Scientific Models & Kepler’s Laws

Scientific Models We know that science is done using the Scientific Method, which includes the following steps : Recognize a Problem Form a Hypothesis Predict Consequences of the Hypothesis Perform an Experiment to test Predictions Communicate your results

Scientific Models When communicating your results, you are trying to organize your hypothesis, prediction, experimental steps and conclusions so that they can be communicated and understood. A good way to do this is to develop a Scientific Model. A Scientific Model is just a description of a scientific idea.

Examples of Scientific Models A scientific model can be a word description. For Example : A star is big ball of burning gasses. A scientific model can be an actual physical model. For Example : A globe. A scientific model can be a mathematical equation or graph. For Example : E = mc 2 or F = ma

Developing a Scientific Model Initial Observations or Assumptions Model Make Predictions Based on Model Compare Observations to Predictions Revise Model Mathematics Physics Simplicity This is where the scientific method comes in! It is important to understand, that any model must be capable of producing predictions that can be tested. If these predictions are verified by observation or experiment, this gives evidence that supports the model. If these preictions are shown to be false then the model MUST be revised!!! If it can’t be revised, then it MUST be thrown out!!!!

The ancient Babylonians were prolific astronomers who created very detailed records of the positions of the “heavenly bodies”. These charts showed a phenomena of planetary motion called retrograde motion. Retrograde motion is the apparent backwards motion of the planets in the night sky. This motion is not a true motion of the planets, but any good model of the solar system must be able to explain this observation.

In ancient Greece, a scientist by the name of Aristotle ( BC) developed a model of the universe (5 planets and the background stars). His model was “geocentric”. This means the Earth was at the center of our Solar System and everything, including the Sun moved around the Earth. One problem of this model was its inability to explain retrograde motion.

Claudius Ptolemy, around AD 125, revised earlier attempts at a geocentric model. In his model the Earth was a little off center. The Sun and the Moon each orbited the Earth. Each planet orbited a point, called the epicenter, that orbited the Earth at varying speeds. This model allowed for retrograde motion and made fairly accurate predictions for the position of the stars and planets (5 – 10% error). C Claudius Ptolemy

 In 1514 Nicolaus Copernicus developed a heliocentric (Sun- centered) model.  In his model, the “Heavenly Spheres”, revolved around the Sun in circular orbits and the Earth spun on its axis.  The stars were also much farther from the Sun than the planets.

Copernicus’ Heliocentric Model  Retrograde motion is explained by the relative motion of the planets to each other.  Copernicus’ model was only as accurate in predicting the positions of the planets, the Sun and the Moon as Ptolemy’s model. (5 – 10%)

Kepler’s Heliocentric Model   In the 1600’s Johannes Kepler used astronomical data recorded by his former boss to develop a heliocentric model of our Solar System.   To do this he applied a condition on his model: That predictions must match observations.

Kepler’s Heliocentric Model  Between 1609 and 1618, Kepler developed his three Laws of Planetary Motion.  These are still used today !!!!!

Law 1 : The Law of Ellipses The orbit of each planet is an ellipse, with the Sun at one focus. An ellipse is like an oval where the distance from one focus to a point on the ellipse and back to the focus is the same.

Law 1: The Law of Ellipses We can tell how close an ellipse is to a circle by its eccentricity. An ellipse with an eccentricity of 0, would be a circle. As the eccentricity approaches 1, the circle becomes more elliptical. Animation

Law 2 : Law of Equal Areas A line drawn from a planet to the Sun sweeps out equal areas in equal time. What this means : The farther a planet is from the Sun the slower it moves. Slower orbital speed Faster orbital speed Animation

Law 3 : Harmonic Law The square of the orbital period, P, (the time it takes a planet revolve around the Sun one time) of a planet is directly proportional to the cube of the planet’s average distance from the Sun, R. What this means for us : The planets farther from the Sun take longer to orbit the Sun. (Much weaker than the above statement)

Where’s the Science ? Each of these models, from Aristotle to Kepler had one problem. There was no scientific reason to accept one over the other. It took Isaac Newton, with a little help from Galileo, to establish a central force that held the universe (Solar System) together. Gravity