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 snopes.com 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.