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.

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 line joining a planet to the sun sweeps out equal areas in the ellipse over equal times.

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. It is moving faster when it is closer to the star, so the planet moves farther along the ellipse in the blue region. The area of the blue region is the same as the area of the purple.

The square of the orbital period of a planet equals the cube of its semimajor axis.

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.

In the absence of an unbalanced force, an object at rest stays at rest and an object in motion stays in motion at a constant speed in a straight line.

This started the concept of a force. The mathematical relationship deriving the nature of forces was defined in Newton's second law. The first law states something fundamental about the behavior of objects. Being at rest is not a "natural state" for an object.

Being at rest has some subtle implications. If an object is at rest, it has not just stopped momentarily, it has been stopped for "a long time." This implies there must be zero net force on it. Staying at rest implies there is still a net force of zero on it.

A force is basically a push or a pull. If there is no net force on an object in motion, there is nothing to speed it up, slow it down, or curve its trajectory.

The net force on an object is equivalent to the product of object's mass and its acceleration

An object can have constant speed and still have nonzero acceleration if it changes direction. Since velocity has a direction, if the direction changes, the velocity changes, even if the speed does not.

Quantities that have magnitude and direction, like velocity and acceleration, are called vectors. Quantities that just have magnitude, like speed, are called scalars.

Simply put, mass is how much "stuff" an object has. Every proton, neutron and electron has mass, so every atom has mass. If you count up all the atoms, and you know how much mass each atom has, you know how much mass in in the object.

In the image above, the pug has four forces acting on it. There is a pull from the rope, a backward pull from friction against the ground, a pushing upward from the ground and a pulling downward from the Earth. Since the pug is not changing its velocity, the net force must be zero.

The opposing Newton's third law force is the gravitational force felt on the earth from the ball. The ball and Earth are both massive objects, and they exert gravitational forces on each other. The ball undergoes an acceleration of g, or 9.8 m/s2. The earth undergoes an acceleration too, but it is much smaller since the mass of Earth is so much greater..

Fball,earth = -Fearth,ball

ma = -ma

There is a common saying, "for every action there is an equal and opposite reaction." It sounds like a restatement of Newton's third law, but it is often meant to mean something quite different. Newton's third law is very specific to forces and doesn't hold for other quantities in general.

Isaac Newton realized that the reason the planets obeyed Kepler's laws was that they felt a gravitational force from the Sun. He derived the equation for the gravitational force, as shown above. Here, G is the gravitational constant, m1 and m2 are the masses of the two objects (in this case, the Sun and planet) and r is the distance between the objects.