Gravity as Presented by Classical Mechanics

Gravity, one of the four known fundamental forces in nature, governs the motion of planets, stars, galaxies, and the everyday objects around us. Within the framework of Newtonian classical mechanics, gravity is understood as an attractive force acting at a distance, exerted between all objects with mass. Though later revised by the theory of General Relativity, Newton's formulation remains crucial for understanding most physical systems encountered in engineering and terrestrial physics.

Table of Contents
  • Introduction
  • What is Gravity
  • What Came Before Gravity
  • Timeline of Gravity Discovery
  • Explanation of Scientific Evidence Collected to Prove Gravity
  • Mathematics of Gravity
  • Summary
Introduction

A foundational observational truth underpins Newtonian gravity: mass always attracts mass. Unlike other forces, gravity never repels. This persistent, attractive interaction is a cornerstone of gravitational theory and is unique among nature’s forces.

What is Gravity

In classical mechanics, gravity is defined as a universal, attractive force that acts between all objects that have mass. It is omnipresent and unavoidable: whether objects are microscopic particles or entire planets, they are drawn toward each other through this force.

Critically, gravity is unique among the four fundamental forces:

  • Electromagnetism can attract or repel depending on charge.
  • The strong nuclear force operates only at subatomic distances to bind quarks and nucleons.
  • The weak nuclear force is responsible for radioactive decay and likewise limited in range.
  • Gravity, however, is always attractive, acts on all mass regardless of composition, and has an infinite range.

There is no known form of negative mass and no known gravitational "shielding." These features make gravity qualitatively distinct from all other interactions in the physical universe.

What Came Before Gravity

Before gravity was formalized, motion and attraction were explained through philosophical doctrines rather than empirical laws. Key historical perspectives included:

  • Aristotle (384–322 BCE): Posited that heavier objects fall faster and that celestial and terrestrial realms obey different principles.
  • Ptolemy (2nd century CE): Advanced a geocentric model with epicycles, explaining planetary motion through geometry, not force.
  • Medieval scholars maintained these ideas, lacking the mathematical framework to describe interactions like gravity.

Notably, none of these early thinkers proposed that all matter in the universe attracts all other matter—an idea introduced and mathematically formalized much later.

Timeline of Gravity Discovery
Year Contributor Contribution
\~1543 Nicolaus Copernicus Proposed heliocentric solar system
1609–1619 Johannes Kepler Laws of planetary motion from Brahe’s data
1604 Galileo Galilei Demonstrated uniform acceleration of falling bodies
1687 Isaac Newton Unified celestial and terrestrial gravity in Principia
1798 Henry Cavendish Measured gravitational constant with torsion balance
Explanation of Scientific Evidence Collected to Prove Gravity

Classical gravity is based on a series of cumulative experiments and astronomical observations:

1. Kepler’s Laws of Planetary Motion

Kepler, analyzing Brahe’s planetary data, found that planets move in elliptical orbits, sweeping equal areas in equal times. These empirical laws implied a central force pulling planets toward the Sun.

2. Galileo’s Experiments

Galileo's inclined plane experiments revealed that all objects, regardless of mass, fall with uniform acceleration, provided air resistance is negligible. This implied that gravity affects all mass equally.

3. Newton’s Unification

Newton demonstrated that the same force responsible for a falling apple also governs the Moon’s orbit. The key realization was that mass attracts mass—not just on Earth, but universally.

“To every action there is always opposed an equal reaction… All bodies gravitate toward every other body.” — Isaac Newton, Philosophiae Naturalis Principia Mathematica (1687)

4. Cavendish’s Measurement of G

Cavendish was the first to measure the strength of gravity between known masses, quantifying the constant $G$. His work confirmed that gravitational attraction exists even between small laboratory-scale masses, supporting Newton’s claim of universality.

Mathematics of Gravity

Newton's Law of Universal Gravitation is given by the equation:

$$ F = G \frac{m_1 m_2}{r^2} $$

Where:

  • $F$ is the gravitational force
  • $G \approx 6.674 \times 10^{-11} \, \text{N·m}^2/\text{kg}^2$
  • $m_1$ and $m_2$ are the interacting masses
  • $r$ is the distance between the centers of mass

This inverse-square law implies that gravitational force weakens with distance, but never vanishes completely.

Key Characteristics:

  • Always attractive
  • Universal across all masses
  • Non-shieldable (no way to block it)
  • Weaker than all other fundamental forces, yet dominates at astronomical scales due to its long range and additivity

In contrast:

  • Electromagnetic forces can cancel due to positive and negative charges
  • Nuclear forces are extremely strong but confined to the atomic nucleus

Thus, gravity is both the weakest and the most pervasive of nature's forces.

Summary

Classical mechanics portrays gravity as a universal, attractive force between masses, mathematically described by Newton’s inverse-square law. The foundational principle that mass always attracts mass distinguishes gravity from all other interactions in the universe. Unlike electromagnetism and the nuclear forces, gravity acts on all matter uniformly, has no repulsive component, and is always cumulative.

Though superseded in precision by Einstein’s General Relativity, Newtonian gravity remains an indispensable framework for understanding and predicting natural phenomena at human and planetary scales. Its conceptual clarity, mathematical elegance, and empirical basis have made it a pillar of classical physics.