Angels, Inertia, and Orbits: Feynman’s Playful Prelude to Classical Dynamics

Exploring Section 7-3 of The Feynman Lectures on Physics

In Chapter 7-3 of The Feynman Lectures on Physics, Richard Feynman leads us into the heart of classical dynamics with characteristic clarity and wit. Here, he explores the transition from Kepler’s observational laws of planetary motion to the mechanistic understanding forged by Galileo and Newton. With a nod to discarded medieval theories — complete with wing-beating angels — Feynman reintroduces us to the foundational principles that govern motion, inertia, and force. This entry examines the development of these ideas, tracing their historical origins and unpacking the method behind Feynman’s deceptively simple explanations.

From Angels to Axioms: Early Theories of Planetary Motion

Feynman opens with characteristic humour, recalling an archaic cosmological explanation: planets were propelled by invisible angels flapping their wings. Such whimsical imagery, though fanciful to modern ears, reflects a genuine philosophical struggle in pre-Newtonian astronomy. Kepler had empirically derived his three laws of planetary motion (notably that planets move in ellipses with the Sun at one focus, and sweep out equal areas in equal times), but he could not explain why planets moved as they did.

Galileo Galilei, working contemporaneously with Kepler, approached a different question — not celestial motion, but terrestrial. What happens when objects fall, roll, or slide? In doing so, he discovered a radical truth: the principle of inertia.

Galileo and the Birth of Inertia

Inertia, as Feynman recounts, is the idea that an object will continue to move in a straight line at constant speed unless disturbed by an external force. Galileo reached this conclusion not by watching planets, but by observing balls rolling down inclined planes. In his Discorsi (1638), Galileo postulated that if friction and air resistance were removed, a body would maintain its motion indefinitely. This was a philosophical departure from Aristotelian physics, which held that continuous motion required continuous force.

Feynman states, “Why does it keep on coasting? We do not know, but that is the way it is.” This humility is emblematic of the scientific approach: recognising the axiomatic nature of certain physical laws. Inertia is not explained — it is accepted as an observed truth from which further consequences can be deduced.

Newton’s Synthesis: Force, Mass, and Acceleration

Sir Isaac Newton took Galileo’s qualitative insights and expressed them quantitatively. His Philosophiæ Naturalis Principia Mathematica (1687) laid out the laws of motion that remain the foundation of classical mechanics. Feynman zeroes in on Newton’s Second Law — that the force acting on a body is equal to its mass times its acceleration:

F = ma

What Feynman captures beautifully is the subtlety of Newton’s leap: to accelerate an object (that is, to change its velocity or direction), a force must be applied. But crucially, no force is needed to sustain motion — only to alter it.

This demolishes the need for angelic propulsion. A planet, once in motion, would coast eternally in a straight line were it not for some force altering that path. The fact that it orbits — curving continually — indicates a force acting perpendicularly to its motion. As Feynman notes, “The actual motion deviates from the line… the deviation being essentially at right angles to the motion.”

This insight leads directly to the concept of centripetal force — a force directed inward, toward the centre of the circle. For a planet orbiting the Sun, this force is gravity.

Feynman’s Methodology

Feynman’s teaching method is distinctive: he does not begin with abstract formulae, but with ideas. He uses metaphors (e.g. angels, coasting stones, whirling strings) to reveal hidden symmetries. This mirrors the historical development of physics: Galileo and Newton did not arrive at their conclusions through formulae alone, but through careful observation, vivid thought experiments, and practical reasoning.

Take Feynman’s example of a stone on a string. To keep it moving in a circle, one must pull inward on the string — not in the direction of the motion, but perpendicular to it. If the string breaks, the stone flies off in a straight line. The analogy is apt for planetary motion: gravity plays the role of the string, constantly redirecting the planet inward, but never speeding it up tangentially. This is consistent with Newton’s laws, and reflects the elegance of his universal law of gravitation:

Historical Sources: Bridging Feynman’s Account with Original Texts

Feynman summarises hundreds of years of scientific revolution in a single lecture. For readers wishing to go deeper, primary historical sources enrich our understanding:

• Galileo’s “Two New Sciences” (1638) — presents his inclined plane experiments and the first clear statement of inertia.

• Newton’s “Principia” (1687) — a mathematically rigorous framework uniting celestial and terrestrial motion under universal laws.

• Kepler’s “Astronomia Nova” (1609) — where his first two laws are laid out following extensive analysis of Tycho Brahe’s planetary data.

Historian Alexandre Koyré, in From the Closed World to the Infinite Universe (1957), and more recently James Gleick in Isaac Newton (2003), provide accessible accounts of how these thinkers reshaped the cosmos.