Calculations and simulations confirm that on average, Mercury is the nearest planet to Earth—and to every other planet in the solar system.
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.
Simple but wrong
To calculate the average distance between two planets, The Planets and other websites assume the orbits are coplanar and subtract the average radius of the inner orbit, r1, from the average radius of the outer orbit, r2. The distance between Earth (1 astronomical unit from the Sun) and Venus (0.72 AU) comes out to 0.28 AU. The table at the bottom of the article shows the calculated distance between each pair of planets using that method.
Although it feels intuitive that the average distance between every point on two concentric ellipses would be the difference in their radii, in reality that difference determines only the average distance of the ellipses’ closest points. Indeed, when Earth and Venus are at their closest approach, their separation is roughly 0.28 AU—no other planet gets nearer to Earth. But just as often, the two planets are at their most distant, when Venus is on the side of the Sun opposite Earth, 1.72 AU away. We can improve the flawed calculation by averaging the distances of closest and farthest approach (resulting in an average distance of 1 AU between Earth and Venus), but finding the true solution requires a bit more effort.
A better approach
To more accurately capture the average distance between planets, we devised the point-circle method. The PCM treats the orbits of two objects as circular, concentric, and coplanar. For our solar system, that’s a pretty reasonable assumption: 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 constant velocity, which means that over a sufficiently long period, it is equally likely to be in any position in that orbit. We consider a planet’s position at any given time as a uniform probabilistic distribution around a circle defined by the average orbital radius, as shown in figure 1a. The average distance between two planets can therefore be described as the average distance of every point on the circle c2, defined by r2, to every point on the circle c1, defined by r1.