What are the Time Zones on Mercury? I normally post on worldbuilding, but this question is merely about facts of a planets orbit and spin. I am trying to figure out how time periods work on Mercury to possibly make a worldbuilding guide for the planet. I recently heard on an educational video that the eccentricity of Mercuries orbit can cause the sun to temporarily become still on mercury, and then move in the opposite direction, then become still again, and move along it's normal course in the sky. The possible effects of this are that certain regions of mercury could experience a &quot;season&quot; where the son only goes partway through the sky before turning around and setting creating something of a cycle of &quot;short days&quot; and &quot;long days&quot;. I imagine because of mercury's mathematically synchronized orbit, these short days can only be experience on small bands of the planet, I would imagine there is only one circular band going around the world along a line of longitude that is like this.
What I am trying to understand is how different parts of mercury experience the day and not simply the length of mercuries day in absolute terms. I am wondering how a hypothetical person that would be following the &quot;evening&quot; and &quot;morning&quot; sections of mercury would experience the backwards movement of the sun over the course of the mercurian year. I am wondering if this backwards movement of the sun causes one side of the planet to experience less daylight than the other side, but I will leave the practical effects of this on colonization for a worldbuilding SE.
Simply put: I am trying to understand how different regions of mercury experience the day/night cycle and the way the day/night cycle travels over the planet. This is ultimately a question of what mercuries natural time zones are and the length (and irregularity) of the day-night cycle on the different parts of the planet.
Partial answer about the retrograde motion only:
Yes, the Sun has yearly retrograde motion as seen from Mercury
I've written a simple script to generate the orbital motion of Mercury based on its eccentricity. I've used reduced units with $GM = a = 1$ and period $T = 2 \pi$.
Mercury's rotational period is 2/3 of its orbital period.
I've plotted the rotational angle of mercury minus the angle of the Sun as seen from Mercury's position. To address retrograde motion, it's not necessary to consider from where on Mercury you are looking,
There are tiny dips below zero every year.


import numpy as np
import matplotlib.pyplot as plt
from scipy.integrate import odeint as ODEint

def deriv(X, t):
    x, v = X.reshape(2, -1)
    acc = - x * ((x**2).sum())**-1.5
    return np.hstack((v, acc))

halfpi, pi, twopi, fourpi, sixpi = [f*np.pi for f in (0.5, 1, 2, 4, 6)]
to_degs, to_rads = 180/pi, pi/180

# Mercury
# https://space.stackexchange.com/questions/43213/what-is-the-analytical-closed-form-solution-of-the-two-body-problem-to-verify-it/43237#43237
# https://solarsystem.nasa.gov/planets/mercury/by-the-numbers/


e = 0.20563593
a = 1
peri = (1 - e) * a
v_peri = np.sqrt(2/peri - 1/a)

X0 = np.array([peri, 0, 0, v_peri])
times = np.linspace(0, sixpi, 1001)
dt_years = (times[1] - times[0]) / twopi

answer, info = ODEint(deriv, X0, times, full_output=True)
xy = answer.T[:2]
x, y = xy
r = np.sqrt((xy**2).sum(axis=0))

theta_rot = np.mod((3/2) * times, twopi)
sun = np.zeros(2)[:, None] - xy
theta_sun = np.arctan2(sun[1], sun[0])

if True:
    plt.figure()
    plt.subplot(2, 1, 1)
    angle = theta_rot - theta_sun
    dangle = np.mod(angle[1:] - angle[:-1]+halfpi, twopi)-halfpi
    dangle_dt = dangle / dt_years
    angle = np.mod(angle+halfpi, twopi)-halfpi
    plt.plot(times/twopi, angle)
    plt.ylabel('angle (rad)')
    plt.subplot(2, 1, 2)
    plt.plot(times[1:]/twopi, dangle_dt)
    plt.plot(times[1:]/twopi, np.zeros_like(dangle_dt), '-k', lw=0.5)
    plt.ylabel('dangle/dt (rad/year)')
    plt.xlabel('years')
    plt.show()


if True:
    plt.figure()
    plt.subplot(3, 1, 1)
    plt.plot(x, y)
    plt.plot(x[:1], y[:1], 'ok', ms=2)
    plt.plot([0], [0], 'oy', ms=8)
    plt.gca().set_aspect('equal')
    plt.subplot(3, 1, 2)
    plt.plot(times/twopi, x)
    plt.plot(times/twopi, y)
    plt.plot(times/twopi, r, '-k')
    plt.subplot(3, 1, 3)
    plt.plot(times/twopi, theta_rot)
    plt.plot(times/twopi, theta_sun)
    plt.show()