Two Against One, And It’s Not Even Close

On a brisk walk across campus when I hear Vinnie yell from Al’s coffee shop. “Hey! Sy! Me and Al got this argument going you gotta settle.”

“Happy to be a peacemaker, but it’ll cost you a mug of Al’s coffee and a strawberry scone.”

“Coffee’s no charge, Sy, but the scone goes on Vinnie’s tab. What’s your pleasure?”

“It’s morning, Al, time for black mud. What’s the argument, Vinnie?”

“Al read in one of his astronomy magazines that the Moon’s drifting away from us. Is that true, and if it is, how’s it happen? Al thinks Jupiter’s gravity’s lifting it but I think it’s because of Solar winds pushing it. So which is it?”

“Here you go, Sy, straight from the bottom of the pot.”

“Perfect, Al, thanks. Yes, it’s true. The drift rate is about 1¼ nanometers per second, 1½ inches per year. As to your argument, you’re both wrong.”

“Huh?”
”Aw, c’mon!”

“Al, let’s put some numbers to your hypothesis. <pulling out Old Reliable and screen‑tapping> I’m going to compare Jupiter’s pull on the Moon to Earth’s when the two planets are closest together. OK?”

“I suppose.”

“Alright. Newton’s Law tells us the pull is proportional to the mass. Jupiter’s mass is about 320 times Earth, which is pretty impressive, right? But the attraction drops with the square of the distance. The Moon is 1¼ lightseconds from Earth. At closest approach, Jupiter is almost 2100 lightseconds away, 1680 times further than the Moon. We need to divide the 320 mass factor by a 1680‑squared distance factor and that makes <key taps> Jupiter’s pull on the Moon is only 0.011 percent of Earth’s. It’ll be <taps> half that when Jupiter’s on the other side of the Sun. Not much competition, eh?”

“Yeah, but a little bit at a time, it adds up.”

“We’re not done yet. The Moon feels the big guy’s pull on both sides of its orbit around Earth. On the side where the Moon’s moving away from Jupiter, you’re right, Jupiter’s gravity slows the Moon down, a little. But on the moving-toward-Jupiter side, the motion’s sped up. Put it all together, Jupiter’s teeny pull cancels itself out over every month’s orbiting.”

“Gotcha, Al. So what about my theory, Sy?”

“Basically the same logic, Vinnie. The Solar wind varies, thanks to the Sun’s variable activity, but satellite measurements put its pressure somewhere around a nanopascal, a nanonewton per square meter. Multiply that by the Moon’s cross‑sectional area and we get <tap, tap> a bit less than ten thousand newtons of force on the Moon. Meanwhile, Newton’s Law says the Earth’s pull on the Moon comes to <tapping>
G×(Earth’s mass)×(Moon’s mass)/(Earth-Moon distance)²
and that comes to 2×1011 newtons. Earth wins by a 107‑fold landslide. Anyway, the pressure slows the Moon for only half of each month and speeds it up the other half so we’ve got another cancellation going on.”

“So what is it then?”
”So what is it then?”

“Tides. Not just ocean tides, rock tides in Earth’s fluid outer mantle. Earth bulges, just a bit, toward the Moon. But Earth also rotates, so the bulge circles the planet every day.”

“Reminds me of the wave in the Interstellar movie, but why don’t we see it?”

“The movie’s wave was hundreds of times higher than ours, Al. It was water, not rock, and the wave‑raiser was a huge black hole close by the planet. The Moon’s tidal pull on Earth produces only a one‑meter variation on a 6,400,000‑meter radius. Not a big deal to us. Of course, it makes a lot of difference to the material that’s being kneaded up and down. There’s a lot of friction in those layers.”

“Friction makes heat, Sy. Rock tides oughta heat up the planet, right?”

“Sure, Vinnie, the process does generate heat. Force times distance equals energy. Raising the Moon by 1¼ nanometers per second against a force of 2×1021 newtons gives us <taping furiously> an energy transfer rate of 4×10‑23 joules per second per kilogram of Earth’s 6×1024‑kilogram mass. It takes about a thousand joules to heat a kilogram of rock by one kelvin so we’re looking at a temperature rise near 10‑27 kelvins per second. Not significant.”

“No blaming climate change on the Moon, huh?”

~~ Rich Olcott

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