As I've established in previous postings, every now and then I have a mild attack of math when I'm watching a movie or reading a book, and end up either going down the rabbit hole or through the looking glass, depending on your preference for Alice novels. Most recently, this happened when I watched the first sneak peak from the upcoming Invincible animated series, scheduled for a March 26th debut on Amazon Prime™ Video.
The clip shows a pair of enhanced beings, father and son, hovering in midair as they throw a baseball back and forth while discussing the challenges of being a superhero. Because they're superheroes, they're doing it the hard way: they're throwing the ball AWAY from the other person so that it circumnavigates the planet before being caught.
It's a charming bonding moment, but there's so much extreme physics involved that I couldn't help myself from taking a closer look at what was actually going on.
It takes the baseball approximately 18 seconds to reach the son's glove after the father throws it. (I timed it at 17.98, but let's keep the math simple.) Given that the Earth's circumference is 40,075 kilometers, distance divided by time gives the baseball a speed of 2226.389 km/s, or 8,014,999 km/hr. (speed per second x60 x60.) The escape velocity for Earth is a piddly 11.2 km/s, so that baseball is GONE, headed in a straight line for distant horizons: the Moon, Saturn, Alpha Centauri, whatever the first solid object that gets in the way happens to be*.
But, hey, Dad is a superhero, maybe he can put a LOT of spin on the ball or something like that, so we'll generously assume that the baseball doesn't leave the planet. Regardless, the ball is travelling at 6,542 times the speed of sound, so when Dad asks his son if he hears the ball coming, the son's answer of yes seems impossible, the ball is well out in front of any noise it might be making**. Superhearing is all well and good, but the sound just can't have arrived yet.
But, once again, superheroes: in the interest of fairness, I freely confess that there may be aspects of superhearing that make this possible, although Clark Kent hasn't answered any of my texts on the topic.
However, at that sort of speed, the adiabatic compression of air in front of the ball is going to severely raise its temperature. (If you thought that it was the friction of air that caused heating under these circumstances, welcome to the club, it took me a lot of misdirected searching on Google™ to realize my mistake.) At this point, the math gets complicated, but we can take a lateral approach.
Spacecraft re-entering the Earth's atmosphere are travelling at approximately 25 times the speed of sound (the compression effect doesn't really kick in until you're over the speed of sound, just as a side note for the interested student). This produces temperatures of about 1480 degrees C. The baseball has a much smaller surface area, but it's also travelling at 262 times that speed, and since leather starts to burn at 212 degrees C., it's unlikely that it survives very long on its trip around the world.
Not only that, but that's gotta be a pretty sturdy baseball glove, too. And there's your homework, class: how much energy is released by a baseball travelling at 6,432 times the speed of sound when it hits a solid object? Just to get things started, a standard Major League baseball must weight between 5 and 5 1⁄4 ounces, or 142 and 149 grams. And, as always, please show your work.
