Galileo

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Italian mathematician, astronomer, and physicist. He developed the astronomical telescope and was the first to see sunspots, the four main satellites of Jupiter, and the appearance of Venus going through phases, thus proving it was orbiting the Sun. Galileo discovered that freely falling bodies, heavy or light, have the same, constant acceleration and that this acceleration is due to gravity. He also determined that a body moving on a perfectly smooth horizontal surface would neither speed up nor slow down. He invented a thermometer, a hydrostatic balance, and a compass, and discovered that the path of a projectile is a parabola.

Galileo's work founded the modern scientific method of deducing laws to explain the results of observation and experiment, although the story of his dropping cannonballs from the Leaning Tower of Pisa is questionable. His observations were an unwelcome refutation of the Aristotelian ideas taught at universities, largely because they made plausible for the first time the Sun-centred theory of Polish astronomer Nicolaus Copernicus. Galileo's persuasive Dialogo sopra i due massimi sistemi del mondo/Dialogues on the Two Chief Systems of the World (1632) was banned by the church authorities in Rome and he was made to recant by the Inquisition.

Astronomy and the invention of the telescope
In July 1609, hearing that a Dutch scientist had made a telescope, Galileo worked out the principles involved and made a number of telescopes. He compiled fairly accurate tables of the orbits of four of Jupiter's satellites and proposed that their frequent eclipses could serve as a means of determining longitude on land and at sea. His observations on sunspots and Venus going through phases supported Copernicus's theory that the Earth rotated and orbited the Sun. Galileo's results published in Sidereus Nuncius/The Starry Messenger (1610) were revolutionary.

He believed, however – following both Greek and medieval tradition – that orbits must be circular, not elliptical, in order to maintain the fabric of the cosmos in a state of perfection. This preconception prevented him from deriving a full formulation of the law of inertia, which was later to be attributed to the contemporary French mathematician René Descartes.

The pendulum
Galileo made several fundamental contributions to mechanics. He rejected the impetus theory that a force or push is required to sustain motion. While watching swinging lamps in Pisa Cathedral, Galileo determined that each oscillation of a pendulum takes the same amount of time despite the difference in amplitude, and recognized the potential importance of this observation to timekeeping. In a later publication, he presented his derivation that the square of the period of a pendulum varies with its length (and is independent of the mass of the pendulum bob).

Mechanics and the law of falling bodies
Galileo discovered before Newton that two objects of different weights – an apple and a melon, for instance – falling from the same height would hit the ground at the same time. He realized that gravity not only causes a body to fall, but also determines the motion of rising bodies and, furthermore, that gravity extends to the centre of the Earth. Galileo then showed that the motion of a projectile is made up of two components: one component consists of uniform motion in a horizontal direction, and the other component is vertical motion under acceleration or deceleration due to gravity.

Galileo used this explanation to refute objections to Copernicus. It had been argued, against Copernicus, that a turning Earth would not carry along birds and clouds. Galileo explained that the motion of a bird, like a projectile, has a horizontal component that is provided by the motion of the Earth and that this horizontal component of motion always exists to keep such objects in position even though they are not attached to the ground.

Galileo came to an understanding of uniform velocity and uniform acceleration by measuring the time it takes for bodies to move various distances. He had the brilliant idea of slowing vertical motion by measuring the movement of balls rolling down inclined planes, realizing that the vertical component of this motion is a uniform acceleration due to gravity. It took Galileo many years to arrive at the correct expression of the law of falling bodies, which he presented in Discorsi e dimostrazioni matematiche intorno a due nove scienze/Discourses and Mathematical Discoveries Concerning Two New Sciences (1638) as:

s=1/2at²

where s is speed, a is the acceleration due to gravity, and t is time. He found that the distance travelled by a falling body is proportional to the square of the time of descent.

A summation of his life's work, Discourses also included the facts that the trajectory of a projectile is a parabola, and that the law of falling bodies is perfectly obeyed only in a vacuum, and that air resistance always causes a uniform terminal velocity to be reached.