The Moon's Orbit is WEIRD

In this MinutePhysics explanation, the Moon’s path around the Sun is shown to be nearly circular and always directed toward the Sun, not spiraling away from it. From the Sun’s vantage point, the Earth and Moon move side by side, with tiny nudges and perturbations as they follow their orbits. The video introduces the idea of the Hill radius to explain why Earth’s gravity dominates for practical orbital motion and why the Moon orbits the Earth in a common center of mass. It also uses an epitrochoid-like geometry to illustrate how relative speeds and distances shape trajectories, and it emphasizes that deciding whether something is a satellite or a sun-orbiting body can be tricky and sometimes misleading if you only look at a single trajectory.

Introduction

The video argues that the Moon does not trace a spiral around the Sun. Instead, it follows a near circular path that stays directed toward the Sun, while the Earth–Moon system travels together around the Sun.

"The trajectory never actually makes any sort of a loop, and in fact, it never even curves outwards towards the earth at all. Always inwards towards the sun." - MinutePhysics

The Geometry of Orbits

To convey the motion, the presenter uses a geometric idea akin to an epitrochoid, a curve formed when one circle rolls around another. The Moon’s orbit, relative to the Earth, can look wobbly or slightly spiral depending on speeds and distances, but when viewed in the solar frame it behaves mostly as a gentle inward curve toward the Sun. The speaker describes how orbit shapes—spirals, wobbles, or near-circular paths—depend on the ratio of speeds and the size of the orbit, with faster moons or larger orbits producing more spiral-like trajectories and slower or tighter ones yielding near-circular paths.

"This type of curve, where a circle rotates while attached to another rotating circle, is called an epitrochoid, though they're usually generated by rolling a circle around another circle, but the curves are the same." - MinutePhysics

Hill Radius, Net Forces, and the Sun’s Dominance

Key to understanding the Moon’s motion is the Hill radius: the region where Earth’s gravity dominates over solar gravity for objects bound to Earth. Within this zone, the Sun’s pull is present but Earth's gravity shapes the local motion, making the Moon effectively orbit the Earth in a broad sense while both bodies orbit the Sun. The video notes that the Sun pulls on the Moon with almost twice the force that the Earth does, explaining why the Moon’s trajectory never curves outward away from the Sun. The concept of net forces is refined with centrifugal effects, since the Earth–Moon system moves in a circle around the Sun, and those centrifugal effects can weaken the Sun’s perceived pull relative to Earth’s. The Moon lies inside Earth’s Hill sphere, so practical orbital dynamics are Earth‑dominated even though the Sun is the ultimate driver of the orbit around the Sun.

"Technically speaking, the moon is outside of the Earth's Chebotarov radius, where the pulls from the earth and sun are equivalent." - MinutePhysics

Practical View, Center of Mass, and Conclusions

From a broader perspective, the Moon and Earth both orbit the Earth–Moon system’s center of mass, which sits inside the Earth. If the Moon were significantly different in distance or mass, the center of mass could shift, potentially creating a double-planet scenario but with little impact on the Sunward trajectory. The video closes by acknowledging that classifying a body strictly as a satellite versus an independent sun-orbiter can be both tricky and somewhat futile in a dynamic two-body plus Sun context. Trajectories can be misleading if evaluated in isolation, and the most accurate view comes from considering the full gravitational dance among Earth, Moon, and Sun. The creator also mentions that solving such problems required substantial math and programming, underscoring the value of problem-solving in understanding complex orbital dynamics.

"Ultimately, defining whether something is a satellite versus independently orbiting the sun is actually a really tricky and possibly even futile endeavor." - MinutePhysics