Every time the question of nuclear waste disposal comes up, someone is sure to say, “Why not shoot it into the Sun?” It seems so obvious. The Sun’s a fine big target, and you’ll get there if you shoot straight up. The usual objection is that if a launch rocket failed, we’d get nuclear waste dumped on our heads. No one seems to consider the real objection: the Sun is the most inaccessible destination in our entire solar system.

Moving in Space

Let’s consider some orbital dynamics. If we launch a spacecraft at “escape velocity” (11.2 km/sec), it will never fall back to Earth. As it still shares Earth’s orbital velocity, some 30 km/sec, it remains in orbit around the Sun. It can’t fall into it any more than the Earth can.

A spacecraft launched with more than escape velocity ends up with a residual velocity relative to Earth. If this is directed in the same direction Earth is moving, the spacecraft will enter an elliptical orbit that will take it farther from the Sun. After a little more than a year it will return to Earth’s orbit, but Earth won’t be there. It will have had time to go around a little more than once.

If we direct our spacecraft’s residual velocity against the direction Earth is moving, it will enter an elliptical orbit that will take it closer to the Sun. It will take less than a year to return to Earth’s orbit and, once again, the Earth won’t be there. However, this is a step in the right direction.

The bad news is that to hit the Sun requires reducing the spacecraft’s velocity by nearly all of Earth’s orbital velocity. That is, we have to slow it by 30 km/sec. This is an enormous change in velocity; space probes to the nearer planets make velocity changes of only the order of 4 km/sec.

Since we also have to apply 11.2 km/sec just to get into space, it might seem that we need an acceleration of 41 km/sec to get to the Sun. The good news is that velocities can’t be combined; in space energies are combined. To get from the surface of Earth to the Sun we need an acceleration of “only” 32 km/sec. So how big a rocket do we need to dump one ton of waste into the Sun?

Now for Some Rocket Science

The acceleration a rocket provides depends on two things: how powerful a fuel it uses and how little the rocket’s structure and payload weigh relative to the amount of fuel it can carry. I’ll use some optimistic numbers to spare you the mathematics. For brevity, I’ll use “weighs” to mean “has a mass of.”

Assume we use the best known fuel (liquid hydrogen and liquid oxygen) and suppose that the fuel tanks, the engines, and the control system are 10 percent of the initial mass of the rocket. That is, 90 percent of its take-off mass is fuel. For the moment I’ll ignore the mass of the payload—that is, whatever useful cargo the rocket carries.

The maximum velocity this idealized rocket can achieve is just over 10 km/sec, not quite enough to escape from Earth and a long way short of the 32 km/sec we need to reach the Sun. As soon as we add a load of any kind, the final velocity will be lower. If the payload weighs the same as the structure, the final velocity will be 7.5 km/sec. Our rocket will head into space, slow to a stop, and fall back down again.

The secret of spaceflight is “staging.” Take that 7.5 km/sec rocket and put it on top of a much bigger rocket with the same proportions. The result is a rocket capable of accelerating the original payload to 15 km/sec but at the cost of a large increase in the take-off mass.

Suppose the payload weighs one ton, and assume that the structure of the topmost stage weighs the same. This structure holds nine tons of fuel, so the total mass of the top stage is eleven tons. This mass forms the payload of the bigger stage that lifts it, so the latter weighs 121 tons. If we put another stage underneath, it will weigh 1,331 tons. That’s a total of 1,463 tons, about half as much as a Saturn-V. If each stage adds 7.5 km/sec, we are up to 22.5 km/sec, a remarkable velocity but way short of the 32 km/sec we need.

To cut a long story short, the final Sun rocket not only has to have four stages, but the payload of each stage has to be cut to about 74 percent of the structure mass. To dispose of one ton of nuclear waste will require a 44,000-ton rocket. If we assume a more realistic launch mass of 3,000 tons (about Saturn-V size), the payload that finally reaches the sun will weigh about 68 kg (under 150 lbs). The trash bill comes to about $8 million per pound.

This calculation was based on rather optimistic values for fuel energy and structure mass. It also ignores the fact that a large part of the payload should consist of a steel canister. This serves three purposes: it provides radiation shielding for ground handling, it ensures that a launch failure won’t disperse the waste, and it gives the payload some chance of reaching the Sun without being vaporized and carried away in the solar wind.

