PHY101 Mechanics | Recitation 9: Verifying Newton’s Law of Gravitation (The Moon Test) скачать в хорошем качестве

PHY101 Mechanics | Recitation 9: Verifying Newton’s Law of Gravitation (The Moon Test)

This recitation focuses on the "Moon Test," a pivotal historical argument used to prove that the force of gravity on Earth's surface and the force governing planetary orbits are one and the same. The instructor walks through the observed astrophysical data versus the theoretical predictions made by Newton's inverse-square law. Key Topics Covered: The Comparative Experiment [01:05]: Comparing the distance an object falls near Earth (s₀ ≈ 4.9m in 1 second) to the distance the Moon "falls" toward Earth in the same time interval. Calculating the Moon's "Fall" [02:51]: Using the Moon's orbital period (27.3 days) and orbital radius (Rₘ = 3.8 × 10⁸ m) to determine the angle swept out and the resulting vertical displacement (sₘ). Trigonometric Derivation [04:12]: Deriving the displacement formula sₘ = Rₘ(1 - cos(θ)) and using Taylor series expansions for small angles to simplify it to sₘ ≈ ½ Rₘ θ². [06:42] Newton's Inverse Square Prediction [08:37]: Explaining why Newton used the ratio of these two distances (sₘ / s₀) to test his theory, effectively canceling out unknown constants like the gravitational constant (G) and the mass of the Earth (M). [15:11] The Verification [16:12]: Showing that both the observed ratio and the predicted ratio (Rₑ / Rₘ)² yield the same numerical value (approx. 2.8 × 10⁻⁴), confirming the universal nature of gravity.