Before a science of motion existed, there was an older account of nature. Aristotle, a Greek thinker, held that things fall or rise because of their nature: earth and water carry heaviness and head downward, whereas air and fire carry lightness and head upward. People spent almost 2,000 years before Newton's day assuming that every object tends naturally toward rest, yet the view that replaced this account is quite different. According to it, something at rest stays at rest unless pushed or pulled, and something moving carries on unchanged and stays that way until a force acts on it. A sliding book comes to a halt on a table only because friction acts on it; without friction it would carry on with unchanged speed and direction. A force is simply a push or a pull, which may make an object gain speed, lose speed or change course.
The scientist at the center of this change, Galileo Galilei, came into the world in the city of Pisa on 15 February 1564; his father worked as a court musician. He quit the university there with no degree, yet he went on to be a central figure in the Scientific Revolution. One summary credits him with working out the law of free fall, an inertial principle, the curved, parabolic route of projectiles, and the point that all motion is relative. He also had to answer an objection: if Earth moved, a ball let fall would be left trailing. His reply was that a cannonball released from a tower still comes down at the tower's base, since after release the ball goes on moving together with the tower, which is inertia at work. His final book, Discourses and Mathematical Demonstrations Concerning Two New Sciences, rested on his early work in mechanics; it was smuggled out of Italy and printed in Holland in 1638.
Galileo tried a ball on two facing slopes. Released on one, it climbed the other to roughly the same height, and he attributed any shortfall to friction, which is a force acting against surfaces as they slide or rub. Coarse surfaces create more friction than fine ones, since two coarse sheets of sandpaper are harder to slide against each other than two fine ones. Next he imagined flattening the second slope almost completely: the ball, reaching for its original height, would travel nearly without end. This led toward the idea of inertia, and it backed his view that moving things stop because friction acts on them, not because stopping is their nature. It takes more force to get a heavy crate sliding than to keep it going, since a resting thing meets more friction than a moving one.
Galileo challenged Aristotle's claim that heavier things fall faster with a thought experiment. Tie a heavy body to a light one in mid-fall. The light body ought to drag on the heavy one, but the tied pair outweighs either body, so it ought to fall faster, and the two conclusions clash. Experiments with inclined planes then yielded his law of free fall: the distance fallen from rest grows in proportion to the time squared, so a ball falling for twice as long drops four times as far. Galileo concluded that a heavy object does not fall faster than a light one. Inclined planes are useful machines as well: a ramp makes lifting easier, since pushing a load along a slope takes a push smaller than the load's weight, and the trade is a longer path.
Astronauts later tested the matter on the Moon, which has almost no air. On Apollo 15 a feather and a hammer, with masses of 0.03 and 1.32 kilograms, were dropped from about 1.6 meters, and they reached the Moon's surface at about the same moment, as theory predicted. Moving things are slowed by air and water, a force called drag, and with no fluid there is no drag, so heavy and light bodies alike fall together. NASA described the drop as reassuring rather than surprising, since it agreed with well-established theory on which the journey home depended. The gravitational pull on a thing is its weight, and the gravity of the Moon is about one-sixth that of Earth, so people weigh much less there; near Earth's surface, weight is mass multiplied by g, a value of 9.8 newtons per kilogram.
Isaac Newton's birth took place in Woolsthorpe, a village in Lincolnshire, England, on 25 December 1642 according to the calendar of the day, a few days short of a year after Galileo died. He lived until 1727. Newton had shown little interest in orbits until Robert Hooke opened a short exchange of letters with him in November 1679. Newton noticed that the Moon accelerates inward in its orbit about 3,600 times less than g at Earth's surface, while the Moon sits about 60 Earth radii from Earth's center. Mass does not change from Earth's surface to orbit to the Moon, and near Earth gravity pulls toward the planet's center, so a dropped ball falls. The kilogram measures mass and the newton measures force, weight included, while in America the pound is another unit of weight.
