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# Sundiving, Part 2

(NOTE: After re-reading this post in 2021, I’m starting to doubt the validity of the math and physics here. I’m keeping the post up for posterity, but I’m warning you: read this with a very critical eye.)

In the previous post, I figured out how to get a spacecraft to an altitude of one solar radius (meaning one solar radius above the Sun’s surface, and two solar radii from its center). That’s nice and all, but unless we figure out how to get it the rest of the way down intact, then we’ve essentially done the same thing as a flight engineer who sends an astronaut into orbit in a fully-functional space capsule, but forgets to put a parachute on it. (Not that I know anything about that. Cough cough Kerbal Space Program cough…)

The sun is vicious. Anyone who’s ever had a good peeling sunburn knows this, and cringes at the thought. And anyone who, in spite of their parents’ warnings, has looked directly at the sun, also knows this. But I’ve got a better demonstration. I have a big 8.5 x 11-inch Fresnel lens made to magnify small print. I also have a lovely blowtorch that burns MAP-Pro, a gas that’s mostly propylene, which is as close as a clumsy idiot like me should ever come to acetylene. Propylene burns hot. About 2,200 Kelvin. I turned it on a piece of gravel and a piece of terra cotta. It got them both orange-hot, but that was the best it could do. The Fresnel lens, a cheap-ass plastic thing I bought at a drugstore, melted both in seconds (albeit in very small patches), using nothing more than half a square foot of sunlight.

Actually, the area of that magnifier is handy to have around. It’s 0.0603 square meters. On the surface of the Earth, we get (very roughly) 1,300 watts per square meter of sunlight (that’s called the solar constant). To melt terra cotta, I have to get the spot down to about a centimeter across. The lens intercepts about 80 Watts. If those 80 Watts are focused on a circle a centimeter across, then the target is getting irradiated with 770 solar constants, which, if it was a perfect absorber, would raise its temperature to 2,000 Kelvin. If I can get the spot is half a centimeter across, then we’re talking 3,070 solar constants and temperatures approaching 3,000 Kelvin.

And while I was playing around with my giant magnifier, I made a stupid mistake. Holding the lens with one hand, I reached down to re-position my next target. The light spot, about the size of a credit card, fell on the back of my hand. I said words I usually reserve for when I’ve hit my finger with a hammer. This is why you should always be careful with magnifying lenses. Even small ones can burn you and start fires.

The area of a standard credit card is about 13 times smaller than the area of my lens, so my hand was getting 13 solar constants. And even a measly 13 solar constants was more than enough to sting my skin like I was being attacked by a thousand wasps. Even at the limit of my crappy Fresnel lens, somewhere between 770 and 3,070 solar constants, we’re already in stone-melting territory.

At an altitude of 1 solar radius, our Sundiver will be getting to 11,537 solar constants. Enough to raise a perfect absorber to 4,000 Kelvin, which can melt every material we can make in bulk. Our poor Sundiver hasn’t even reached the surface and already it’s a ball of white-hot slag.

Except that I’ve conveniently neglected one thing: reflectivity. If the Sundiver was blacker than asphalt, sure, it would reach 4,000 Kelvin and melt. But why on Earth would we paint an object black if we’re planning to send it to the place where all that heat-producing sunlight comes from? That’s even sillier than those guys you see wearing black hoodies in high summer.

My first choice for a reflective coating would be silver. But there’s a massive problem with silver. Here are two graphs to explain that problem:

(Source.)

(Source is obvious.)

The top spectrum shows the reflectivities of aluminum (Al), silver (Ag, because Latin), and gold (Au) at wavelengths between 200 nanometers (ultraviolet light; UV-C, to be specific: the kind produced by germicidal lamps) and 5,000 nanometers (mid-infrared, the wavelength heat-seeking missiles use).

The bottom spectrum is the blackbody spectrum for an object at a temperature of 5,778 Kelvin, which is a very good approximation for the solar spectrum. See silver’s massive dip in reflectivity around 350 nanometers? See how it happens, rather inconveniently, right around the peak of the solar emission spectrum? Sure, a silver shield would be good at reflecting most of the infra-red light, but what the hell good is that if it’s still soaking up all that violet and UV?

Gold does a little better (and you can see from that spectrum why they use gold in infrared mirrors), but it still bottoms out right where we don’t want it to. (Interesting note: see how gold is fairly reflective between 500 nanometers and 1,000 nanometers, but not nearly as reflective between 350 nanometers and 500 nanometers? And see how silver stays above 80% reflectivity between 350 and 1,000? That’s the reason gold is gold-colored and silver is silver-colored. Gold absorbs more green, blue, indigo, and violet than it does red, orange, and yellow. Silver is almost-but-not quite constant across this range, which covers the visible spectrum, so it reflects all visible light pretty much equally. Spectra are awesome.)

