Table of Contents

Orbital Mechanics

A Brief History of Gravity

An Introduction to the Main Concepts

Galileo Galilei (1564-1642)

Galileo Galilei was born in Pisa in 1564. At the age of seventeen he was sent by his father to the University of Pisa to study medicine. His family was noble but impoverished, and although his father was a competent mathematician, he had carefully kept his son away from the study of mathematics because he felt it would lead to the disruption of a medical career.

Galileo, however, happened to overhear a lesson in geometry, which aroused his interest, and began, with his father's reluctant permission, to study mathematics and science.

One of Galileo's most famous experimental discoveries, and one of the most important, was the fact that all objects fall at the same rate, regardless of their mass. The experiment is reported to have taken place from the Leaning Tower in Pisa, whereupon Galileo dropped two spheres of equal size from the top of the tower. Although the spheres had very different masses, one sphere being made of lead and the other of soap, both spheres reached the ground at the same instant when they were released simultaneously from the top of the Tower.

This simple experiment overthrew centuries of erroneous Aristotelian science which proclaimed that heavy objects should fall faster than lighter objects.

The simple fact that all objects accelerate at the same rate under the influence of gravity was a major stepping stone towards Isaac Newton's discoveries in mechanics and consequently our own current understanding of orbital mechanics.

Galileo's considerable reputation rests mainly on his discoveries with the telescope. He made his first instrument in 1609 and published his first observation in 1610. Among Galileo's discoveries were the satellites of Jupiter, the phases of Venus, the configuration of the moon, and sunspots.

In 1633, Galileo was tried by the Inquisition, for lending his support to the Copernican view of the universe, which held that the earth and the planets moved around the sun. He recanted under the threat of torture, and was finally allowed to return to Florence.

Galileo spent the remainder of his life in seclusion working on the principles of mechanics, his observations of the moon, and the application of the pendulum to the regulation of clockwork.

The Feather and the Farthing

A very old and famous experiment to demonstrate the fact that all bodies accelerate at the same rate in a gravitational field is called the “ Feather and the Farthing ” demonstration.

In this demonstration a feather and a farthing (a small British coin no longer in circulation) are sealed in a long cylindrical tube from which all the air is evacuated using a vacuum pump.

The audience is challenged to predict which object, the feather or the farthing, will reach the bottom of the tube first when the tube is inverted.

Everyday experience suggests that feathers fall more slowly than coins.

To begin the demonstration the feather and the farthing are initially at the bottom of the tube.

When the tube is quickly flipped over (as shown) the feather and the farthing are suddenly at the top of the tube and fall towards the bottom.

In the absence of any air resistance, both the feather and the farthing are seen to fall at exactly the same rate and reach the bottom of the tube simultaneously.

This seemingly strange behaviour usually surprises most audiences.

In a variation of this demonstration a small valve is attached to the cylinder so that air can be either admitted into the tube (by opening it), or pumped out (by attaching a vacuum pump), and the behaviour of the feather and the farthing studied under both conditions.

Of course it is air resistance that causes one to falsely conclude that heavy objects fall faster, (accelerate more quickly), than light, (low mass), objects.