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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:

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

Tsiol

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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3 thoughts on “Sundiving, Part 1

  1. Pingback: Sundiving, Part 2 | Sublime Curiosity

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