Much to my surprise, our best bet for a one-material reflector is aluminum. My personal experiences with aluminum are almost all foil-related. My blowtorch will melt aluminum, so it might seem like a bad choice, but in space, there’s so little gas that almost all heat transfer is by radiation, so it might still work. And besides, if you electropolish it, aluminum is ridiculously shiny.

(Image from the Finish Line Materials & Processes, Ltd. website.)

That’s shiny. And it’s not just smooth to the human eye–it’s smooth on scales so small you’d need an electron microscope to see them. They electro-polish things like medical implants, to get rid of the microscopic jagged bits that would otherwise really annoy the immune system. So get those images of crinkly foil out of your head. We’re talking a mirror better than you’ve ever seen.

Still, aluminum’s not perfect. Notice how its reflectivity spectrum has an annoying dip at about 800 nanometers. The sun’s pretty bright at that wavelength. Still, it manages 90% or better across almost all of the spectrum we’re concerned about. (Take note, though: in the far ultraviolet, somewhere around 150 nanometers, even aluminum bottoms out, and the sun is still pretty bright even at these short wavelengths. We’ll have to deal with that some other way.)

So our aluminum Sun-shield is reflecting 90% of the 15.7 million watts falling on every square meter. That means it’s absorbing the other 10%, or 1.57 million watts per square meter.

Bad news: even at an altitude of 1 solar radius, and even with a 90% reflective electropolished aluminum shield, the bastard’s still going to melt. It’s going to reach over 2,000 Kelvin, and aluminum melts at 933.

We might be able to improve the situation by using a dielectric mirror. Metal mirrors reflect incoming photons because metal atoms’ outer electrons wander freely from one atom to another, forming a conductive “sea”. Those electrons are easy to set oscillating, and that oscillation releases a photon of similar wavelength, releasing almost all the energy the first photon deposited. Dielectric mirrors, on the other hand, consist of a stack of very thin (tens of nanometers) layers with different refractive indices. For reference, water has a refractive index of 1.333. Those cool, shiny bulletproof Lexan windows that protect bank tellers have a refractive index of about 1.5. High-grade crystal glassware is about the same. Diamonds are so pretty and shiny and sparkly because their refractive index is 2.42, which makes for a lot of refraction and internal reflection.

These kind of reflections are what make dielectric mirrors work. The refractive index measures how fast light travels through a particular medium. It travels at 299,792 km/s through vacuum. It travels at about 225,000 km/s through water and about 124,000 km/s through diamond. This means, effectively, that light has farther to go through the high-index stuff, and if you arrange the layers right, you can set it up so that a photon that makes it through, say, two layers of the stack will have effectively traveled exactly three times the distance, which means the waves will add up rather than canceling out, which means they’re leaving and taking their energy with them, rather than canceling and leaving their energy in your mirror.

This, of course, only works for a wavelength that matches up with the thickness of your layers. Still, close to the target frequency, a dielectric mirror can do better than 99.9% reflectivity. And if you use some scary algorithms to optimize the thicknesses of the different layers, you can set it up so that it reflects over a much broader spectrum, by making the upper layers very thin to reflect short-wavelength light (UV, et cetera) and the deeper layers reflect red and infra-red. The result is a “chirped mirror,” which is yet another scientific name that pleases me in ways I don’t understand. Here’s the reflection spectrum of a good-quality chirped mirror:

(Source.)

Was I inserting that spectrum just an excuse to say “chirped mirror” again? Possibly. Chirped mirror.

Point is, the chirped mirror does better than aluminum for light between 300 and 900 nanometers (which covers most or all of the visible spectrum). But it drops below 90% for long enough that it’s probably going to overheat and melt. And there’s another problem: even at an altitude of 1 solar radius, the Sundiver’s going to be going upwards of 400 kilometers per second. If the Sundiver crosses paths with the smallest of asteroids (thumbnail-sized or smaller), or even a particularly bulky dust grain, there’s going to be trouble. To explain why, here’s a video of a peanut-sized aluminum cylinder hitting a metal gas canister at 7 kilometers per second, 57 times slower than the Sundiver will be moving:

We have a really, really hard time accelerating objects anywhere near this speed. We can’t do too much better than 10 to 20 km/s on the ground, and in space, we can at best double or triple that, and only if we use gravity assists and clever trajectories. On the ground, there are hypersonic dust accelerators, which can accelerate bacterium-sized particles to around 100 km/s, which is a little better.

But no matter the velocity, the news is not good. A 5-micron solid particle will penetrate at least 5 microns into the sunshade (according to Newton’s impact depth approximation). Not only will that rip straight through dozens of layers of our carefully-constructed chirped mirror, but it’s also going to deposit almost all of its kinetic energy inside the shield. A particle that size only masses 21.5 picograms, so its kinetic energy (according to Wolfram Alpha) is about the same required to depress a computer key. Not much, but when you consider that this is a bacterium-sized mote pressing a computer key, that’s a lot of power. It’s also over 17,000 times as much kinetic energy as you’d get from 21.5 picograms of TNT.

