# Applications and Limitations of Newton's Laws

By themselves, the three laws of motion are a crowning achievement, but Newton didn't stop there. He took those ideas and applied them to a problem that had stumped scientists for years -- the motion of planets. Copernicus placed the sun at the center of a family of orbiting planets and moons, while the German astronomer Johannes Kepler proved that the shape of planetary orbits was elliptical, not circular. But no one had been able to explain the mechanics behind this motion. Then, as the story goes, Newton saw an apple fall to the ground and was seized by inspiration. Could a falling apple be related to a revolving planet or moon? Newton believed so. This was his thought process to prove it:

- An apple falling to the ground must be under the influence of a force, according to his second law. That force is gravity, which causes the apple to accelerate toward Earth's center.
- Newton reasoned that the moon might be under the influence of Earth's gravity, as well, but he had to explain why the moon didn't fall into Earth. Unlike the falling apple, it moved parallel to Earth's surface.
- What if, he wondered, the moon moved about the Earth in the same way as a stone whirled around at the end of a string? If the holder of the string let go -- and therefore stopped applying a force -- the stone would obey the law of inertia and continue traveling in a straight line, like a tangent extending from the circumference of the circle.
- But if the holder of the string didn't let go, the stone would travel in a circular path, like the face of a clock. In one instant, the stone would be at 12 o'clock. In the next, it would be at 3 o'clock. A force is required to pull the stone inward so it continues its circular path or orbit. The force comes from the holder of the string.
- Next, Newton reasoned that the moon orbiting Earth was the same as the stone whirling around on its string. Earth behaved as the holder of the string, exerting an inward-directed force on the moon. This force was balanced by the moon's inertia, which tried to keep the moon moving in a straight-line tangent to the circular path.
- Finally, Newton extended this line of reasoning to any of the planets revolving around the sun. Each planet has inertial motion balanced by a gravitational attraction coming from the center of the sun.

It was a stunning insight -- one that eventually led to the universal law of gravitation. According to this law, any two objects in the universe attract each other with a force that depends on two things: the masses of the interacting objects and the distance between them. More massive objects have bigger gravitational attractions. Distance diminishes this attraction. Newton expressed this mathematically in this equation:

F = G(m_{1}m_{2}/r^{2})

where **F** is the force of gravity between masses **m _{1}** and

**m**,

_{2}**G**is a universal constant and

**r**is the distance between the centers of both masses.

Over the years, scientists in just about every discipline have tested Newton's laws of motion and found them to be amazingly predictive and reliable. But there are two instances where Newtonian physics break down. The first involves objects traveling at or near the speed of light. The second problem comes when Newton's laws are applied to very small objects, such as atoms or subatomic particles that fall in the realm of **quantum mechanics**.

Still, these limitations shouldn't take away from his accomplishments, so flip to the next page for more information about Isaac Newton and other geniuses.