3-5 Isaac Newton formulated three laws relating force and motion to describe fundamental properties of physical reality

Until the mid-seventeenth century, virtually all attempts to describe the motions of the heavens were empirical, or based directly on data and observations. From Ptolemy to Kepler, astronomers would adjust their ideas and calculations by trial and error until they ended up with answers that agreed with observation.

Isaac Newton introduced a new approach. He began with three quite general statements, now called Newton’s laws of motion. These laws, deduced from experimental observation, apply to all forces and all objects. Newton then showed that Kepler’s three laws follow logically from these laws of motion and from a formula for the force of gravity that he derived from observation.

In other words, Kepler’s laws are not just an empirical description of the motions of the planets, but a direct consequence of the fundamental laws of physical matter. Using this deeper insight into the nature of motions in the heavens, Newton and his successors were able to accurately describe not just the orbits of the planets but also the orbits of the Moon and comets.

Newton’s First Law of Motion

Newton’s laws of motion describe objects on Earth as well as in the heavens. Thus, we can understand each of these laws by considering the motions of objects around us. We begin with Newton’s first law of motion:

An object remains at rest, or moves in a straight line at a constant speed, unless acted upon by a net outside force.

By force we mean any push or pull that acts on the object. An outside force is one that is exerted on the object by something other than the object itself. The net, or total, outside force is the combined effect of all of the individual outside forces that act on the object.

Right now, you are demonstrating the first part of Newton’s first law. As you sit in your chair reading this, there are two outside forces acting on you: The force of gravity between you and Earth pulls you downward and, at the same time, the chair pushes up on you. These two forces are of equal strength but of opposite direction, so their effects cancel—there is no net outside force. Hence, your body remains at rest as stated in Newton’s first law. If you try to lift yourself out of your chair by grabbing your knees and pulling up, you will remain at rest because this force is not an outside force.

Newton’s first law tells us that if no net outside force acts on a moving object, it can only move in a straight line and at a constant speed. This means that a net outside force must be acting on the planets since they do not move in straight lines, but instead move around elliptical paths. To see why, note that a planet would tend to fly off into space at a steady speed along a straight line if there were no other outside force acting on it to keep it moving around our Sun. Because this does not happen, Newton concluded that a force must act continuously on the planets to keep them in their elliptical orbits.

Newton’s Second Law of Motion

Newton’s second law describes how the motion of an object changes if there is a net outside force acting on it. To appreciate Newton’s second law, we must first understand quantities that describe motion: speed, velocity, and acceleration.

Speed is a measure of how fast an object is moving. Speed and direction of motion together constitute an object’s velocity. Compared with a car driving north at 100 km/h (62 mi/h), a car driving east at 100 km/h has the same speed but a different velocity. We can restate Newton’s first law to say that an object has a constant velocity (its speed and direction of motion do not change) if no net outside force acts on the object.

Acceleration is the rate at which velocity changes. Because velocity involves both speed and direction, acceleration can result from changes in either. Contrary to popular use of the term, acceleration does not simply mean speeding up. A car is accelerating if it is speeding up, and it is also accelerating if it is slowing down or turning (that is, changing the direction in which it is moving).

You can verify these statements about acceleration if you think about the sensations of riding in a car. If the car is moving with a constant velocity (in a straight line at a constant speed), you feel the same as if the car were not moving at all. But you can feel it when the car accelerates in any way: You feel thrown back in your seat if the car speeds up, thrown forward if the car slows down, and thrown sideways if the car changes direction in a tight turn.

An apple falling from a tree is a good example of acceleration that involves only an increase in speed. Initially, at the moment the stem breaks, the apple’s speed is zero. After 1 s, its downward speed is 9.8 meters per second, or 9.8 m/s (32 feet per second, or 32 ft/s). After 2 s, the apple’s speed is twice this, or 19.6 m/s. After 3 s, the speed is 29.4 m/s. Because the apple’s speed increases by 9.8 m/s for each second of free fall, the rate of acceleration is 9.8 meters per second per second, or 9.8 m/s² (32 ft/s²). Thus, Earth’s gravity gives the apple a constant acceleration of 9.8 m/s² downward, toward the center of Earth.

A planet revolving about the Sun along a perfectly circular orbit is an example of acceleration that involves change of direction only. As the planet moves along its orbit, its speed remains constant. Nevertheless, the planet is continuously being accelerated because its direction of motion is continuously changing.

Newton’s second law of motion says that in order to give an object an acceleration (that is, to change its velocity), a net outside force must act on the object. To be specific, this law says that the acceleration of an object is proportional to the net outside force acting on the object. That is, the harder you push on an object, the greater the resulting acceleration. This law can be succinctly stated as an equation. If a net outside force F acts on an object of mass m, the object will experience an acceleration a described by the following mathematical equation:

Newton’s second law

The mass of an object is a measure of the total amount of material in the object. It is usually expressed in kilograms (kg). For example, the mass of the Sun is 2 × 10³⁰ kg, the mass of a hydrogen atom is 1.7 × 10⁻²⁷ kg, and the mass of an average adult is 75 kg. The Sun, a hydrogen atom, and a person have these masses regardless of where they happen to be in the universe.

We can use Newton’s second law to relate mass and weight. We have seen that the acceleration caused by Earth’s gravity is 9.8 m/s². When a 50-kg swimmer falls from a diving board, the only outside force acting on her as she falls is her weight. Thus, from Newton’s second law (F = ma), her weight is equal to her mass multiplied by the acceleration due to gravity:

Note that this answer is correct only when the swimmer is on Earth. She would weigh less on the Moon, where the gravitational attraction between the swimmer and the Moon is weaker because the Moon has less mass than Earth. Alternatively, she would weigh more on Jupiter because Jupiter has more mass and the gravitational attraction between the two is greater. Floating deep in space, she would have no weight at all; she would be “weightless.” Nevertheless, in all these circumstances, she would always have exactly the same mass, because mass is an inherent property of matter regardless of where it is located. Whenever we describe the properties of planets, stars, or galaxies, we speak of their masses, never of their weights.

We have seen that a planet is continually accelerating as it orbits the Sun. From Newton’s second law, this means that there must be a net outside force that acts continually on each of the planets. As we will see in the next section, these forces are the gravitational attractions between the planets and our Sun.

Newton’s Third Law of Motion

The last of Newton’s general laws of motion, called Newton’s third law of motion, is the famous statement about action and reaction:

Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first object.

For example, if you weigh 110 lb, when you are standing up you are pressing down on the floor with a force of 110 lb. Newton’s third law tells us that the floor is also pushing up against your feet with an equal force of 110 lb. You can think of each of these forces as a reaction to the other force, which is the origin of the often used phrase “every action has an equal and opposite reaction.”

Newton realized that because each planet is gravitationally attracted to the Sun, the Sun must also be attracted to the planets. However, the planets are much less massive than the Sun (for example, Earth has only 1/300,000 of the Sun’s mass). Therefore, although the Sun’s attraction to a planet is the same as the planet’s attraction to the Sun, the planet’s much smaller mass gives it a much larger acceleration and moves it significantly more than the Sun. This is why the planets circle the Sun instead of vice versa. Thus, Newton’s laws reveal the reason for our heliocentric solar system.