As for a rock visible to the naked eye (100 microns in diameter, as thick as a hair), the news just gets worse. A particle that size delivers 110.3 Joules, twenty times as much as a regular camera’s flash, and one-tenth as much as one of those blinding studio flashbulbs. All concentrated on a volume too small to squeeze a dust mite into.

And if the Sundiver should collide with a decent-sized rock (1 centimeter diameter, about the size of a thumbnail), well, you might as well just go ahead and press the self-destruct button yourself, because that pebble would deliver as much energy as 26 kilos (over 50 pounds) of TNT. We’re talking a bomb bigger than a softball. You know that delicately-layered dielectric mirror we built, with its precisely-tuned structure chemically deposited to sub-nanometer precision? Yeah. So much for that. It’s now a trillion interestingly-structured fragments falling to their death in the Sun.

My point is that a dielectric mirror, although it’s much more reflective than a metal one, won’t cut it. Not where we’re going. We have to figure out another way to get rid of that extra heat. And here’s how we’re going to do it: heat pipes.

The temperature of the shield will only reach 2,000 Kelvin if its only pathway for getting rid of absorbed heat is re-radiating it. And it just so happens that our ideal shield material, aluminum, is a wimp and can’t even handle 1,000 Kelvin. But aluminum is a good conductor of heat, so we can just thread the sunshade with copper pipes, sweep the heat away with a coolant, and transfer it to a radiator.

But how much heat are we going to have to move? And has anybody invented a way to move it without me having to do a ridiculous handwave? To find that out, we’re going to need to know the area of our sunshade. Here’s a diagram of that sunshade.

I wanted to make a puerile joke about that, but the more I look at it, the less I think “sex toy” and the more I think “lava lamp.” In this diagram, the sunshade is the long cone. The weird eggplant-shaped dotted line is the hermetically-sealed module containing the payload. That payload will more than likely be scientific instruments, and not a nuclear bomb with the mass of Manhattan island, because that was probably the most ridiculous thing about Sunshine. Although (spoiler alert), Captain Pinbacker was pretty out there, too.

The shield is cone-shaped for many reasons. One is that, for any given cross-sectional radius, you’re going to be absorbing the same amount of heat no matter the shield’s area, but the amount you can radiate depends on total, not cross-sectional, area. Let’s say the cone is 5 meters long and 2 meters in diameter at the base. If it’s made of 90% reflective electropolished aluminum, it’s going to absorb 4.93 megawatts of solar radiation at an altitude of 1 solar radius. Its cross-section is 3.142 square meters, but its total surface area is 16.02 square meters. That means that, to lose all its heat by radiation alone, the shield would have to reach a blackbody temperature of 1,500 Kelvin. Still almost twice aluminum’s melting point, but already a lot more bearable. If we weren’t going to get any closer than an altitude of 1 solar radius, we could swap the aluminum mirror out for aluminum-coated graphite and we could just let the shield cool itself. I imagine this is why the original solar probe designs used conical or angled bowl-shaped shields: small cross-sectional area, but a large area to radiate heat. But where we’re going, I suspect passive cooling is going to be insufficient sooner or later, so we might as well install our active cooling system now.

Heat pipes are awesome things. You can find them in most laptops. They’re the bewildering little copper tubes that don’t seem to serve any purpose. But they do serve a purpose. They’re hollow. Inside them is a working fluid (which, at laptop temperatures, is usually water or ammonia). The tube is evacuated to a fairly low pressure, so that, even near its freezing point, water will start to boil. The inner walls of the heat pipe are covered with either a metallic sponge or with a series of thin inward-pointing fins. These let the coolant wick to the hot end, where it evaporates. Evaporation is excellent for removing heat. It deposits that heat at the cold end, where something (a passive or active radiator or, in the case of a laptop, a fan and heat sink) disposes of the heat.

Many spacecraft use heat pipes for two reasons. 1) The absence of an atmosphere means the only way to get rid of heat is to radiate it, either from the spacecraft itself, or, more often, by moving the heat to a radiator and letting it radiate from there; heat pipes do this kind of job beautifully; 2) most heat pipes contain no moving parts whatsoever, and will happily go on doing their jobs forever as long as there’s a temperature difference between the ends, and as long as they don’t spring a leak or get clogged.

On top of this, some heat pipes can conduct heat even better than solid copper. Copper’s thermal conductivity is 400 Watts per meter per Kelvin difference, which is surpassed only by diamond (and graphene, which we can’t yet produce in bulk). But heat pipes can do better than one-piece bulk materials: Wikipedia says 100,000 Watts per meter per Kelvin difference, which my research leads me to believe is entirely reasonable. (Fun fact: high-temperature heat pipes have been used to transport heat from experimental nuclear reactor cores to machinery that can turn that heat into electricity. These heat pipes use molten frickin’ metal and metal vapor as their working fluids.)

