Astronomy

Aristarchus. Ancient Greek mathematician who is credited with first advocating a heliocentric solar system.

Ptolemy. Greek geometer and astronomer who refined the geocentric model of the solar system using circular orbits and systems of epicycles.

Parallax: The difference in the observed size (the subtended angle) of an object or of two stars, when viewed from different positions. (Remember our measurement of the distance between two dots on the blackboard from different distances.)

Epicycle. A circular orbit whose center itself is traveling along another circular (or epicyclic) orbit.

Copernicus. Polish astronomer whose book De Revolutionibus Orbium Coelestium expounded a heliocentric solar system. His model still used circular orbits with epicycles but was simpler and more accurate than the Ptolemaic system.

Galileo. First trained a telescope on the heavens. His findings included:

• The moons of Jupiter. (Galileo saw this as another solar system in miniature.)
• The rings of Saturn.
• The "mountains" of the moon.
• Sunspots (these "blemishes" contradicted Aristotle who claimed the sun to be perfect in form and shape).
• The phases of Venus. The importance of the phases that he viewed is that the geocentric model predicted limited phases. The observation of a "full" Venus contradicts the geocentric model in which Venus is always supposed to be between the earth and the sun.
• Individual stars in the milky way.

Tycho Brahe. Danish astronomer-mathematician-nobleman who had his own island observatory. He made excellent precise observations; his observation of mars were so good that Kepler used them to develop his theory of elliptical orbits. He also observed a stella nouva (a "new" star that suddenly appeared in the sky) and showed that it had no observable parallax. He also argued that comets, contrary to Aristotle, were outside the lunar orbit.

Kepler's Laws.

1. Planets travel in elliptical orbits with the sun located at one of the focal points.
2. Planets travel so that the line connecting the planet to the sun sweeps out equal areas in equal times.
3. The period of revolution (T) of a planet about the sun and the mean distance (R) of the planet from the sun is related by the relationship:

F = Gm₁m₂/r²

Make sure you can use the formula to calculate the force between objects.

Newton's laws of motion:

1. An object in motion will travel in a straight line at a constant speed unless acted upon by a force. An object at rest stays at rest unless acted upon by a force.
2. F = ma. Force equals mass times acceleration.
3. For every force there is an opposing equal force (the jet engine principle).

Newton used his laws of motion and his law of gravity to explain the motions of the planets and moons in the solar system. This was published in the "Principia" in 1687.

Henry Cavendish 1731-1810. In 1798 he calculated the value of G the constant of proportionality in Newton's Law of gravity. Thereby he was able to "weigh the Earth."

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