Are You Stronger Than Jupiter?

A comment on my earlier piece comparing the acceleration due to gravity that we feel from the Moon compared to what we feel from someone else in the room challenged me: how strong is the gravitational pull from Jupiter, compared to that of someone else in the room? Jupiter has a great edge in mass: someone else in the room weighs in at somewhere around 75 kilograms, while the planet comes to around 1,898,600,000,000,000,000,000,000,000 kilograms. On the other hand, your neighbor is somewhere around one meter away, while Jupiter will be something like 816,520,800,000 meters away. Maybe farther: that’s the farthest Jupiter gets from the Sun, and the Earth can be on the opposite side of the Sun from Jupiter, so add up to another 152,098,232,000 meters on top of that.

That distance is going to be a little bit of a nuisance. The acceleration we feel towards any planet will be stronger the nearer it gets, and while, say, Neptune is always about the same distance from the Earth, there are times that Venus and Mars are surprisingly close. Usually these are announced by clouds of forwarded e-mails announcing that Mars will be closer to the Earth than it’s been in 33,000 years, and will appear to be as large as the Empire State Building. Before you have even had the chance to delete these e-mails unread the spoilsport in your group of e-mail friends will pass along the report that none of this is true and the e-mail has been going around unaltered since 1997 anyway. But there is still a smallest distance and a greatest distance any planet gets from the Earth.

If we want to give planets the best shot, let’s look at the smallest distance any planet gets from the Earth. For Mercury and Venus, this happens when the planet is at aphelion, the farthest it gets from the Sun, and the Earth at perihelion, the nearest it gets. For the outer planets, it happens with the Earth at aphelion and the other planet at perihelion. (Some might say ‘apogee’ and ‘perigee’, although these are properly speaking only the words to use when something orbits the Earth. Some might say ‘apoapsis’ and ‘periapsis’, which talk about the nearest and farthest points of an orbit without being particular about what is being orbited, but no one actually does.) Here I’m making the assumption that there’s no weird orbital locks where, say, the Earth can’t be at perihelion while Venus is at aphelion, which might even be true. It’s probably close enough.

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A Planet Is Not A Dot

A lot of what I said in describing how we might fall into the Moon, if you and I were in the same room and suddenly the rest of the world stopped existing, was incorrect. That isn’t to say it was wrong or even bad to consider; it just means that the equations that I produced and the numbers that came out from them aren’t exactly what would happen if the sudden-failure-of-planet-Earth case were to happen. I knew the wouldn’t be exactly right going in, which leaves us the question of what I thought I was doing and why I bothered doing it.

The first reason, and the reason why it wasn’t a waste of time to consider these simple approximations of how strongly the Moon is attracting us — how fast we are falling into it, and how fast we would be falling if the Earth weren’t falling into the Moon along with us — is thanks to something which Isaac Asimov perfectly described. In an essay called “The Relativity Of Wrong”, he wrote about — well, the title says it. Ideas are not just right or wrong; they can be wrong by differing amounts, and can be wrong by such a tiny amount that it isn’t worth the complications to get it exactly right. Probably the most familiar example is the flatness of the Earth. To model the globe, or a large nation, the idea that the Earth is nearly flat is sufficiently wrong as to produce measurable, important errors where plots of land are justifiably claimed by multiple owners, maybe from multiple governments, or aren’t claimed at all and form the basis for nowhere towns in which mild fantasy or comic stories can be set. But if one wants to draw a map of the town, or of one’s own property, the curvature of the Earth is not worth considering. We can pretend the Earth is flat and get our work done a lot sooner. Other sources of error will mess up the precise result before that does.

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In Case Of Sudden Failure Of Planet Earth

Have you ever figured out just exactly what you would do if the Earth were to suddenly disappear from the universe, leaving just you and whatever’s around to fall towards whatever the nearest heavenly bodies are? No, me neither. Asked to improvise one, I suppose I’d suffocate within minutes and then everything else becomes not so interesting to me, although possibly my heirs might be interested, if they’re somewhere.

My mother accidentally got me thinking about this fate. She’s taking a course about the science and world view of the Ancient Egyptians. (In talking about it she asked if I knew anything about the science of the Ancient Egyptians, and I tried to say I didn’t really know more than the average lay reader might, although when I got to mentioning that I knew of their awareness of the Sothic Cycle and where we get the name “Sothic Cycle” I realized that I can’t really call myself ignorant about the science of the Ancient Egyptians.) But the class had reached the point where astrological beliefs of the ancients were under discussion, and apparently some of the students insisted that astrology really and truly works, and my mother wanted me to figure out how strong the force of gravity of the Moon is, compared to the force of gravity of another person in the same room. This would allow her to go into class armed with numbers which have never dissuaded anyone from believing in astrology, but, it’s fun for someone.

I did double-check, though, that she meant the gravitational pull of the Moon, rather than its tidal pull. The shorthand reason for this is that arguments for astrology having some physical basis tend to run along the lines of, the Moon creates the tides (the Sun does too, but smaller ones), tides are made of water (rock moves, too, although much less), human bodies are mostly water (I don’t know what the fluid properties of cytoplasm are, but I’m almost curious enough to look them up), so there must be something tide-like in human bodies too (so there). The gravitational pull of the Moon, meanwhile, doesn’t really mean much: the Moon is going to accelerate the Earth and the people standing on it by just about the same amount. The force of gravity between two objects grows with the two objects’ masses, and the Earth is more massive than any person on it. But this means the Earth feels a greater force pulling it towards the Moon, and the acceleration works out tobe just the same. The force of gravity between two objects falls off as the square of the distance between them, and the people on the surface of the Earth are a little bit closer or a little bit farther away from the Moon than the center of the Earth is, but that’s not very different considering just how far away the Moon is. We spend all our lives falling into the Moon, as fast as we possibly can, and we are falling into the Moon as fast as the Earth is.

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