The temperature difference is going to be the difference between the temperature of the shield (in this case, around 1,500 Kelvin at the beginning) and outer space (which is full of cosmic background radiation at an effective temperature of 2.3 Kelvin, but let’s say 50 Kelvin to account for things like reflected light off zodiacal dust, light from the solar corona, and because it’s always better to over-build a spacecraft than to under-build it).

When you do the math, at an altitude of 1 solar radius, we need to transport 4.93 megawatts of heat over a distance of 5 meters across a temperature differential of 1,450 Kelvin. That comes out to 680 Watts per meter per Kelvin difference. Solid copper can’t quite manage it, but a suitable heat pipe could do it with no trouble.

But we still have to get rid of the heat. For reasons that will become clear when Sundiver gets closer to the Sun, the back of the spacecraft has to be very close to a flat disk. So we’ve got 3.142 square meters in which to fit our radiator. Let’s say 3 square meters, since we’re probably going to want to mount things like thruster ports and antennae on the protected back side. Since we’re dumping 4.93 megawatts through a radiator with an area of 3 square meters, that radiator’s going to have to be able to handle a temperature of at least 2,320 Kelvin. Luckily, that’s more than manageable. Tungsten would work, but graphite is probably our best choice, because it’s fairly tough, it’s unreactive, and it’s a hell of a lot lighter than tungsten, which is so dense they use it in eco-friendly bullets as a replacement for lead (yes, there’s such a thing as eco-friendly bullets). Let’s go with graphite for now, and see if it’s still a good choice closer to the Sun. (After graphite, our second-best choice would be niobium, which is only about as dense as iron, with a melting point of 2,750 Kelvin. I’m sticking with graphite, because things are going to get hot pretty fast, and the niobium probably won’t cut it. (Plus, “graphite radiator” has a nicer ring to it than “niboium radiator.”)

Our radiator’s going to be glowing orange-hot. We’ll need a lot of insulation to minimize thermal contact between the shield-and-radiator structure and the payload, but we can do that with more mirrors, more heat pipes, and insulating cladding made from stuff like like calcium silicate or thermal tiles filled with silica aerogel.

Of course, all the computations so far have been done for an altitude of 1 solar radius. And I didn’t ask for a ship that could survive a trip to 1 solar radius. I want to reach the freakin surface! Life is already hard for our space probe, and it’s going to get worse very rapidly. So let’s re-set our clock, with T=0 seconds being the moment the Sundiver passes an altitude of 1 solar radius.

T+50 minutes, 46 seconds

Speed: 504 km/s

Solar irradiance: 28 megawatts per square meter (20,600 solar constants)

Temperature of a perfect absorber: 4,700 Kelvin (hot enough to boil titanium and melt niobium)

Total heat flux: 8.79 megawatts

Temperature of a 90% reflective flat shield: 2,700 Kelvin (almost hot enough to boil aluminum)

Temperature of Sundiver’s conical shield (radiation only): 1,764 Kelvin (still too hot for aluminum)

Required heat conductivity: 1,000 Watts per meter per Kelvin difference (manageable)

T+1 hour, 0 minutes, 40 seconds

Speed: 553 km/s

Solar irradiance: 40.3 megawatts per square meter (29,600)

Temperature of a perfect absorber: 5,200 Kelvin (hot enough to boil almost all metals. Not tungsten, though. Niobium boils.)

Total heat flux: 12.66 megawatts

Temperature of a 90% reflective flat shield: 2,900 Kelvin (more than hot enough to boil aluminum)

Temperature of Sundiver’s conical shield (radiation only): 1,900 Kelvin (way too hot for aluminum)

Required heat conductivity: 1,400 Watts per meter per kelvin difference (manageable)

T+1 hour, 5 minutes, 25 seconds

Speed: 589 km/s

Solar irradiance: 52 megawatts per square meter

Temperature of a perfect absorber: 5,500 Kelvin (tungsten melts, but still doesn’t boil; tungsten’s tough stuff; niobium is boiling)

Total heat flux: 16.34 megawatts

Temperature of a flat shield: 3,000 Kelvin (tungsten doesn’t melt, but it’s probably uncomfortable)

Temperature of our conical shield: 2,000 Kelvin (getting uncomfortably close to aluminum’s boiling point)

Radiator temperature: 3,100 Kelvin (tungsten and carbon are both giving each other worried looks; the shield can cause fatal radiant burns from several meters)

Required heat conductivity: 1,600 watts per meter per kelvin difference (still manageable, much to my surprise)

T+1 hour, 8 minutes, 11 seconds

Speed: 615 km/s

Irradiance: 61 megawatts per square meter

Temperature of a perfect absorber: 5,700 Kelvin (graphite evaporates, but tungsten is just barely hanging on)

Total heat flux: 19.38 megawatts

Temperature of a flat shield: 3,200 Kelvin (most materials have melted; tungsten and graphite are still holding on)

