GRAVITY: KEPLER'S AND NEWTON'S LAWS

Planetary Orbits: Circles or Ellipses?

Planets orbit the sun, but what is the shape of the orbital path and how does the planet move along this orbital path?

Two closed paths are the circle and the ellipse.

These closed curves are of the same family of curves; all that distinguished them from one another is how elongated (flattened) they are. This flattening is called eccentricity. A circle has e = 0, or zero eccentricty (they are perferctly round). Ellipses have verying degrees of eccentricity, somewhere between slightly greater than zero and slightly less than one ( 0 < e < 1 ).

The parts of a circle are basically a center, a radius, and a circumference. The circumference is the distance around the circle. The radius is the distance from the center to the circumference. The parts of an ellipse are two focus points (called foci, "fo-sigh"), the major axis and the minor axis. As eccentricty increases the ellipse becomes more flattened.

Kepler's Laws of Planetary Motion

It has long been thought that the circle was the orbital path of planets. That wisdom was proved incorrect.

Keplers's 1st Law: The orbital path of planets are ellipses. The sun is situated at one of the foci.

Two important terms are: aphelion is the farthest point from the sun in the orbit; perihelion is the closest point from the sun in the orbit. (Both are on the major axis).

Kepler's 2nd Law:. A line from a planet to the sun sweeps out equal areas in equal times.

This crazy statement is really a statement about the speed at which a planet orbits the sun. When it is at perihelion, it is moving fastest; when it is aphelion it is moving slowest. That is, planets do not move along their orbital path with constant speed; their speed actually changes as they orbit the sun. Kepler's second law is a statement about the conservation of angular momentum.

Newton's Law of Gravitational Attraction

All matter has mass. Mass is a measure of how matter resists forces that would change the present motion of the matter. For example, the resistance a billiard ball has to being struck by a queue stick.

All masses attract one another. All masses.

The force of the attraction is called gravity. The force of gravity has a very specific and well known behavior. The greater the masses, the greater the gravity (mutual attraction). The closer in distance the masses are, the greater the gravity. And, of course the converse is true. The lesser the masses, the weaker the gravity. The farther the distance the masses are, the weaker the gravity.

Just like the inverse square law for light... gravity is also an inverse square law..... two examples.... (for details, see the table in the notes).

If two masses are separated by a distance 2 times greater than their original distance, the gravity gets 4 times weaker. Imagine it. Think about it.

If two masses are separated by a distance 1/2 of their original distance, the gravity gets 4 times stronger. Imagine it. Think about it.

So, what is an orbit? Too much to explain. Hopefully you saw the demonstration in class of the cannon ball shot at different speed around the earth.