in polar orbit around Saturn), which then direct he beam onto Titan. Fresnel lenses or diffraction gratings could be used as substitutes for mirrors, if desired.

The other advantage of this system is the beam can actually be allowed to diverge, since it can be refocused by the relay mirrors or lenses between the Sun and Saturn.

Answer 4

Focusing light this way is not really the way light works, as the nice answer by MichaelK describes. However, simply focusing the Sun's light is a sortof-naïve thing to do anyway. Making enormous mirrors or especially lenses is difficult, and visible light suffers some diffraction-related issues. Hence:

The engineering and Physics problems are greatly reduced if, should you want to "beam" something, you make the beam yourself.

Specifically, I suggest gathering energy, and then using it to pump a high-frequency laser. This can be done with solar panels (in orbit, or on an asteroid (which you would have to move into place)). Near the Sun, panels can pick up more energy, but heat is a major problem. Perhaps a thermocouple from e.g. Mercury's surface to its interior would work better.

On the Titan side, you scoop up most of the laser's energy and use it. An IR laser would be easier to generate, but a gamma-ray laser carries more energy and also would have less diffraction. Happily, since Titan has a thick atmosphere, vacuum frequency lasers can be used to heat the atmosphere directly.

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But the whole idea of interplanetary-scale beamed power is sortof impractical overall. In 300 years, optimistically we have fusion, and Saturn is a rich source of fusible isotopes with a relatively shallow gravity well.

Also, since Titan is almost literally made out of rocket fuel, blasting it into a nearer Solar orbit (catalyze Oxygen compounds out of the rocks) might be easier.

Finally, if you don't care about hard-science, then you can play silly games like opening a wormhole from low-solar orbit to high-Titan orbit.

Answer 5

Light is already beamed to Saturn from the sun, however for it to have any consequences different to the usual (bit of light and heat) then you would need to separate an individual member from the spectrum of light. Essentially I'm talking about a laser. Unfortunately a focused beam of light from the sun can not have any obstruction. Fortunately space is mostly an empty void and this is unlikely to happen. However in the case of a moon orbiting Saturn it is likely that the moon will be eclipsed by its host most of the time. That is a huge problem. Another issue is that focusing light across such a long distance is incredibly hard as light disperse over distance. My only modern solution would essentially be an extremely long fibre optic cable. Lastly it will be have a very small difference on the heating effect of the whole moon but instead on a very small single point. I hope this helps.