Temperature of our conical shield: 2,100 Kelvin (titanium melts)

Radiator temperature: 3,200 Kelvin (tungsten and graphite are still stable, but at this point, the radiator itself is almost as much of a hazard as the Sun)

Required heat conductivity: 1,900 Watts per meter per Kelvin difference (we’re still okay, although we’re running into trouble)

The Sundiver finally strikes the Sun’s surface traveling at 618 kilometers per second. Except “strike” is a little melodramatic. The Sundiver’s no more striking the Sun than I strike the air when I jump off a diving board. The Sun’s surface is (somewhat) arbitrarily defined as the depth the sun’s plasma gets thin enough to transmit over half the light that hits it. At an altitude of 0 solar radii, the Sun’s density is a tenth of a microgram per cubic centimeter. For comparison, the Earth’s atmosphere doesn’t get that thin until you get 60 kilometers (about 30 miles) up, which is higher than even the best high-altitude balloons can go. Even a good laboratory vacuum is denser than this.

But even this thin plasma is a problem. The problem isn’t necessarily that the Sundiver is crashing into too much matter, it’s that it’s that the matter it is hitting is depositing a lot of kinetic energy. Falling at 618 kilometers per second, it encounters solar wind protons traveling the opposite direction at upwards of 700 kilometers per second, for a total velocity of 1,300 kilometers per second. Even at photosphere densities, when the gas is hitting you at 1,300 kilometers per second, it transfers a lot of energy. We’re talking 17 gigawatts per square centimeter, enough to heat the shield to a quarter of a million Kelvin.

This spells the end for the Sundiver. It might survive a few seconds of this torture, but its heat shield is going to be evaporating very rapidly. It won’t get more than a few thousand kilometers into the photosphere before the whole spacecraft vaporizes.

In fact, even at much lower densities (a million hydrogen atoms per cubic centimeter), the energy flux due to the impacts of protons alone is greater than one solar constant. (XKCD’s What-If, the inspiration for this whole damn blog, pointed this out when talking about dropping tungsten countertops into the sun.) At 1.0011 solar radii, the proton flux is more than enough to heat the shield up hotter than a lightning bolt. As a matter of fact, when the solar wind density exceeds 0.001 picograms per cubic centimeter (1e-15 g/cc), the energy flux from protons alone is going to overheat the shield. It’s hard to work out at what altitude this will happen, since we still don’t know very much about the environment and the solar wind close to the sun (one of the questions Solar Probe+ will hopefully answer when (if) it makes its more pedestrian and sensible trip to 8 solar radii.) But we know for certain the shield will overheat by the time we hit zero altitude. The whole Sundiver will turn into a wisp of purplish-white vapor that’ll twist and whirl away on the Sun’s magnetic field.

But even if heating from the solar wind wasn’t a problem, the probe was never going to get much deeper than zero altitude. Here’s a list of all the problems that would kill it, even if the heat from the solar wind didn’t:

1) This close to the Sun, the sun’s disk fills half the sky, meaning anything that’s not inside the sunshade is going to be in direct sunlight and get burned off. That’s why I said earlier that the back of the Sundiver had to be very close to flat.

2) The radiator will reach its melting point. Besides, we would probably need high-power heat pumps rather than heat pipes to keep heat flowing from the 2,000 Kelvin shield to the 3,000-Kelvin radiator. And even that might not be enough.

3) Even if we ignore the energy added by the proton flux, those protons are going to erode the shield mechanically. According to SRIM, the conical part of the shield (which has a half-angle of 11 degrees) is going to lose one atom of aluminum for every three proton impacts. At this rate, the shield’s going to be losing 18.3 milligrams of aluminum per second to impacts alone. While that’s not enough to wear through the shield, even if it’s only a millimeter thick, my hunch is that all that sputtering is going to play hell with the aluminum’s structure, and probably make it a lot less reflective.

4) Moving at 618 kilometers per second through a magnetic field is a bad idea. Unless the field is perfectly uniform (the Sun’s is the exact opposite of uniform: it looks like what happens if you give a kitten amphetamines and set it loose on a ball of yarn), you’re going to be dealing with some major eddy currents induced by the field, and that means even more heating. And we can’t afford any extra heating.

5) This is related to 1): even if the Sun had a perfectly well-defined surface (it doesn’t), the moment Sundiver passed through that surface, its radiator would be less than useless. In practical terms, the vital temperature differential between the radiator and empty space would vanish, since even in the upper reaches of the photosphere, the temperature exceeds 4,000 Kelvin. There simply wouldn’t be anywhere for the heat to go. So if we handwaved away all the other problems, Sundiver would still burn up.