Aiming for the Stars

Putting a spacecraft on a non-return flight into interstellar space is much easier than hitting the Sun. To reach the Sun you need to subtract 100 percent of Earth’s orbital velocity; to reach solar escape velocity you need only add 41 percent to it. The total velocity increment from takeoff becomes 16.73 km/sec. A three-stage rocket with a launch mass of 120 tons could send one ton of nuclear waste to the stars; a Saturn-V sized rocket could send twenty-five tons.

The Sun would be a great trash-can, but it’s too darn difficult to get to.

Verne’s novels contain much technical detail. Is this real science or is it technobabble—that mishmash of scientific-sounding terms that obscures the otherwise unspecified means by which a story’s protagonists achieve their goals? Does forgotten Victorian technology that could power today’s electric cars lie behind Verne’s stories, or was he merely bamboozling his readers?

The Search for the Source

I read several of Verne’s stories when I was about twelve. Back then it bothered me that his characters seemingly derived unlimited electrical power from a relatively small battery. I recently reread “Five Weeks in a Balloon” to refresh my memory. This book is not great literature but was Verne’s first best seller, and it was the story that drew my junior skeptic’s attention.

A few months ago I was browsing through Barnes and Noble’s bargain books and noticed some omnibus editions of classic authors. Sure enough, there was a heavy volume containing seven Verne stories. It didn’t reproduce the original illustrations, but it cost much less than online sellers were asking for used copies of “Five Weeks in a Balloon” alone.

Taking to the Air

“Five Weeks in a Balloon,” published in 1863, is a straight-forward adventure story set in Africa. By the 1860s, Africa had been explored by Europeans for a century or more. Expedition after expedition had returned with most of their members dead from disease, starvation, or the predations of hostile natives. Verne’s proposal was that if a balloon’s altitude could be controlled without constantly dumping ballast or venting gas, it could cross Africa driven only by the prevailing winds. Rivers, rough terrain, and unfriendly aborigines could be avoided by flying over them. The three adventurers of “Five Weeks in a Balloon” set off from Zanzibar and, after many harrowing escapes, arrive in Senegal.

At the time Verne was writing, hydrogen-filled balloons had just found their first practical application as battlefield observation platforms in the American Civil War. Elongated, powered, steerable balloons were still forty years in the future. He proposed a technological solution similar to that used in today’s long-distance balloon flights. His balloon had two gas bags, one inside the other and both containing hydrogen. The height of the balloon was controlled by circulating the gas through a heated tube. As the heat expanded, the hydrogen in the balloon rose; cutting off the heat let the balloon descend. Simple!

In modern balloons, one gas bag contains helium to provide most of the lift, and the other contains air heated by a propane burner. How long a modern balloon can stay in the air depends on how many propane tanks it can carry at lift-off.

Infinite Hot Air

Verne circumvents the issue of fuel consumption with some pseudoscientific hand-waving of which our present-day free-energy promoters would be proud. Like them, he makes things sound plausible until you look at the numbers. The hydrogen in Verne’s balloon is heated by burning a mixture of hydrogen and oxygen. (Remember Dennis Lee and Brown’s gas? Verne used it first.) These gases are produced by “decomposing” water with electricity from a “powerful Buntzen [sic] battery.”

This battery reappears in later books as the Bunsen battery, the real but low-power battery invented by Robert Wilhelm Bunsen in 1841. Like the feeble dry cells of my youth, the Bunsen battery had electrodes of graphite and zinc; Bunsen used chromic acid as the electrolyte rather than ammonium chloride. Verne’s battery is apparently capable of providing thousands of kilowatt hours from a weight of a few hundred pounds.

Battery technology has improved considerably since Verne’s time, but this is still a performance that car manufacturers would kill for. Practical capacities are orders of magnitude lower than Verne assumes.

Electrolysis Does the Trick

There is a hint in the story that limitless supplies of separated hydrogen and oxygen can be had just by applying voltage to water. This nonsensical idea has been embraced by free-energy and improved-gas-mileage promoters alike. Fiction has metamorphosed into fraud in only 145 years. In real life the rate of gas production is proportional to the current that flows, and thus it is proportional to the electrical power consumed.

