The Earth-Moon system

The orbit is not a circle

Goal: see the Moon's varying distance in real data, and work out what a "supermoon" is actually worth.

Run

import datetime as dt
from moonfield import moon, time as mtime

start = dt.datetime(2026, 1, 1, tzinfo=mtime.UTC)
distances = []
for day in range(60):
    when = start + dt.timedelta(days=day)
    distances.append((when, moon.position(when).distance_km))

near = min(distances, key=lambda x: x[1])
far  = max(distances, key=lambda x: x[1])
print(f"perigee {near[0]:%Y-%m-%d}  {near[1]:,.0f} km")
print(f"apogee  {far[0]:%Y-%m-%d}  {far[1]:,.0f} km")
print(f"ratio   {far[1] / near[1]:.3f}")

Perigee ~356,500 km, apogee ~406,700 km. About a 12% variation.

What follows from it

Apparent size varies by the same 12%, 0.49° to 0.56°.

Speed varies too: fastest at perigee, slowest at apogee (Kepler's second law). This is the direct cause of the up-to-half-a-day disagreement between the two phase models in module 02.

Tidal force varies as 1/r³, so it swings by about 40% between perigee and apogee, much more than the size does. Perigean spring tides are the highest of the year.

Supermoons

A "supermoon" is a full Moon near perigee. It is genuinely about 14% wider and 30% brighter than a full Moon at apogee, but you can only tell by measuring, because you never see the two side by side.

The dramatic photographs are telephoto compression, not the supermoon.

Try it yourself

  1. Find the perigean spring tides in the next year and check them against a real

tide table

  1. Photograph the Moon at perigee and apogee with identical settings and measure

the pixel diameter

  1. Plot distance against time for a year. The pattern is not a clean sine, why?

Checkpoint

Next: Module 04, Tides.