Figure 3: A simulation of an Earth year’s worth of orbits by the terrestrial
planets begins to reveal that Mercury (gray in orbital animation) has the small-
est average distance from Earth (blue) and is most frequently Earth’s nearest
neighbor. A longer run of the simulation can be seen on YouTube. In addition,
planetary geoscientist David Rothery ran a solar system simulation for the BBC
radio program More or Less and came up with similar results.
what we call the whirly-dirly corollary (named after an episode of the cartoon
Rick and Morty): For two bodies with roughly coplanar, concentric, circular
orbits, the average distance between the two bodies decreases as the radius of
the inner orbit decreases. It’s clear from this corollary, and from the table,
that Mercury (average orbital radius of 0.39 AU), not Venus (average radius of
0.72 AU), is the closest planet to Earth on average. In fact, Mercury is even
the closest planet to Neptune. (And yes, to Pluto too: Though the corollary
doesn’t work as well for the dwarf planet, with its orbital inclination of 17° and
eccentricity of 0.25, its nearest neighbor is also Mercury.)
4 Simulation validation
We ran a simulation to conﬁrm the whirly-dirly corollary, using a Python library
called PyEphem to chart the positions of all eight planets in the solar system
for 10 000 years. An animation illustrating the simulation is shown in ﬁgure
2. After each 24 hours of simulated time, the program records the distances
between each pair of planets.
In the table we list the average measured distances over the 10 millennia
and compare them with the results from the PCM and the traditional method.
The simulation results diﬀer from the ﬂawed numbers by up to 300 %, but
they deviate from the PCM ﬁgures by less than 1 %. Figure 3 compares the
results from both methods with the simulation of the average distance between
Neptune and the seven other planets.