I have long held an intuition: Kepler’s Laws and the Principle of the Lever are subtly connected.

Proposed by Archimedes, the Principle of the Lever centers on the equation:
Force × Effort Arm = Resistance × Resistance Arm.
At its core, it describes energy transfer and motion under the equilibrium of torques.
Kepler’s Three Laws, by contrast, precisely characterize the orbital geometry and dynamical relationships of planets orbiting the Sun. If we regard the Sun as the fulcrum of the orbital system, these two sets of laws—one belonging to statics, the other to celestial mechanics—reveal profound logical correspondence and mathematical isomorphism.

Kepler’s First Law states that planets orbit the Sun along ellipses, with the Sun at one focus. In a lever system, the fulcrum is the center of torque equilibrium. Similarly, the Sun acts as the gravitational fulcrum: its gravitational force always points toward the planet’s center of mass, analogous to the force exerted by the fulcrum on the lever. The perihelion and aphelion of the elliptical orbit may be compared to the two ends of a lever: at perihelion, the planet is close to the Sun, like the short arm of a lever; at aphelion, it is far away, like the long arm. This spatial correspondence lays the foundation for connecting the two principles.

Kepler’s Second Law—the Law of Equal Areas embodies their deepest connection.
It holds that the line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. From the perspective of torque, the Sun’s gravitational pull is a central force, producing zero torque on the planet. Thus, the planet’s angular momentum is conserved, expressed as:
L = m v r
where m = planetary mass, v = linear speed, r = distance from the Sun.
The torque formula for levers is:
M = F L
The forms are strikingly similar:
r in angular momentum corresponds to the lever arm L; the product mv corresponds to the effect of the applied force F.

At perihelion, r decreases; to conserve L, v increases.
At aphelion, r increases; thus v decreases.
This mirrors the lever principle: a shorter arm requires a greater force.
With the Sun as fulcrum, the “short arm” at perihelion corresponds to higher speed, and the “long arm” at aphelion to lower speed—both fundamentally maintaining conservation and equilibrium.

Kepler’s Third Law relates orbital period to semi-major axis:
\frac{a^3}{T^2} = k
where a = semi-major axis, T = orbital period, k = constant dependent on the central body.
From an extended lever perspective, a acts as the average lever arm, and T relates to the lever’s cycle of motion. Planets with larger orbits act like longer levers, with correspondingly longer periods—fully consistent with Kepler’s Third Law.

To be clear: Kepler’s Laws govern celestial motion in a gravitational field, while the Lever Principle applies to static equilibrium of rigid bodies. They differ in physical domain and fundamental nature. Yet interpreting the Sun as a fulcrum reveals their shared logic: balance and conservation.
Exploring this connection deepens our understanding of celestial motion and reflects the underlying unity across different branches of physics.

Archimedes once said:
Give me a place to stand, and I shall move the Earth with a lever.

Today I say:
That fulcrum is the Sun.
Archimedes may rest in peace.

Kepler fulfilled Archimedes’ prophecy. I have only given it voice.