Universal Gravitation at All Scales

In Chapter 7-5 of The Feynman Lectures on Physics, titled Universal Gravitation, Richard Feynman offers a profound reflection on how far Newton’s law of gravitation can be stretched—beyond apples and planetary orbits, out to the farthest reaches of the cosmos. It is a tour not just of gravitational theory, but of its explanatory power, its history, and the surprising way it links local phenomena to the structure of the universe itself.

Let us walk through this chapter, adding historical depth and scientific detail to the many examples Feynman touches upon.

The Shape of the Earth and Other Spheres

Feynman opens with a deceptively simple question: Why is the Earth round? The answer, grounded in Newton’s law, is that gravity pulls matter inward, trying to minimise potential energy. The Earth’s roughly spherical shape is the result of gravity acting uniformly in all directions over geologic time.

But the Earth isn’t a perfect sphere—it’s slightly flattened at the poles and bulged at the equator. This is due to its rotation, which introduces a centrifugal effect. The faster a body spins, the more this effect resists gravitational collapse around the equator, creating an oblate spheroid.

Feynman remarks that this shape can be derived quantitatively using Newtonian gravitation, demonstrating how the same principles explain not just the form of the Earth, but also the general spherical tendency of massive bodies like the Moon and the Sun.

Roemer’s Insight and the Speed of Light

Next, Feynman introduces a classic episode in the history of science: Ole Rømer’s observation of Jupiter’s moons in the 1670s. These moons appeared early when Jupiter was near Earth, and latewhen it was far. This puzzled astronomers until Rømer proposed a bold hypothesis: light has a finite speed.

In 1676, using these timing variations, Rømer estimated the speed of light to be about 220,000 km/s—a rough, yet foundational step toward our modern value (~299,792 km/s). The gravitational motions of Jupiter’s moons, expected to be regular under Newton’s laws, were being delayed or advanced by light’s travel time across the Solar System.

This elegant solution did not invalidate Newton’s laws; instead, it uncovered a new law of nature altogether.

The Perturbed Path of Uranus and the Discovery of Neptune

Gravitation becomes more complex when you realise that planets pull on each other, not just on moons or apples. Jupiter and Saturn, for example, subtly influence each other’s orbits. This gives rise to small perturbations, or deviations from perfect ellipses.

In the 19th century, astronomers noticed that Uranus was not following the path predicted by Newton’s laws, even when accounting for known planetary influences. Was Newton wrong?

Enter John Couch Adams in England and Urbain Le Verrier in France. Working independently, both theorised that the anomalies in Uranus’s orbit could be explained by the gravity of an unseen planet. They calculated its expected position and urged observatories to look there.

On 23 September 1846, Johann Galle, acting on Le Verrier’s data, discovered Neptune, less than 1° away from the predicted location. This was a stunning triumph for Newtonian gravitation, validating it not only as a descriptive tool but as a predictive one.

Binary Stars: Newton’s Laws Beyond the Solar System

Feynman then takes us to the realm of binary stars—pairs of stars bound together by gravity, orbiting a common centre of mass. He refers to observations of systems like Sirius A and B, where their orbital paths can be tracked over decades.

While their orbits appear elliptical, Sirius A does not lie at the focus, at least not in two-dimensional sky projections. Feynman explains this is due to perspective effects: we are viewing the ellipse from an angle. In three dimensions, the stars obey Kepler’s laws and Newtonian gravity faithfully.

This is critical evidence that Newton’s laws apply beyond the Solar System, to stellar systems light years away.

Globular Clusters and Galactic Gravitation

Feynman next describes globular clusters—spherical collections of tens of thousands of stars, such as M13 in Hercules. Although they appear densely packed in images, these clusters are actually vast, with stars spaced light years apart.

The distribution of stars—denser in the centre, sparser on the edges—suggests a gravitational equilibrium. This distribution arises naturally from gravitation: the cluster as a whole is bound together by mutual attraction, much like the solar system, only on a vastly larger scale.

Even at distances 100,000 times the width of the Solar System, Newtonian gravity still structures the cosmos.

Galaxies and Angular Momentum

Feynman then scales up again, to entire galaxies, such as the Andromeda Galaxy or our own Milky Way. Why are they shaped like discs with spiral arms, and not spheres?

His answer lies in angular momentum. When matter contracts under gravity, any initial rotation becomes more pronounced. Just like a spinning ice skater pulling in their arms, a rotating cloud collapses into a disc, conserving its spin.

The spiral arms, he notes, are still not fully understood. They likely involve density waves, star formation, and the dynamics of rotating gas clouds. It remains a fertile area for research, but the overall structure of galaxies is clearly dominated by gravity.

Clusters of Galaxies and Cosmic Scale Gravitation

The journey doesn’t end at individual galaxies. Feynman points out that galaxies themselves form clusters, gravitationally bound to each other across millions of light years. The same principles that explain apple falls, binary stars, and planetary orbits also explain the architecture of the cosmos.

We are observing gravitational clumping on a scale of tens of millions of light years, as if Newton’s law stretches endlessly across the universe.

Star Formation: From Dust to Light

The final image Feynman explores is that of a stellar nursery—a nebula where gravity causes diffuse clouds of gas and dust to collapse into stars. He shows a pair of photographs taken seven years apart, in which two bright spots appear.

Could this be direct evidence of star formation—gravity gathering matter until nuclear fusion ignites? Perhaps. The timescale is suspiciously short, and it is uncertain whether we were simply lucky or whether the spots are due to other effects (like variable stars or lighting geometry).

Nonetheless, gravity is clearly the engine that starts the stellar life cycle.

Conclusion: Gravitation, Universal in Every Sense

In Chapter 7-5, Feynman illustrates that Newton’s law of gravitation is not just a local rule—it’s a universal principle. From the bulge of the Earth to the spirals of galaxies, from the speed of light to the discovery of Neptune, gravitation proves itself again and again.

This chapter is a celebration of scientific deduction, observational perseverance, and the power of a single idea to explain the structure of everything we see. As Feynman hints at the end, the story isn’t over. The arms of galaxies, the origins of stars, and the fate of the cosmos are still open questions. But what we know, we owe in large part to Newton’s universal gravitation—and to those who dared to ask, what else can we understand when we understand gravity?