6) Ram pressure. Ram pressure is what you get when the fluid you’re moving through is too thin for proper fluid dynamics to come into play. The photosphere might be, as astronomers say, a red-hot vacuum, but the Sundiver is moving through it at six hundred times the speed of a rifle bullet, and ram pressure is proportional to gas density and the square of velocity. Sundiver is going to get blown to bits by the rushing gas, and even if it doesn’t, by the time it reaches altitude zero, it’s going to be experiencing the force of nine Space Shuttle solid rocket boosters across its tiny 3.142-square-meter shield. For a 1,000-kilogram spacecraft, that’s a deceleration of 1,200 gees and a pressure higher than the pressure at the bottom of the Mariana Trench. But at the bottom of the trench, at least that pressure would be coming equally from all directions. In this case, the pressure at the front of the shield would be a thousand atmospheres and the pressure at the back would be very close to zero. Atoms of spacecraft vapor and swept-up hydrogen are going to fly from front to back faster than the jet from a pressure washer, and they’re going to play hell with whatever’s left of the spacecraft.

Here’s the closest I could come to a pretty picture of what would happen to Sundiver. Why do my thought experiments never have happy endings?

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# Sundiving, Part 1

Ever since I saw the bizarre, quirky, and entertaining film Sunshine, I’ve been mildly obsessed with the idea of spacecraft flying very close to the Sun. I must give a SPOILER ALERT, but the ship in Sunshine flew right into the Sun. We humans haven’t come anywhere near that close. There’s MESSENGER, the recently-deceased spacecraft that gave us our best-yet view of Mercury. And then there’s Helios 2, which came within 43 million kilometers of the Sun, which is closer to the Sun than Mercury ever gets. (Helios 2 holds another awesome record: the fastest-moving human artifact. At perihelion, it was going over 70 kilometers per second. If you fired an M-16 at one end of a football field at the moment Helios 2 passed the start line (I’m borrowing XKCD’s awesome metaphor here), the bullet would barely have traveled four and a half feet by the time Helios 2 got to the other end. Also, Helios 2 would be far beyond the finish line by the time your brain even registered that it had crossed the start line.)

There are plans to probe the Sun much closer, though. NASA is currently working on Solar Probe+, which I’m really hoping doesn’t get canned next budget cycle. Solar Probe+ will, after half a dozen Venus gravity assists, pass eight times closer to the Sun than Mercury: 5.9 million kilometers, or 8.5 solar radii. I must point out that the original design, which never got a proper name, was much, much cooler. It looked like this

(Source.)

and it was going to make one hell of a trip. It was going to fly out to Jupiter, get a reverse gravity assist to kill its angular momentum, and then plunge down within 4.5 solar radii. Here’s what a sunrise would look like if Earth orbited at 4.5 solar radii:

(Rendered, of course, with Celestia.)

See that tiny object in the top-right corner? That’s the Moon, for comparison. Hold me. I’m scared.

Both the original Solar Probe mission and Solar Probe+ had to solve all sorts of brand-new engineering problems. For instance: how do you design a solar panel that can operate hotter than boiling water? How do you pack instruments onto a spacecraft when the shadow of its shield is a cone not much bigger than the shield itself? What the hell do you even build a shield out of, when it has to operate well above 1,000 Kelvin, has to cope with sunlight  3,000 times as intense as what we get on Earth, and has to be mounted on a spacecraft that will, at closest approach, be traveling 291 times faster than a rifle bullet, and will therefore be crashing through solar wind protons and dust grains moving at least as fast as that?

But that’s nothing compared to what I have in mind (to nobody’s surprise). I don’t want to design a probe that can get within 4.5 radii of the Sun. I want a probe that can get closer than one solar radius. I want a space probe that can dive straight into the sun. Not only that, but I want it to be alive and intact when it hits the Sun’s “surface.” This is why NASA will never, ever hire me.

To my surprise, the first problem I have to solve has nothing to do with heat (which will be more than enough to boil a block of iron) or radiation (which will be more than enough to sterilize a cubic meter of that sludge that festers in un-flushed gas-station toilets). The first problem is: How the hell do we get there in the first place?)

I’ll refer you to Konstantin Tsiolkovsky (whose proper Russian name isКонстанти́н Циолко́вский. Why am I telling you that? Because I really like the look of Cyrillic.) Tsiolkovsky is one of those guys who was so ahead of his time he makes you half believe in time travel. He was imagining rockets and space elevators in the freakin’ late 1800s. Before there were even cars, he was thinking about flying to other planets. And he graced us frail mortals with one of the coolest equations in engineering

To put it in less mathematical (and far uglier) terms: the mass ratio R of your rocket (that is, its mass when it’s full of fuel divided by its mass when the tanks are all empty) must be equal to the exponential of your desired change in velocity (delta-V) divided by your effective exhaust velocity (v_e, which is a measure of how efficient your rocket is).

Believe it or not, there’s a reason I’m taking this insane roundabout route to my point. In its orbit around the Sun, the Earth travels about 30 kilometers per second. A spacecraft that just barely manages to escape Earth’s gravity well will be traveling very close to zero speed, relative to the Earth, which means it will also be traveling at around 30 kilometers per second. In order to know how big a booster we’ll need to kill 30 kilometers per second (which will let our probe drop straight down into the Sun), we use 30 km/s as our delta-V. But what’s our exhaust velocity?

