If this description is taken literally, it would seem that Archimedes figured out the gearing needed to mimic the motion of the planets, including the retrograde motion where they appear to stop and reverse direction for a while before proceeding in their usual direction.

“This instrument was just like any other celestial sphere, except with the addition of indicators for the Sun, Moon, the planets moving over the sphere and a mechanism inside the sphere to move them,” Mr. Wright said.

In the spring, he began building his version of the Archimedes sphere. He presented it in public for the first time at the conference.

“I can’t guarantee that the original was like this,” Mr. Wright said. “What I can say is this, in the simplest way that I can imagine it, fits the evidence we have. We’ve been talking for 2,000 years about this thing that Archimedes made, and nobody seems to have offered to show people what it was like. I had an idea. I thought it was worth making, even if it was so people could have an argument about it and disagree with it. That’s a good way to get things going.”

Dr. Rorres said the singular genius of Archimedes was that he not only was able to solve abstract mathematics problems, but also used mathematics to solve physics problems, and he then engineered devices to take advantage of the physics. “He came up with fundamental laws of nature, proved them mathematically and then was able to apply them,” Dr. Rorres said.

Archimedes oversaw the defenses of Syracuse, and while death ray mirrors and steam cannons (another supposed Archimedes invention debunked by “Mythbusters”) were too fanciful, the Archimedes claw appears to have been a real weapon used against the Roman navy.

It is very likely that it took advantage of two scientific principles Archimedes discovered.

With his law of buoyancy, he was able to determine whether a paraboloid (a shape similar to the nose cone of a jetliner) would float upright or tip over, a principle of utmost importance to ship designers, and Archimedes probably realized that the Roman ships were vulnerable as they came close to the city walls.