What Is Newton's Law of Universal Gravitation?
Discover Newton's law of universal gravitation: the fundamental force explaining why objects fall and planets orbit. Learn the formula, history, examples, and its role in modern physics in this concise guide.
Newton's law of universal gravitation describes the attractive force between any two objects with mass. Proposed by Sir Isaac Newton in 1687, it states that every particle in the universe attracts every other with a force proportional to their masses and inversely proportional to the square of the distance between them. This principle revolutionized our understanding of motion in the cosmos.
Historical Background
Isaac Newton developed the law while working on his Philosophiæ Naturalis Principia Mathematica, published in 1687. Inspired by observations like the falling apple and Johannes Kepler's laws of planetary motion, Newton unified terrestrial and celestial mechanics. The law built on earlier ideas from Galileo and Hooke, providing a mathematical framework for gravity.
It marked the birth of classical mechanics, enabling predictions of orbits and tides. Newton's work laid the groundwork for later theories, including Einstein's general relativity.
The Mathematical Formula
The law is expressed as F = G × (m₁ × m₂) / r², where F is the gravitational force, m₁ and m₂ are the masses of the objects, r is the distance between their centers, and G is the gravitational constant (approximately 6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻²).
This inverse square law means force weakens rapidly with distance—doubling the distance reduces force to a quarter. The attraction is always along the line connecting the centers of mass.
Symmetric force: The force on each object equals the force on the other, per Newton's third law.
Universal application: Applies to all masses, from apples to galaxies.
Real-World Examples
On Earth, the law explains why objects fall: Earth's mass pulls them downward with acceleration of about 9.8 m/s². It also governs the Moon's orbit around Earth, balancing centrifugal force with gravitational pull.
Planetary orbits: Explains elliptical paths described by Kepler, as in Jupiter orbiting the Sun.
Tides: Moon and Sun's gravity cause ocean bulges, creating high and low tides.
Cavendish experiment (1798): Henry Cavendish measured G using torsion balance with lead spheres, confirming the law at small scales.
Significance and Limitations
Newton's law predicted comet paths, enabling space missions like Apollo. It's essential for engineering satellites and understanding black holes in approximation. However, it fails at very high speeds or strong fields, where general relativity provides corrections.
Modern uses include GPS satellites, accounting for weaker gravity at altitude.
Conclusion
Newton's law of universal gravitation remains a cornerstone of physics, elegantly explaining cosmic order. For deeper study, explore simulations or Kepler's laws to see its predictive power in action.