Science › Classical physics
Newton's laws of motion
1687· Theory
ProvenTested many times; part of working physics.
Three rules, published in 1687, that describe how forces change the motion of any object.
See it on the Science map →How it works
First: an object keeps moving at a steady speed in a straight line, or stays at rest, unless a force acts on it. Second: force equals mass times acceleration (F = ma), so the same push moves a light cart faster than a loaded truck. Third: every force has an equal and opposite partner; a rocket pushes gas backward, and the gas pushes the rocket forward.
Why it matters
They turned motion into calculation. Bridges, cars, artillery, orbits and building structures are all designed with them.
Think of it like
Every load on a beam is met by an equal reaction at its supports. That is the third law, and why structural engineers can balance a building's loads.
How we know
Three centuries of successful predictions, from planetary positions to Moon landings. They break down only near light speed (relativity) and at atomic sizes (quantum mechanics), where newer theories take over but reproduce them as approximations.
Connections (3)
▸Isaac Newton wrote Newton's laws of motionProven
The relationship
Newton took Galileo's insight about inertia and Kepler's planetary data and condensed them into three general laws. He framed motion in terms of forces: anything that changes an object's speed or direction. One method now described cannonballs, pendulums, tides and planets, replacing a patchwork of separate rules.
How the link was found
Newton published them in the 'Philosophiæ Naturalis Principia Mathematica' in July 1687, prompted and paid for by Edmond Halley.
Why it's proven
Centuries of precise predictions, including spacecraft navigation. Limits found in the 20th century (relativity, quantum mechanics) refined rather than overturned them at everyday scales.
Open questions and mysteries
Why objects have inertia at all, and what ultimately sets their mass, are only partly answered, through the Higgs field and debates over Mach's principle.
▸Calculus: the math of change is the language of Newton's laws of motionProven
The relationship
Newton's second law links force to acceleration; acceleration is the rate of change of velocity, which is the rate of change of position. Calculus handles those rates. Given the forces, integration runs the motion forward step by step to predict where anything will be at any later time. Without calculus, the laws could only handle simple cases.
How the link was found
Newton built both together in the 1660s–1680s. Leonhard Euler wrote the laws in their modern calculus form around 1750.
Why it's proven
Every successful trajectory calculation, from artillery tables to Apollo, uses this pairing. Computer simulations of motion are calculus done numerically.
Open questions and mysteries
Calculus assumes space and time are perfectly smooth. Whether they stay smooth at the tiniest scales, where quantum gravity matters, is unknown.
▸Newton's laws of motion was corrected at high speed by Special relativityProven
The relationship
Newton's laws assume time and space are the same for everyone and that speeds simply add. Special relativity keeps the laws' spirit but corrects them: momentum and energy grow without limit as speed approaches light's, so no amount of push gets a mass to light speed. At everyday speeds the corrections are far too small to notice.
How the link was found
Einstein in 1905; Max Planck and others reworked the formulas for momentum and energy in 1906-1908.
Why it's proven
Particle accelerators must use relativistic formulas to steer beams. Bertozzi's 1964 experiment showed electrons getting more energetic but never exceeding light speed.
Open questions and mysteries
None major for this link; it is settled physics.