Newton's Three Laws of Motion

Kepler's three laws say how the planets move: elliptical orbits, equal areas swept in equal times, a period tied to the semi-major axis. They do not say why. That answer lies in the three laws of motion Isaac Newton published in Philosophiæ Naturalis Principia Mathematica — the book the Royal Society had promised to print but could not fund, and which appeared in 1687 largely because Edmond Halley paid for it out of his own pocket.

Those three laws are not about planets in particular. They are about every object that has mass.

The three statements

NASA renders the three laws from the Principia as follows:

1. "Every body continues in a state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed upon it."
2. "The change of motion (linear momentum) is proportional to the force impressed and is made in the direction of the straight line in which that force is impressed."
3. "To every action there is always an equal and opposite reaction; or, the mutual actions of two bodies upon each other are always equal, and act in opposite directions."

The order is not accidental: the first law says what happens when there is no force, the second quantifies what happens when there is one, and the third says a force never travels alone.

First law: inertia, and what it does not say

NASA calls the first law the definition of inertia. Its content runs against intuition at one point: keeping something moving takes no force at all — only changing its motion does.

As NASA Glenn puts it: if all the external forces cancel each other out, so that there is no net force, the object keeps its velocity — both magnitude and direction. So "at rest" and "drifting in a straight line at constant speed" are the same dynamical state; the difference lies only in where the observer stands.

That is why "what keeps a planet flying?" is the wrong question: nothing needs to keep it going. The right question is what makes its path curve.

Second law: force is the rate of change of momentum

The rigorous form of the second law is not F = ma. NASA states it this way: force F equals the change in momentum with respect to time; for an object of constant mass m, that reduces to mass times acceleration, F = ma.

The distinction is practical, not formal: a rocket's mass drops every second as it throws propellant out the back, so a rocket problem has to be worked in momentum — applying F = ma with a fixed m there is using the wrong form of the law.

NIST lists the newton (symbol N) as the SI derived unit with a special name for force, written in base units as kg·m·s⁻². Read that expression backwards and the second law comes out of it: one newton is the force that gives one kilogram an acceleration of one metre per second squared. Multiply a newton by a metre and you get a joule, the unit of energy.

Third law: two forces, on two different objects

The word that causes the most trouble in the third law is "cancel". If every force has an equal and opposite partner, how does anything ever move?

NASA Glenn undoes the knot in one sentence: "notice that the forces are exerted on different objects". The two forces in an action–reaction pair never add up on the same object, so they do not lock any object in place. Only forces on the same object add together — and that is the second law's business.

NASA's own example is an aircraft wing: the shape and motion of the wing deflect the passing air downward — that is the wing's action on the air; the reaction is the air pushing the wing up.

This pairing is also why gravity always runs both ways: the Earth pulls on you, and you pull on the Earth with exactly the same magnitude.

Why Kepler needed Newton

Kepler drew his three laws from observational data and knew nothing of gravity. According to NASA, those laws later became the material from which Newton built his theory of universal gravitation — the theory that explained the unknown force behind Kepler's third law.

The direction of that advance is worth stating plainly: Newton did not re-measure the planets. He proposed a cause — an attraction between masses — and then showed that this cause, fed into the second law, forces the planets to move exactly as Kepler had described. Three descriptive regularities became consequences of one cause.

The power of that view is measurable in a prediction: perturbations in the orbit of Uranus were turned into coordinates for a planet nobody had ever seen, and Neptune was found in 1846 close to the spot the arithmetic pointed at.

How far the three laws hold

Not absolutely, but further than many people assume. NASA says it plainly in its spaceflight navigation material: since spacecraft velocities do not approach a significant fraction of the speed of light, Newtonian physics serves well for operating and navigating throughout the solar system.

The same material notes one exception running every day: the GPS satellite fleet does require special-relativity calculations to give accurate positions. That is where the boundary sits — for everyday life and for most interplanetary work, Newton's three laws are the right tool; at speeds near that of light, the tool has to change.