What took more energy, the building of the Great Pyramid of Giza or the Apollo Mission? If we could convert the energy to build the Great Pyramid, would it be enough to send a rocket to the Moon and back?

Michael Marmol

No.

A Saturn V's fuel contains enough stored energy to lift up and stack about 20 pyramids worth of rock from the surface.

That's the simple physicist-style answer, based on calculating the energy required to lift idealized blocks of stone against the Earth's gravity.[1]Assume a spherical pyramid in a vacuum ... In practice, pyramid construction wasn't so simple. Thanks to friction, the Egyptians probably expended more energy dragging the stones across the ground than lifting them upward—and the "lifting upward" involved a lot of friction, too.

Most of the energy they expended was lost to the heat of friction, but about 10¹² joules of it remains in the Great Pyramid, stored as gravitational potential energy. If all this energy were liberated and—somehow—used to accelerate an Apollo spacecraft ...

... it wouldn't be enough to launch it to the Moon.

On the other hand, the reverse probably wouldn't work, either.

But maybe we're making the wrong kind of comparison. Why did Michael—like many others—compare the pyramids to the Apollo program in the first place? Perhaps it's simply that they both look like they took a huge amount of work—and maybe that's the best way to compare them.

The Great Pyramid, according to one analysis, took an average of 13,200 people 10 years to construct. The Apollo project took an average of about 200,000 people, working over a similar period of time, to launch six Moon landings and another 6-10 missions using the same equipment before and after—which, if you divided it up equally,[2]Which is a bit of a stretch, since launching a second Apollo mission probably lets you reuse a lot more of your work on the first one than building a second pyramid. is about 15,000 hours each. In other words, each Apollo mission took about the same amount of work as each pyramid.[3]The Apollo program was unpopular at the time; people thought it was a waste of money. While it's easy to remember only the excited children gathered around TVs to watch the first Moon landing, the truth is, spending public money on space exploration has never been all that popular with the general public. For all we know, the pyramids were just as unpopular with the Egyptian public in their time. They probably weren't built by slaves, but that doesn't mean everyone was happy about them.

There are all kinds of ways we could measure the energy that went into various megaprojects, but we end up making a lot of subjective judgment calls about what counts as part of the project. Instead, let's go back to the simple idea of gravitational potential energy, and see how the Great Pyramid compares to other structures by that measure.

The gravitational energy locked up in the Great Pyramid—on the order of 10¹² joules—is more than in even the biggest modern skyscrapers. The Burj Khalifa may be huge, but it's mostly empty space. Egyptian pyramids, on the other hand, are solid rock nearly all the way through.

However, the Great Pyramid isn't the human structure with the highest "gravitational potential energy" score. The Three Gorges Dam, built across the Yangtze River in China, is both taller and heavier than the Great Pyramid. It contains an order of magnitude more potential energy than the pyramid in its concrete and steel alone—without even considering the far larger potential energy of the water behind it.

The Great Pyramid has a few other big competitors. The former Fresh Kills Landfill probably had more gravitational potential energy, as do various other giant dams. The Great Pyramid of Cholula in Mexico has a larger volume than the pyramid at Giza, though probably weighs slightly less and has less potential energy.

But these are all dwarfed by our biggest rock-and-dirt-lifting projects: mines. Mining involves lifting even more matter against gravity than building concrete dams, pyramids, or landfills. Humans have put a huge amount of industrial power into digging mines, so it's no surprise that the biggest mines involve 10¹⁴ to 10¹⁵ joules of gravitational energy—orders of magnitude more than the biggest aboveground structures. After all, open-pit mines are basically reverse pyramids:

These projects are pretty big. However, the Dutch have envisioned something bigger.

In 2011, a Dutch writer launched Die berg komt er, a semi-serious plan to build an artificial mountain in the Netherlands. Some versions of the plan would involve moving far more material than in even the largest mines, and the immense weight would probably cause the Dutch countryside to sink—which isn't really something they need more of.[4]For this reason, most serious proposals involve a hollow mountain. I mean, serious compared to the other ones.

This plan is obviously impractical. Fortunately, someone else has come up with a better one.

A group of Germans, led by architect Jakob Tigges, have decided that Berlin already has an artificial mountain. Built on the site of the former Tempelhof Airport, "The Berg" towers 1,071 meters above the surrounding landscape, edging out the Burj Khalifa as the tallest manmade structure on Earth. It has a website, a Facebook group, photos, testimonials, and tourism information.

Now, nobody can see this mountain. But supporters insist that it's there.

If only the Egyptians had thought of that one.

I've occasionally seen "radar enforced" on speed limit signs, and I can't help but ask: How intense would radio waves have to be to stop a car from going over the speed limit, and what would happen if this were attempted?

—joausc

Radio waves exert force on things.

Not a lot of force. The average cell phone transmitter exerts about a billionth of a newton of pressure on its surroundings. That means that it would take several trillion cell phones to collectively levitate a snowflake; the pressure from one phone wouldn't even measurably slow it down.

If the phone did put out enough energy to levitate a snowflake by radiation pressure, the power flowing through the snowflake (a few kilowatts) would quickly cause the snowflake to become a raindrop, which would quickly become water vapor, which would quickly become the least of your problems.

The fate of the snowflake hints at what kinds of problems our car will encounter.

If you want to slow down a one-ton car by radiation pressure, your radar gun would need to deliver about two trillion joules worth of radiation—the energy of a small nuclear weapon.[1]The formula for figuring out that amount out is simple: The energy required is equal to the desired change in speed (say, 20 mph) times the mass of the car times the speed of light. mass-energy of the car (mc²). The radar gun would need to emit even more energy than that, since not all of the radiation will be absorbed (or reflected) by the car.[2]The fact that some of it is reflected makes things easier, since that doubles the momentum delivered by the radiation. This is why simple solar sails are white and not black. For more on radar reflectivity of materials, you can check out one of the worst scanned PDFs I've ever seen.

Your radar gun would also vaporize the car. This is a problem, in one sense, but it's also a solution. Even if most of the energy is reflected, the portion that was absorbed would convert the materials in the car into gas or plasma. The expanding cloud would exert a lot more pressure on the car than the radiation itself.[3]This process, called ablation, is also what got rid of the Moon in the What If #13. This is convenient—it means that we wouldn't need nearly as much energy to stop the car as we would using radiation pressure alone.

There are even simpler ways to slow down a car with radiation. For example, you could aim a radiation beam at the tires and melt them, or use the electromagnetic radiation to knock out the car's electrical systems. Or just use a laser pointer to blind the driver and hope they reflexively slow down.

Of course, you don't need any of those things. If your goal is to slow down the car—rather than to catch speeders—your radar gun doesn't need any power. You can just stand by the side of the road next to a police car holding a fake radar gun.

In the end, a radar gun capable of slowing cars through radiation pressure would be roughly equivalent to a nuclear weapon, and using nuclear strikes in response to traffic violations is probably overkill. It would work, in the literal sense, but it would also destroy the offender, car, police officer, road, and all other traffic for miles around.[4]It would also cause fragments of the driver to violate the speed limit in all directions at once.

Of course, maybe using the apocalyptic radar gun wouldn't be necessary; just the threat of a nuclear strike against drivers would probably deter speeding.

Come to think of it, maybe that's what those other signs you sometimes see are hinting at.