Consider the awesome Rocketdyne F-1 engine, five of which powered the Saturn V’s first stage

That’s Wernher von Braun standing by the tail end of a Saturn V first stage, with the five amazing and terrifying F-1 engines behind him. This image fills me with childish glee, because I’ve actually stood exactly where von Braun stood without even knowing it. I’ve seen that very booster. I’ve had my picture taken standing by those mighty engine bells. That’s because that first stage is on display (or at least it was last time I checked) at the U.S. Space and Rocket center in Huntsville, Alabama, which was my favorite place to go on vacation when I was a kid. Suffice to say, those engines are every bit as impressive as they look.

The F-1 engines burned liquid oxygen and ultra-high-grade kerosene (which amuses me). They managed a specific impulse (another measure of efficiency which will be very familiar to my fellow Kerbal Space Program addicts) of 263 seconds, for an effective exhaust velocity of 2.579 km/s. Plugging that into our formula, we get a horrifying number: 112,700. That’s right: if we want to kill our orbital velocity relative to the Sun using Saturn V engines, our rocket is going to have to be over a hundred thousand times heavier when full than when empty. That means that, out of the total mass of our rocket when it reaches interplanetary space, only 0.0009% can be anything other than fuel. For comparison, the Saturn V itself had a mass ratio of somewhere around 25, and as far as rockets go, that’s ridiculously large. 112,700 is just dumb, like giving an RPG character a sword the size of an armor plate off a battleship (I’m looking at youFinal Fantasy…).

The problem is that damnable exponent. As we learned in a recent post, as soon as you start putting decent-sized numbers in an exponent, you get ridiculous numbers out the other end.

Lucky for us, there are engines with much higher exhaust velocities. If you have an afternoon to spare, have a wander around Winchell Chung’s unbelievably awesome website Project Rho, which also fills me with childish glee. He’s compiled an amazing compendium of all the facts and equations a lover of science, fiction, and science fiction could ever want. Everything from the exhaust velocities of all the engines physics allows to the number of cubic meters of living space a crewmember needs to stay sane.

According to Project Rho and some of my own research, the NERVA engine (which quite literally produced thrust by passing hydrogen gas over the extremely hot core of a nuclear reactor) managed an exhaust velocity of about 8 km/s in vacuum. (Once again, Kerbal Space Program players will be no stranger to the nuclear rocket’s excellent efficiency and terrible, mosquito-fart thrust.) Putting 8 km/s into the rocket equation, we get a mass ratio of 43. Let’s say our sun-diving spacecraft weighs 1000 kilograms, the miscellaneous equipment weighs 100 kilograms, and for every kilogram of liquid hydrogen, we need a kilogram of fuel tank (that’s a pretty low-ball estimate, surprisingly. I did the math, and now I feel like my brain is frying in my skull. I’ve gotta lay off these side calculations…) Then our spacecraft will mass 46,200 kilograms. That’s surprisingly manageable. Wolfram Alpha tells me you could carry that mass in a 747’s cargo hold. Of course, you have to get that whole mass to Earth escape velocity somehow, which means at least another 92,000 kilograms. Not unmanageable, but pretty out-there.

Besides, there are better options. We could, for instance, use an ion engine. Ion engines are infamous for being absurdly efficient (the one on the Dawn spacecraft that’s currently orbiting Ceres manages 30 km/s exhaust velocity), but having thrusts that make a mosquito fart look like an atom bomb. The thrust of Dawn‘s NSTAR engine is equivalent to the weight of a coin resting on your palm. Thing is, ion engines can keep this thrust up for years at a time. And they have, which Dawn proves (it’s been firing its engine on and off for almost eight years straight). Using an ion engine, we’d need a rocket with a surprisingly sensible mass ratio of 2.72. The NSTAR engine uses xenon as propellant, so let’s say you need 10 kilograms of tank per kilogram of xenon. Even so, we’re only looking at a 1,300 kilogram spacecraft, which is only slightly larger than Dawn itself. So far, Dawn holds the record for the most delta-V expended by any spacecraft engine, at 10 km/s. It’s not too much of a stretch to imagine our sundiver canceling its 30 km/s orbital velocity.

There’s a catch. Remember that mosquito-fart thrust I was talking about? That’s going to give us an acceleration of 70 microns per second per second. My calculus is rusty, so I’ll do the naive thing and just divide 30 km/s by 70 um/s^2. That gives us 13 years. It’s gonna take 13 years for our sundiver to stop. And then it’s still got to fall all the way to the Sun. I’m not that patient.

So why not use the most awesome propulsion system ever designed by human hands. I’m not joking, either. This is, in my opinion, the coolest practical space propulsion concept I’ve ever seen: Project Orion.

