BAN #427: What is the closest planet to Earth on average?

[Hubble image of NGC 3603. Credit: NASA, ESA, R. O'Connell (UVa), F. Paresce (NIA, Bologna, Italy), E. Young (USRA/Ames Research Center), the WFC3 Science Oversight Committee, and the Hubble Heritage Team (STScI/AURA)]

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Astro Tidbit

A brief synopsis of some interesting astronomy/science news that may be too short for the blog, too long for Twitter, but just right (and cool enough to talk about) for here.

What is the closest planet to Earth?

This is one of those questions I see a lot, and people expect an easy answer, but you have to be careful! If you ask them to clarify, usually the person will say “what planet gets closest to Earth?”

You can guess it’s either Venus or Mars, because they are the next planets inward to and outward from the Sun, respectively. A little thought will show you that we get closest to Venus when it’s farthest from the Sun in its orbit at the same time Earth is closest, and we’re closest to Mars when it’s closest to the Sun in its orbit and we’re farthest (this is complicated a little bit due to the fact that planets orbit on ellipses, but we can just look up the numbers we need).

These points are called perihelion (closest to the Sun) and aphelion (farthest from the Sun). You can look them up for all the planets on this NASA site. Venus at aphelion is about 109 million km from the Sun, and Earth at perihelion is 147. That means Venus gets as close as 147 – 109 = 38 million kilometers.

Mars at perihelion is about 207 million km, and Earth at aphelion is about 152, so Mars gets as close as 207 – 152 = 55 million km.

Venus wins. It’s our nearest neighbor.

There are caveats, because the orbits don’t align perfectly, and so Mars is probably never (or at least extremely rarely) at perihelion at the same time Earth is at aphelion, but the difference is nowhere near enough to close the 17 million km gap Venus enjoys over Mars.

But… what if the question were phrased differently? What if we said “Which planet is closest to Earth on average?”

[Spoiler alert. Credit: NASA/Johns Hopkins University Applied Physics Laboratory/Carnegie Institution of Washington]

That changes things. A lot. It may not feel intuitive, but the answer is… Mercury. Yup. Seriously.

The math on this is a little tricky — there’s a paper explaining it if you care — but a couple of videos explain it as well.

Here’s one:

And here’s another:

To be honest I had never really thought about this before, and when this popped up in my social media feeds I was handed the explanation before I had a chance to really think about it first. I suspect I would’ve guessed correctly, though, but I suppose I’ll never know.

So anyway, how does this work?

[The orbit of Venus brings it as close as 38 million km from Earth (right) and as far as 254 million (left). Credit: Phil Plait, hand drawn for you, BAN subbies.]

Things change because now we’re looking over the entire orbit of a planet, and not just its closest point to Earth. Venus gets closest to us, but it also can be on the other side of the Sun from us. That distance (called apogee, farthest from Earth) is the diameter of Venus’s orbit (roughly 216 million km) plus the distance it gets to us at its closest, 38 million, for a total of 254 million. Being very crude here, the average distance to Venus is (the closest it gets) / (the farthest it gets) / 2 = (254 + 38) / 2 = 146 million km. 

While Mercury doesn’t get as close to us, it doesn’t get as far either because its orbit is smaller. Its orbit is highly elliptical, but taking some averages it gets as close as 77 million kilometers, while its orbit is 116 million kilometers wide. (116 + 77) / 2 = 97 million km.

You’d really have to do the full-up math to get this right (due to the orbits not only being ellipses but also being on different tilts, and taking an integral over the paths of the planets), but even my crude approximation shows that Mercury is closer to us than Venus on average. If you do this for the other planets you’ll find they’re all farther away from us than Mercury on average.

In fact, this is true for every planet: On average, Mercury is the closest planet to any and all the planets in the solar system. This would even be true if another planet got much closer to Earth! Say its orbit is just a little bigger than ours; then on average its distance is the about same as the distance of the Earth from the Sun, 150 million km or so. That’s still much farther than Mercury’s average.

How about that? Our intuition when it comes to circles — as with many things — is not terribly reliable. But that’s why we have math and science: So we can check to make sure we’re not making assumptions that will lead us astray.

Pretty neat. And pretty handy if you ever get in a Nerd Night trivia contest.

Et alia

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