Understanding some basic physics, including Kepler's laws, will be important in understanding topics like galaxy rotation and the discovery of dark matter. In the 17th century, Johannes Kepler made a major contribution to understanding the dynamics of astronomical bodies by analyzing a lifetime of observations take by his mentor, Tycho Brahe. These observations included decades of observing the positions of the planets against the background of stars. He recognized that there was a pattern associated with the orbital periods of the planets, and used this knowledge to determine the relative sizes of the planets orbits about the sun. He found the orbital speeds of the planets by comparing their motions over time.

Kepler's discoveries can be summarized in three laws.

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A circle is a special case of an ellipse, with only one focal point. An ellipse typically has two focal points. The farther apart the focal points, the greater the ellipticity of the ellipse. The "diameter" across the long side is called the major axis. The semi-major axis (a) is one-half the major axis. This diagram is greatly exaggerated, most planet orbits in our solar system are nearly circular.

A planet moves faster when it is closer to the sun and slower when it is farther away. In the image above, the same amount of time elapsed while tracing out the blue area as the purple area.

This interactive simulation from the Astronomy department of the University of Nebraska-Lincoln allows you to investigate Kepler's second law by varying the eccentricity of the orbit and distance between the star and planet. Please also check out the tabs for Kepler's first and third laws while you are there.

Isaac Newton revolutionized the understanding of the behaviors of massive objects. Before his day, people believed that the natural state of an object was to be at rest, as close to the center of the universe (the earth) as possible. They thought that if you hit an object, you gave it energy. The energy would be used up, and the object would go back to its natural state of rest. It is understandable that people thought this way, because that is what most objects seem to do. Newton developed a new way of understanding the mechanics of motion, which can be summed up in three laws.

Before Newton, people thought that the natural state of an object was to be at rest as close to the center of the universe as possible. They assumed the center of the universe was the Earth, so for example, a rock would get as close to the Earth as it could and stop. If you came along and kicked it, the rock would move, go back to Earth and stop.

Newton's first law states something fundamentally different about the behavior of objects. An object doesn't have a natural state of rest. This law also introduced the concept of force. In the simplest sense, a force is a push or pull.

In the image above, the donkey has three forces acting on it. There is a push from behind, a pull from the rope, and a push backward from the ground. Since the donkey is not changing its velocity, the net force must be zero.

There is one more thing to consider here. We need to define what mass means. Mass is related to weight. Weight is defined as mass x acceleration due to gravity. Acceleration due to gravity is often represented by the letter g. mathematically we would write

W = mg

Now the acceleration due to gravity is pretty nearly constant on the surface of Earth, but it is very much different, say, on the moon. Your mass is the same on Earth and on the moon, but your weight is very different.