If you don’t know, Project Orion was a propulsion system studied in the ’50s and ’60s in the U.S. The propulsion would be provided by nuclear bombs. Nuclear bombs dropped out the back of the ship and detonated once a second. The weirdest part of all this is that, if you ask me (and many other science nerds), Orion actually falls into the “so crazy it might actually work) category. As Scott Manley said, Project Orion is the only interplanetary propulsion system that meets three vital criteria: 1) It provides a decent amount of thrust. 2) It provides that thrust at a reasonable efficiency. and 3) It is based on technologies we already understand. That last one is very important. Maybe we’ll figure out how to build a fusion reactor someday. But, for better or for worse, we already know how to build a nuclear bomb. Not only that, but we know how to make a nuclear bomb direct its energy preferentially in one direction (since, according to Stanislav Ulam, as quoted by Scott Manley, you need to be able to do that in order to build a hydrogen bomb).

An Orion-powered spacecraft has an effective exhaust velocity of 40 km/s. That means we need a spacecraft with a mass ratio of 2.1. There’s a catch, though: the pusher plate in that diagram has to be at least 20 meters across. So, no matter how large or small our spacecraft, we’re going to have to tow that building-sized nuclear shock absorber with us. Let’s say it masses 2,000,000 kilograms (which was about the mass of a fully-loaded space shuttle). We’re looking at 4,200 metric tons of spacecraft, and we have to get all that to escape velocity first.

But this is the impatient way to kill 30 km/s. This is the way I solve problems in Kerbal Space Program, which is always a good sign that it’s not a practical solution.

Funnily enough, the practical solution is very similar to the trajectory in that comic… Instead of trying to kill 30 kilometers per second, we’re going to reach Earth escape velocity, boost ourselves into an elliptical orbit that makes us arrive slightly ahead of Jupiter in its orbit, and use Jupiter’s deep gravity well to sling us backwards along its orbit. A transfer from 1 AU to Jupiter’s distance (5.2 AU) means we’ll only be going 17 km/s when we get there, and a gravity slingshot like I’ve described allows you to change velocity by up to twice the planet’s orbital speed (and for Jupiter, orbital speed is 13 km/s, so we can have an effective delta-V of up to 26 km/s from Jupiter alone (give or take)). We don’t want that much delta-V, since we only want to cancel our 17 km/s velocity, but we can adjust how much of a kick we get simply by changing how close we come to Jupiter. The important thing is that the kick available is at least 17 km/s, which it is, with room to spare.

So we’re getting 17 km/s for free. (Not really: the energy change is always balanced perfectly between the change in velocity of the spacecraft and the (infinitesimal, but nonzero) change in velocity of the planet, as a result of their mutual gravitation.) To put it better: we’re getting 17 km/s without having to fire our engines. But we do have to fire our engines to get to Jupiter in the first place. If we do a standard Hohmann transfer,

we’ll need a delta-V of 16 km/s. If we use a NERVA engine (which I’m choosing because it’s a sensible middle-ground between the pathetic efficiency of the NSTAR and the a-little-too-much awesomeness of Orion), we can do that using a spacecraft with a mass ratio of 7. If we use Project Rho’s mass for a NERVA engine and assume 10 kilograms of tank per kilogram of hydrogen, we end up with a 17,100-kilogram interplanetary rocket. You could get that in to low Earth orbit using either a Saturn V or the much cooler-looking (but, unfortunately, more deadly) Soviet N1. By the time you get to low Earth Orbit, you’re already traveling at 7.67 kilometers per second, and to reach escape velocity only takes 3.18 km/s more. The rocket involved in launching 17,000 kilograms’ worth of interplanetary stage plus 3.18 km/s worth of Earth-escape engine is probably going to be among the largest ever constructed, but it’ll probably be no bigger than the Saturn V, the N1, or the Space Shuttle.

But as I said, I’m not a patient man. How long is it going to take to get to the Sun? The time to launch and reach escape velocity are negligible. The Hohmann transfer to Jupiter is not, requiring 2 years and 8 months. The fall inwards from Jupiter needs another 2 years and 1 month, for a total of 4 years 9 months. A lot better than the 13 years it was going to take us just to stop from Earth orbit.

And that’s where I’m going to end Part 1. Our Sundiver has launched from Earth on a skyscraper-sized rocket a little bigger than a Saturn V, entered low Earth orbit, boosted to escape velocity with its upper stage, made the transfer to Jupiter, done its swing-by, and fallen the 780 million kilometers to the Sun. As it reaches an altitude of 1 solar radius from the Sun’s surface, it’s traveling at 438 kilometers per second, which is 0.146% of the speed of light and six times faster than Helios 2. Remember how, at the beginning, I said the heat shield and the radiation weren’t the first problem? Well, now that we’re only 1 solar radius above the Sun’s surface, we can no longer ignore them. But I’ll leave that for Part 2.

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