Even though the heliocentric model gained acceptance after Galileo published his observations, it still didn't do a great job of predicting planets' positions in the sky over time. This was a problem!
Tycho Brahe was the most careful observer of the time, and made very detailed and accurate observations of planetary positions. When he died, his student Johannes Kepler used the data collected by Tycho to determine the source of the discrepancy between the observed and predicted planetary positions.
In doing so, Kepler realized that there was a fundamental flaw with Copernicus' heliocentric model: it assumed that the planets orbited the Sun in circular orbits. He realized that this was not true, and developed three laws that accurately describe the motions of the planets. These are known as Kepler's Laws of Planetary Motion, and they are:
Kepler's First Law: Planets' orbits are ellipses, with the Sun at one focus. Here is a simulation that illustrates Kepler's First Law.
Kepler's Second Law: Planets sweep out equal areas in equal times. Comparison with circular orbits - clock analogy. Here is a simulation that illustrates Kepler's Second Law.
Kepler's Third Law: p2 = a3. Here, p is a planet's orbital period in years and a is the planet's orbital semi-major axis, or average distance to the Sun in AU. What this means: if you know the distance of a planet from the Sun, you can calculate how long it will take to go around the Sun. Conversely, if you know how long it takes a planet to orbit the Sun, you can calculate its distance from the Sun.
Let's do a couple of examples that allow us to work with Kepler's Third Law, p2 = a3
Practical application of Kepler's Third Law: artificial satellites
The legend goes that Sir Isaac Newton was sitting under a tree one day when an apple fell and hit him on the head, causing him to come up with the idea of gravity. This is probably not exactly how it happened, but it's a good story.
Newton realized that there must be some force that keeps the planet in orbit around the Sun: GRAVITY (some thought earlier that it was magnetism!... this was WRONG).
Newton's Law of Gravitation is given by the following equation:
Fg = G [(M1 M2)/(R2)], where
G is called the gravitational constant
M1 is the mass of object 1
M2 is the mass of object 2
R is the distance between objects 1 and 2
The most important things to remember about gravity are the following:
You will hear about these quantities this week in lab, so let's review what they mean.