Venus is not the nearest neighbor to the Earth

Quick: Which planet is closest to the Earth? Ask an astronomer or a search engine, and you will probably hear that, although the situation changes frequently, Venus is the closest to the values ​​depending on the duration. Several educational websites, such as The Planets and Space Dictionary, publish the distance between each pair of planets. They all indicate that Venus is on average the closest to the Earth. They are all wrong. NASA's literature even tells us that Venus is "our nearest planetary neighbor", which is true if we are talking about the planet that has the closest approach to the Earth but not if we want to know what planet is on average the closest.

It turns out that, by some phenomenon of carelessness, ambiguity or group thinking, the scientific popularizers have disseminated information based on an erroneous assumption about the average distance between the planets. Using a mathematical method that we have developed, we determine that, on average, the nearest neighbor of the Earth is Mercury.

This correction concerns more than the neighbors of the Earth. The solution can be generalized to include any two bodies in roughly circular, concentric and coplanar orbits. Using a more accurate method to estimate the average distance between two bodies in orbit, we find that this distance is proportional to the relative radius of the internal orbit. In other words, Mercury is on average closer to Earth than Venus because it turns more around the Sun. In addition, Mercury is the closest neighbor, on average, to each of the seven other planets in the solar system.

Simple but false

To calculate the average distance between two planets, The Planets and other websites assume that the orbits are coplanar and subtract the average radius from the internal orbit. r₁, from the mean radius of the outer orbit, r₂. The distance between the Earth (1 astronomical unit of the Sun) and Venus (0.72 AU) rises to 0.28 AU. The table at the bottom of the article shows the calculated distance between each pair of planets using this method.

Although it is intuitive that the average distance between each point of two concentric ellipses is the difference of their radii, this difference actually determines only the average distance of the points closest to the ellipses. Indeed, when Earth and Venus are at their closest approach, their separation is about 0.28 AU – no other planet is closer to the Earth. But just as often, the two planets are at their farthest point, when Venus is on the side of the Sun opposite the Earth, at 1.72 AU. We can improve the erroneous calculation by averaging the closest and the farthest distances (which gives an average distance of 1 AU between the Earth and Venus), but finding the real solution requires a little more effort .

A better approach

To capture more precisely the average distance between planets, we designed the circle of points method. The PCM treats the orbits of two objects as circular, concentric, and coplanar. For our solar system, this assumption is quite reasonable: the eight planets have an average orbital inclination of 2.6 ° ± 2.2 ° and the average eccentricity is 0.06 ± 0.06. An object in a circular orbit maintains a constant velocity, which means that over a sufficiently long period it is also likely to be in any position on that orbit. We consider at any time the position of a planet as a uniform probability distribution around a circle defined by the mean orbital radius, as shown in Figure 1a. The average distance between two planets can therefore be described as the average distance of each point of the circle. c₂, Defined by r₂at each point of the circle c₁, Defined by r₁.

Due to the rotational symmetry, the average distance re from a particular point on c₂ at every point on c₁ is the same for any other point chosen on c₂. So, re is also equivalent to the average distance of a single point on c₂ at every point on c₁as shown in Figure 1b. It can be determined by integrating the point-to-point distance around c₁, simplified in equation 1, which defines the MCP:

$\mathrm{re}$

= 2 π r 1 + r 2 E 2 r 1 r 2 r 1 + r 2

or E(X) is an elliptic integral of the second type. The average distances between pairs of planets determined by the PCM are included in the table. Venus is averaging 1.14 AU from the Earth, but Mercury is much closer to 1.04 AU.

According to the PCM, we found that the distance between two bodies in orbit is minimal when the internal orbit is minimal. This observation leads to what we call the swirling corollary (named after an episode of the cartoon Rick and Morty): For two bodies with roughly coplanar, concentric and circular circular orbits, the average distance between the two bodies decreases as the radius of the internal orbit decreases. It is clear from this corollary and from the table that Mercury (average orbital radius of 0.39 AU), and not Venus (average radius of 0.72 AU), is on average the planet closest to the Earth. In fact, Mercury is even the closest planet to Neptune. (And yes, to Pluto too: although the corollary does not work as well for the dwarf planet, with its orbital inclination of 17 ° and its eccentricity of 0.25, its nearest neighbor is also Mercury.)

Validation of the simulation

We performed a simulation to confirm this corollary, using a Python library called PyEphem to map the positions of the eight planets in the solar system for 10,000 years. An animation illustrating the simulation is shown in Figure 2. Every 24 hours of simulated time, the program records the distances between each pair of planets.

In the table, we list the average distances measured over 10,000 years and compare them to the PCM and traditional results. The results of the simulation differ from the erroneous numbers up to 300%, but they differ from the PCM figures by less than 1%. Figure 3 compares the results of the two methods with the simulation of the average distance between Neptune and the other seven planets.

As far as we can judge, no one has come up with a concept such as PCM to compare orbits. With the right assumptions, PCM could possibly be used to get a quick estimate of the average distance between any set of bodies in orbit. Perhaps this can be useful for quickly estimating satellite communication relays, for which the signal strength decreases with the square of the distance. In any case, at least we now know that Venus is not our nearest neighbor and that Mercury belongs to everyone.

Tom Stockman is a PhD candidate at the University of Alabama in Huntsville (UAH) and a graduate research assistant at the Los Alamos National Laboratory (LANL). Gabriel Monroe is a mechanical engineer at the Research and Development Center of the US Army Engineer (ERDC). Samuel Cordner is a mechanical engineer at NASA. The opinions 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 AI Solutions, who used the FreeFlyer Astrodynamics software to independently validate the simulation results; Andrew Heaton of NASA for validation of results and interesting information; and Paul Fabel from Mississippi State University for an interesting and entertaining discussion on the subject.