If you’re a “Man of Steel” fan, chances are you’ve read some creative explanations for how Christopher Reeve managed to reverse the Earth’s spin back in 1978. The concept has sparked heavy debate over the years, but in a move that warms the cockles of our nerdy hearts, a group of physics students from the University of Leicester have calculated how fast Superman would have had to fly to make it happen.
Now, before we get into the good stuff, there are a few things to note. First, Superman wasn’t reversing the Earth’s spin, he was flying fast enough to go backwards in time. Second, stopping the Earth from spinning (let alone reversing its spin) would have catastrophic results. Most notably, a lot of this:
And probably some of this:
OK, fine. Not that, but it would be very, very bad. But if Superman did spin the Earth backwards, he would need some mechanism to transfer inertia to the planet. For the purposes of this explainer we’re going to assume he has one (comic book physics, and all that jazz).
Through their calculations, the University of Leicester team concluded that Kal-El would have had to fly at an angular velocity of 46.296 radians per second, or 660,000,000 miles per hour — 98% the speed of light (!) — to reverse the spin of the Pale Blue Dot. But that’s not all: compared to the Earth, Superman is a very small blob. In order to have a measurable effect on the massive celestial body then, he would also have to increase his own mass 13.7 million times over.
So, that seals the deal – the act is impossible. Mass, is mass, right? Actually, no.
The secret to Superman’s ability to become more massive is hiding in Einstein’s famous equation E=mc², which explains the the relationship between energy and mass. By this equation, energy (E) is equal to mass times the speed of light (c) squared. When we humans talk about “mass,” what we’re usually referring to is “rest mass,” that is, the mass of an object is weighed in a stationary frame of reference (not moving relative to the scale used to measure its weight).
“Rest mass doesn’t change, as it is independent of speed by definition,” explains Caltech applied mathematician Dr. Spyridon Michalakis. “Still, there is another ‘mass,’ known as ‘relativistic mass,’ which refers to the mass of an object that is moving very, very fast.”
By rearranging uncle Albert’s equation E=mc² as m=E/c², we see how a huge boost of energy on the right side of the equation, say the amount needed to move at near-lightspeed, would make the mass on the left side of the equation bigger as well. This new, larger mass is the relativistic mass. “It’s larger than the ‘rest mass’ because of the extra kinetic energy in the system,” says Michalakis.
The speed of light is approximately 669,600,000 mph, which is very close to the calculated flight-speed necessary for Superman’s Earth-bending maneuver. By hitting this velocity, he would wrack up an immense amount of energy, which in turn, would produce an equally large relativistic mass. If the now-massive Kent could transfer his inertia to Earth, it would act like a brake.
But there is one problem: with mass, comes gravity. This brings us back to the impending doom our outside-underwearing friend would unleash on the planet, should he succeed in stopping it. “Whilst there is no danger of the moon being significantly affected by Superman, the act would would have set near-Earth objects such as asteroids on a course for Earth,” write the authors. Not to mention the resulting changes in atmospheric pressure and wind speeds would likely cause the extinction of the human race, and every other land-going species on the planet. So, in the end, Lois is toast – but on the plus side, Lex’s antics wouldn’t really matter anymore.