Chapter 7: Gravitation – From Newton to Einstein

The discussion of the theory of gravitation introduces one of the most fundamental and elegant generalizations concerning nature, asserting that every object in the universe exerts an attractive force on every other object. This force is mathematically defined as being proportional to the product of the two masses and inversely proportional to the square of the distance between them. Historically, the foundation for this law was laid by analyzing astronomical observations, notably the precise measurements recorded by Tycho Brahe, which were then utilized by Kepler to formulate his three laws of planetary motion. Kepler's laws state that planets travel in elliptical orbits with the sun at one focus; that the radius vector sweeps out equal areas in equal times; and that the square of the orbital period is proportional to the three-halves power of the semi-major axis. Building on these insights and incorporating Galileo’s development of dynamics, Sir Isaac Newton understood that the force responsible for accelerating falling objects on Earth is identical to the force that keeps the moon in its orbit, thereby establishing the principle of universal gravitation. Newton demonstrated that the moon, which otherwise would move in a straight line, is constantly pulled toward the Earth at a rate consistent with the inverse square law when calculating its deviation from a straight path over time. This comprehensive law explains diverse phenomena, including the ocean tides (caused by the differential gravitational pull of the moon and sun on the Earth's water) and the subtle orbital perturbations of planets like Uranus, which led to the mathematical prediction and subsequent discovery of Neptune. Furthermore, the chapter describes how Henry Cavendish experimentally measured the gravitational constant (G) using a torsion balance, providing a precise numerical value for the force and effectively determining the mass of the Earth. While the mathematical form of the law is exceptionally accurate for calculating motions, the fundamental mechanism of gravity itself remains mysterious. The chapter concludes by noting that Einstein's theory of relativity introduced necessary modifications, particularly concerning the finite speed of gravitational effects, correctly predicting the bending of light by massive bodies and improving accuracy, although the pursuit of a complete quantum theory of gravitation continues.