Mercury -- Not Venus -- is the Closest Planet To Earth on Average, New Research Finds (gizmodo.com)

That's the finding presented by a team of scientists who have published their results this week in an article in the magazine Physics Today. From a report: They explain that our methods of calculating which planet is "the closest" oversimplifies the matter. But that's not all. "Further, Mercury is the closest neighbor, on average, to each of the other seven planets in the solar system," they write. Wait -- what?

Our misconceptions about how close the planets are to one another comes from the way we usually estimate the distances to other planets. Normally, we calculate the average distance from the planet to the Sun. The Earth's average distance is 1 astronomical unit (AU), while Venus' is around 0.72 AU. If you subtract one from the other, you calculate the average distance from Earth to Venus as 0.28 AU, the smallest distance for any pair of planets. But a trio of researchers realized that this isn't an accurate way to calculate the distances to planets. After all, Earth spends just as much time on the opposite side of its orbit from Venus, placing it 1.72 AU away.

One must instead average the distance between every point along one planet's orbit and every point along the other planet's orbit. The researchers ran a simulation based on two assumptions: that the planets' orbits were approximately circular, and that their orbits weren't at an angle relative to one another.

Comments

Of course it's pedantic

[Headw1nd]

I saw some comments on the Physics Today article about this being pedantic, but astronomy is and always has been about pedantry. It's taking into account tiny details and vanishingly small deviations that allows us to do things like observe the composition of faraway stars or compute the age of the universe.

Re:I call bullsht

[Solandri]

perfectly circular, average distance from any planet to any planet should be equal to the center of their path circle, which is, drum roll please, the center of the sun.

No. Distance is a scalar, not a vector. So the average distance doesn't work out to the center of the sun. It works out to the the sum of all points along the circular orbit. For Venus' case, since its orbit is bigger, the scalar distance to each equivalent point in Mercury's orbit is on average bigger because it's at a greater angle from the Earth (with Earth-to-sun line being the shortest distance).

e.g. Pretend Mercury is located in the sun, and Venus has the same orbit as Earth. Consider four points on each orbit spaced 90 degrees apart.

• When Earth, Venus, and Mercury are in line with the sun all on the same side, Mercury is as far as the sun from the Earth (call it R), Venus is on top of the Earth, so its distance is zero.
• When Venus and Mercury are on opposite sides of the sun from Earth, Again, Mercury is distance R, Venus is 2R.
• When Venus and Mercury are at 90 degrees to the right of the sun from Earth, this creates a 45 degree right triangle. Mercury is still at R, Venus is at 2sin(45)R, or 1.414R.
• Likewise when Venus and Mercury are at 90 degrees to the left of the sun, you have the same 45 degree right triangle flipped. And Mercury is at R, Venus is at 1.414R.

Average these four points. The first two cancel out (both average a distance R). The second two result in Mercury being at distance R, Venus at 1.414R. And hence Mercury is on average closer than Venus, even though we're pretending Venus has the same orbit as the Earth.