Orbits

A teacher Institute workshop on 13 December, 2003

Copernicus wrote the book titled "On the Revolution of the Heavenly Bodies" which contained such idea changing concepts that its title word came to be the name for any great change, a revolution. The revolutionary idea was that the Earth Orbited the sun.

Language note: Planets revolve about the sun in their orbits and rotate about their axes.
Also by this naming the six-shooter handgun of the American west should be a rotator not a revolver.

Kepler used Tycho Brahe's observations of the motions of the planets to come up with three laws of planwetary motion.

1. Orbits of planets in our solar system are ellipses with the sun at one focus.

2. Planets sweep out equal areas in equal times.

3. The period of a planets orbit squared is proportional to the radius of the orbit cubed.

Newton then showed that all of Kepler's observations were produced by a force of gravity that obeyed an inverse square law.

Falling, If you shoot a bullet horizontally out over a lake, and drop a bullet at the same instant, both bullets will hit the water at the same time.

Fire a bullet in the absence of an atmosphere at just the right speed and it can fall at the same rate that the surface of the spherical earth falls away. This bullet is then in orbit. A Swift rifle can fire a bullet with a high enough velocity to orbit the moon and hit the shooter in the back of the head.

How to Fly. In the "Hitchikers Guide to the Galaxy" Arthur Dent discovers the secret of flying. When you trip and start to fall toward the ground, get distracted so that you miss the ground. This is a good description of an orbit, you fall but you miss the ground.

Gravity Well:

Many science museums have a "Gravity Well" exhibit. A toy coin bank version of the gravity well is also available. Balls rolled in the well model the behavior of planets orbiting the sun in nearly circular orbits. Planets far from the sun travel at low velocity over a large circumference and take a long time to orbit. Planets close to the sun travel a short distance at a high speed during each orbit.

Here is how to explore a gravity well. Gravity Well

You can also explore orbits in different force fields, rolling balls in spherical bottomed bowls or balloons, or in straight sided funnels. Balls rolling inside a sphere travel so slowly as they near the bottom of the sphere that the orbital period remains the same even though the circumference of their orbit is small. Gravity Well Math Root

Gravity Assist

Planetary scientists send spacecraft to the planets using "gravity assist" maneuvers. They fly a spacecraft near a planet and gain energy from the contact-free "collision" between the spacecraft and the planet.

You can model this energy gain by dropping two balls together.

Bouncing Balls

Gravity assist

You might correctly expect that an object that gains energy by falling toward the earth would lose the same amount of energy when it moved away from the earth. Just as a ball dropped on the floor can never bounce higher than the height from which it is dropped.

However if three bodies such as the sun the earth and a satellite are involved then the satellite can gain energy relative to its motion about the sun. This is obvious when two balls are dropped together toward the earth, one can bounce to a much greater height than that from which it is dropped.

Complex Orbits

Recently, over 400 years after Isaac Newton, scientists discovered some interesting orbital possibilities exhibited by two co-orbital satellites of earth.

The Three Moons of Earth, scientists have recently discovered two more co-orbital partners of the earth in addition to the Moon: Cruithne a 5 km diameter asteroid in a horseshoe orbit, and 2002AA29, a 100 m diameter asteroid which orbits the earth over the poles.