Planetary Motion and the Birth of Universal Gravitation
The law of gravitation: F = G\,m m'/r^2. Observation replaced argument: Tycho's high-precision star catalogues → Kepler's laws → Newton's unification of dynamics and gravitation.
Core picture: Nature governs complex celestial phenomena with extremely simple laws; humans reveal these laws through quantitative measurement and deduction.
📐Kepler's Three Laws
- Elliptical orbits: The Sun sits at one focus of the ellipse.
- Equal area law: The line connecting a planet and the Sun sweeps out equal areas in equal times (indicating the force points toward the Sun).
- Period-semimajor axis relation: T ∝ a^{3/2}, a scaling law across planets.
⚙️Foundation of Dynamics: Inertia and Centripetal Force
Galileo: the principle of inertia. Newton: force causes acceleration (changing direction requires a transverse force). Planets need no tangential "push" — only a centripetal gravitational force directed toward the Sun.
\vec F = m\,\vec a
🧲Newton's Gravitation and Its Consequences
The Moon is also "falling": Its deviation from a straight-line path matches free fall on Earth's surface → verification of the 1/r^2 law.
Different launch speeds from one point: 5 mi/s yields a near-Earth orbit; faster means a higher orbit.
Tides: Near/far side imbalance produces two tidal bulges.
Predictive power: Proof of elliptical orbits; planetary mutual perturbations cause orbital precession and small deviations.
Discovery of Neptune: From Uranus anomalies → deduced position of unknown planet → confirmed by observation.
🌌Universality of Gravitation: From Binary Stars to Galaxy Clusters
- Binary star orbits: Relative motion is elliptical (line-of-sight inclination shifts the focus).
- Globular clusters/galaxies/galaxy clusters: Large-scale aggregation reveals the long-term action of gravity.
- Rømer's measurement of light speed via planetary satellites: Finite speed of light explains "early/late" appearances.
⚖️Cavendish Torsion Balance: Measuring G and "Weighing the Earth"
The first direct measurement of gravitational force between small objects, verifying 1/r^2, yielding the gravitational constant:
G ≈ 6.670 × 10^{-11} N·m²/kg²
Combined with surface gravity, one can deduce Earth's mass.
❓The "Mechanism" of Gravity?
Historical particle "pushing" models would predict noticeable drag, contradicting observations. Physical laws are mostly abstract-mathematical in form, requiring no specific "mechanical device."
Electrical and gravitational forces both follow 1/r^2, but the strength contrast is extreme: the ratio of electrostatic repulsion to gravitational attraction between electrons ≈ 4.17×10^{42}. Unification attempts have not yet succeeded; the hypothesis that "G varies with the age of the universe" conflicts with solar/terrestrial conditions.
🛰️Gravity and Relativity
- Newtonian gravity is not instantaneous; Einstein's correction gives relativistic gravity, propagating at the speed of light.
- Energy is equivalent to mass: light bends near the Sun (confirmed during solar eclipse observations).
- Equivalence principle: Inertial mass = gravitational mass (Eötvös/Dicke experiments to 1e-9 precision).
- Quantum gravity: A complete theory compatible with quantum mechanics has not yet been established.
✨Key Points
Kepler's three laws + Newton's dynamics ⇒ universal gravitation F ∝ 1/r^2.
Gravity is universal: unified explanation from lunar tides to galaxy cluster aggregation.
The Cavendish experiment measured G, enabling quantification of Earth's mass, etc.
Relativistic corrections and the equivalence principle hold; quantum gravity remains a frontier challenge.