Since 60 squared is 3,600, one inverse-square force could account for both falling objects and the Moon's orbit. Inverse-square laws appear throughout nature: a source's strength is spread over the surface of a sphere, which grows as the distance squared, so twice the distance leaves a quarter of the pull, which is to say that doubling the distance weakens the pull fourfold. Gravity strengthens with the mass involved, which is why Earth's gravity comes from all its mass, and it weakens as things separate; like any push or pull it has both a size and a direction. In late 1684 Newton sent Edmond Halley a nine-page manuscript, De Motu Corporum in Gyrum, which means On the Motion of Bodies in Orbit, and the Royal Society entered it in its register that December. Earth's gravity draws things toward the ground.
Over the period from late 1684 to early 1687, Newton grew that short tract, the one entered into the Royal Society's register, into the Principia, roughly 500 pages, with 192 propositions derived within them. Book 1 reached London in spring 1686, and Books 2 and 3 in March and April 1687. The Principia's conclusion was that the force keeping planets in orbit is of the same kind as gravity on Earth, which ended the long-held view, traceable at least to Aristotle, that the heavens and the earth below the Moon each need their own science. Taken together with Kepler's laws, Newton's laws also explained why planetary orbits are elliptical instead of circular. Motion in a circle requires a force toward the center, called centripetal, or center-seeking, and a spinning ball whose string breaks flies off straight, because nothing then turns it.
Newton's three laws of motion, which he stated himself, form the base on which the study of how forces alter motion is built. The first law, about inertia, says that an object at rest remains at rest and an object in motion keeps going. A sled on level ground with neither friction nor air resistance shows it: gravity and the snow's upward push cancel, so the sled would travel on unchanged. Net force means all forces acting on a thing, summed. Forces that are equal and opposite are balanced and cancel, leaving the motion unchanged, while an unbalanced force changes the motion, and when none acts nothing changes. The first law can also be seen as the special case of the second law in which the net external force is zero, and both assume an inertial frame, meaning one that is not itself accelerating.
The second law links change in motion to force and mass: a larger force means more change and a larger mass means less, so a heavy thing responds less than a light thing to the same push. The third law states that if one object pushes a second, the second pushes the first just as hard in the opposite direction. A fish swims forward as it drives water back, and the water drives the fish ahead. These paired forces are equal and opposite, yet they do not cancel, since each acts on a different object; a swimmer shoves the wall, and only the wall's shove changes the swimmer's motion. In a car turning a corner, riders sense an outward push, but really the car is accelerating inward while their bodies tend straight on, and a centripetal force like friction on the tires turns the car.
Not everyone accepted this account at first. Through much of the 18th century Newton's theory was disputed, chiefly because it offered no contact mechanism for how gravity pulls across empty space, and Leibniz and Huygens opposed the idea of action at a distance. The work of Émilie du Châtelet, a philosopher, writer and scientist, helped establish Newton's gravitation as the accurate and overarching law, and her use of calculus to explain gravity helped lead to its acceptance. Even today the laws fit objects that move far below the speed of light and are bigger than most molecules, with relativity and quantum mechanics handling the very fast and the very small. In 1933 the astronomer Fritz Zwicky saw that galaxies in the Coma Cluster moved too quickly for the gravity of the matter we can see. He suggested that an invisible form of matter was supplying extra gravity to hold them together.
Expressed fully, the second law concerns momentum: force is the change in momentum, mass times velocity, in a given time, and F = ma is the special case in which mass stays constant. That form applies only to the net external force and not directly when mass changes, as with a burning rocket. Take a 1,400-kilogram car at 15 meters per second: its momentum is 21,000 kg·m/s, and a heavy, fast object carries more momentum than a light, slow one. A rocket moves forward by throwing gas backward at high speed, with the gas pushing the rocket ahead. The DART spacecraft shows the third law at a larger scale: debris thrown off the asteroid Dimorphos recoiled and added to the push, as air rushing out of a balloon moves the balloon the opposite way.
Words to know
- manuscript: handwritten work
- Principia: Newton's book
- inertia: resisting change
- parabolic: curved path
- propositions: claims proved