The heat generated by burning the gases evolved from an electrolytic cell is significantly less than the heat that could be generated from the original electrical input. Verne’s explorers should have connected an electric heater directly to the battery. The extra complication of electrolysis is just there to befuddle the reader.

The Ubiquitous Bunsen Battery

The Bunsen battery crops up again in “A Journey to the Center of the Earth.” One obvious problem with underground adventuring is how to provide illumination. Verne’s solution is an antique version of today’s compact fluorescent lamp. His heroes carry “Ruhmkorff’s apparatus,” which, a footnote explains, is a Bunsen pile (battery), an induction coil, and an evacuated spiral tube. These devices are apparently capable of supplying light for many weeks, a task that would defeat any modern battery, even one that, like Verne’s, is carried in a backpack.

Modern backpackers must envy Verne’s three heroes. After several weeks underground they congratulate themselves on still having four weeks’ food remaining. Considering that they are also carrying ropes, guns, ammunition, fifty pounds of guncotton(!), shovels, blankets, and Ruhmkorff’s apparatus, one wonders how they managed even to stand up.

The electric battery reaches its apotheosis in “20,000 Leagues under the Sea.” Captain Nemo’s Nautilus is powered by sodium, presumably used as a battery electrode. This sodium is replenished at an underground base where coal is mined and used to extract the sodium from seawater. Curiously, the immense screw of the Nautilus is turned by the electrical equivalent of a reciprocating steam engine with electromagnets taking the place of the cylinders. One shudders to think how inefficient this would be.

Space Travel

Verne’s technobabble reaches its peak in “From the Earth to the Moon.” In this book and its sequel “Around the Moon,” Verne goes into great circumstantial detail, quoting so many weights and dimensions that one wonders why no Ark hunters have switched their focus to Florida, where Verne’s equally mythical 900-foot moon gun is presumed to still lie buried in Stone Hill. With 68,000 tons of cast iron as a prize, perhaps the only thing deterring them is the difficulty of locating a 1,600-foot hill in Florida.

Many commentators have pointed out that being fired from a giant cannon would reduce any passengers to a pulp. Once in space, Verne’s travelers feel a diminishing pull toward Earth. This leads to weightlessness only at the “neutral point” between the Earth and the moon. In the century prior to the Apollo missions, Verne’s misapprehension became common wisdom. The idea that the projectile and its occupants are falling freely and hence are equally weightless has never quite taken hold.

On the plus side, Verne’s heroes quite properly use rockets to adjust the course of their projectile. We can’t blame Verne for the once common belief that space travel is impossible because “rockets need air to push against.”

Verne’s Chemistry

Supplying the vessel with air would be possible in theory. Potassium chlorate is heated to release oxygen. This is standard Victorian chemistry, although Verne omits the addition of manganese dioxide as a catalyst to speed up the rate of oxygen evolution. Exhaled carbon dioxide is absorbed by potassium hydroxide.

The potassium chlorate is heated by burning what seems to be methane (Verne’s chemical terminology can be confusing) whose source is unspecified and, seemingly, unlimited. This gas also supplies light when sunlight is not sufficient. Burning gas, of course, uses up some fraction of the evolved oxygen. Oddly enough, that ideal source of heat and light, the amazing Bunsen battery, doesn’t appear in either “From the Earth to the Moon” or its sequel.

The air-regenerating chemicals carried in the vessel are quoted as being sufficient for three people for two months. With no recycling, each person in a spacecraft consumes about a kilogram of oxygen per day. A back-of-envelope calculation indicates that Verne’s oxygen generator would need an initial supply of nearly half a ton of potassium chlorate. A comparable quantity of potassium hydroxide would be needed to absorb carbon dioxide.

However, neither potassium chlorate nor potassium hydroxide are substances I would want to carry with me in a confined space. When ignited, potassium chlorate reacts explosively with flammable materials, and the corrosive effect of spilt potassium hydroxide on the aluminum hull would be spectacular.

Accident or Purpose?

From our modern perspective, Verne’s stories contain many scientific blunders. Some reflect the common beliefs of the time, and some reveal Verne’s unfamiliarity with astrophysics. Often the science is sound enough, but he greatly exaggerates the available resources. On the other hand, much that passes for science is simply a great author not letting the facts get in the way of telling an engrossing story.