Newton's Law of Universal Gravitation

Introduction

• Describes gravity as a force of attraction between particles.
• Force is proportional to the product of their masses and inversely proportional to the square of the distance between centers.
• Known as the "first great unification" as it unified gravity on Earth with astronomical behaviors.

Historical Context

• Formulated by Isaac Newton in "Philosophi Naturalis Principia Mathematica," published in 1687.
• Derived through empirical observations and inductive reasoning.
• The Cavendish experiment in 1798 was the first laboratory test of this law.

Mathematical Formulation

• Universal gravitation equation: [ F = G \frac{m_1 m_2}{r^2} ]
  • ( F ): gravitational force
  • ( m_1, m_2 ): masses of the objects
  • ( r ): distance between centers of masses
  • ( G ): gravitational constant

Comparison to Coulomb's Law

• Newton's law resembles Coulomb's law for electrical forces.
• Both are inverse-square laws.

Successors and Limitations

• Superseded by Einstein's theory of general relativity for extreme conditions.
• Universality of ( G ) remains intact for most applications.

Early Theories of Gravity

• Pre-Newtonian philosophers like Aristotle had different explanations for gravity.
• Galileo and Kepler contributed through observations and laws of motion.

Newton's Contributions

• Newton applied his law to celestial bodies, explaining Kepler's laws.
• Encountered accusations from contemporaries like Robert Hooke.
• Newton was uncomfortable with "action at a distance," a concept implied by his law.

Modern Interpretation

• Every point mass attracts another with a force along the line joining them.
• Involves vector form for more than two objects.

Gravitational Fields

• Describes force applied to an object in space per unit mass.
• Utilizes concepts like gravitational potential field and Gauss's law.

Limitations of Newton's Gravity

• Inaccuracies in predicting precession of planetary orbits, e.g., Mercury.
• Insufficient to explain light deflection by gravity.
• General relativity offers corrections and explanations.

Recent Developments

• Non-inverse square terms explored through neutron interferometry.
• Solutions to n-body problems in celestial mechanics remain challenging.

See Also

• Related topics include Kepler orbits, Gauss's law for gravity, and Einstein's general relativity.
• Notable experiments like Feather and Hammer Drop on the Moon.