Why is the Closest Planet Also the Most Difficult to Visit? NASA's MESSENGER Mercury Probe

[Uncle Joe]

[mahatmakanejeeves]

1. Closest? I had a hard time with this. At its closest, Venus is 25 million miles from Earth.

True, but at its farthest, it's farther from Earth than Mercury is at its farthest. You have to average over time. That's how Mercury comes out ahead.

I'll have to read this a few more times.

Venus is not Earth’s closest neighbor

Calculations and simulations confirm that on average, Mercury is the nearest planet to Earth—and to every other planet in the solar system.

Tom Stockman
Gabriel Monroe
Samuel Cordner

Quick: Which planet is closest to Earth? Ask an astronomer or a search engine, and you’ll probably hear that though the situation changes frequently, Venus is the closest when averaged over time. Several educational websites, such as The Planets and Space Dictionary, publish the distance between each pair of planets, and they all show that Venus is nearest to Earth on average. They’re all wrong. NASA literature even tells us Venus is “our closest planetary neighbor,” which is true if we are talking about which planet has the closest approach to Earth but not if we want to know which planet is closest on average.

As it turns out, by some phenomenon of carelessness, ambiguity, or groupthink, science popularizers have disseminated information based on a flawed assumption about the average distance between planets. Using a mathematical method that we devised, we determine that when averaged over time, Earth’s nearest neighbor is in fact Mercury.

That correction is relevant to more than just Earth’s neighbors. The solution can be generalized to include any two bodies in roughly circular, concentric, and coplanar orbits. By using a more accurate method for estimating the average distance between two orbiting bodies, we find that this distance is proportional to the relative radius of the inner orbit. In other words, Mercury is closer to Earth, on average, than Venus is because it orbits the Sun more closely. Further, Mercury is the closest neighbor, on average, to each of the other seven planets in the solar system.

{snip}

Tom Stockman is a PhD candidate at the University of Alabama in Huntsville (UAH) and a graduate research assistant at Los Alamos National Laboratory (LANL). Gabriel Monroe is a research mechanical engineer at the US Army’s Engineer Research Development Center (ERDC). Samuel Cordner is a mechanical engineer at NASA. The views expressed in this article do not necessarily represent the views of UAH, LANL, ERDC, NASA, or the US government. The authors would like to thank Michael Barton of a.i. solutions, who used FreeFlyer astrodynamics software to independently validate the simulation results; Andrew Heaton at NASA for validation of results and interesting insights; and Paul Fabel of Mississippi State University for valuable and entertaining discussion on the subject.

[Jeebo]

3. I've always thought of planetary distances as between their orbits.

So, I suppose this shows that it depends on how you look at it. I still think of the next planet in as Venus and as the next planet out as Mars. Mercury, Venus, Earth, Mars, asteroid belt, Jupiter, Saturn, Uranus, Neptune. Which planet is closest to the sun? Mercury. Which is the second closest planet to the sun? Venus. Which is the third planet? Earth. And so on. Venus is our closest planetary neighbor because it comes closer to us than any other planet. And its orbit is always closest to our orbit.

-- Ron

[muriel_volestrangler]

4. Here's a way to think of it for perfectly circular and thus constant angular velocity orbits

Think of a diagram of the Sun, an inner planet, orbit radius r, and an outer planet, orbit radius R. The planets both orbit at constant angular velocity, so the difference in angular velocity is constant - the inner is always going at x degrees per day, and the outer at y degrees per day, so you could draw the diagram with the outer planet stationary, and the inner going round at a constant (x-y) degrees per day. Then let's divide the orbit of the inner planet like a clock, from 1 to 12. Put the outer planet above 12.

The distances at the times 12 and 6 are (R-r) and (R+r), so those average to exactly R.

The distances at 1 and 5 can be found with Pythagoras, and then averaged; but we know the purely vertical distance would average out to R again, and there's a sideways component too - r/2, so we expect the averages to be more than R. The same will go for 11 and 7. For 2 and 4, the sideways component is 0.866r (square root of 3, over 2). And for 3, the sideways component is r. The average will be "R and a bit", with the "bit" increasing with r.

So, for any planet inside us, our orbit gives R, and the inner planet r. The bigger r is, the bigger the average distance will be. So Mercury is the closest on average. And for any planet outside us, our orbit determines r, and the other one determines R, so that is well more than for any planet inside us.