After what time interval do the closest approaches of Mercury to the Earth repeat?
@Glorfindel's explanation is very clear. I wondered about how big of an effect &quot;everything else&quot; would have, but I couldn't figure out how to add an image to a comment. Here is a graph from 2018 to 2023 of the distance between Mercury and Earth. You can see every 3rd minimum is a bit deeper than the others just like Glorfindel said. The details of each local minimum change in a somewhat irregular way (about 10% of the closest distance variation), but the broad pattern fits the simple explanation well.

Here is python code to generate such a graph yourself for a different time period. It uses skyfield to access JPL's data on the planetary positions and matplotlib to graph it.
from skyfield.api import load
import numpy as np
import matplotlib.pyplot as plt

planets = load(&quot;de421.bsp&quot;)
ts = load.timescale()

times = ts.utc(2018,1,np.linspace(0,365*5,10000))

distances = (planets[&quot;Mercury&quot;] - planets[&quot;Earth&quot;]).at(times).distance()

plt.plot(times.utc_datetime(), distances.km);
plt.title(&quot;Distance from Mercury to Earth in km versus time&quot;);

plt.savefig(&quot;Mercury-Earth-2018-2023.png&quot;);
plt.close()