1. From an Earth-Centered to a Sun-Centered System
Chapter 2
From an Earth-Centered to a Sun-Centered System

2. 2-1 Science and Its Ways of Knowing
Science is about discovering the rules that govern nature.
It also refers to the body of knowledge resulting from the collective efforts of people throughout history.
Science progresses through the interaction of observations and theory.
Testing predictions against observations and verifying experiments are essential components.

3. The scientific method involves the following steps:
Recognize a problem.
Form a hypothesis about the solution.
Predict the consequences of that hypothesis.
Perform experiments to test the predictions.
Organize as simply as possible the hypothesis, predictions, and experimental outcome into a theory.
This processes continually repeats.

4. Hypothesis: An educated guess made in describing observations
Hypothesis: An educated guess made in describing observations. It can be widely speculative but must be testable.
A good hypothesis makes predictions that can be confirmed or refuted. A repeatedly verified hypothesis may become a law or principle.
Fact: A close agreement by competent observers of a series of observations of the same phenomenon.

5. Theory: A synthesis of a large body of information that encompasses well-tested hypothesis about some aspect of nature.
It can't be proved true but data could prove it false.
Models: A model is an idea, a logical framework, that accounts for a set of observations and/or allows us to create explanations of how we think a part of nature works.
In science, reality is described by models.

6. Criteria for Scientific Models
Three criteria are applied to a scientific model:
It must fit the data.
It must make predictions that can be tested. These tests must make it possible to disprove the model, or show it needs to be modified.
It must be as simple as possible with as few arbitrary and unverifiable assumptions as possible. This criterion is known as Occam's Razor.

7. 2-2 From a Sun-Centered to an Earth-Centered System
The search to understand Earth's relationship to other astronomical objects began thousands of years ago.
See how the Earth fits into the scheme of things.
See how the criteria for a good scientific theory are applied and developed.
To understand how astronomy (and science) works we follow how it progresses with time.

8. 2-3 The Greek Geocentric Model
Ancient Greeks were the first to be interested in astronomy because of a pure philosophical desire to understand how the universe works.
Pythagoras and followers proposed the universe was spherical and all things moved around a central “fire.” They also taught that the Earth was spherical.
Aristotle later argued that the Earth was fixed at the center instead. He based this on the evidence available at the time.

9. Aristotle argued that if the Earth moved we should be able to see stellar parallax.
Parallax: The apparent shifting of nearby objects with respect to distant ones as the position of the observer changes.
As the Earth moves we should see parallax of a nearby star as it shifts its position against background stars.

10. Observations of the stars over time showed no parallax.
Therefore Aristotle concluded the Earth was not moving.
This is a good example of a correct argument but incomplete data leading to the wrong conclusion.
The largest parallax of any star is only 1.5 arcseconds.
Stellar parallax was not observed until 1838.

11. Aristotle viewed the Earth and heavens differently:
Natural motion on Earth – things fall to its center.
Natural motion in the heavens – circle the Earth.
Greeks sought geometric explanations for nature:
Perfect spheres were thought to carry all celestial objects, with the Earth at the center.

12. Ptolemaic model is the geocentric model that resulted.
Ptolemy lived about 150 BC. The model was used for 1400 years. It explained the general motion of everything with:
A fixed Earth at the center.
Celestial objects moved on perfect circles around the Earth.
The Moon was closest, then the Sun, then the planets, then the stars on an outermost celestial sphere.

13. A Model of Planetary Motion: Epicycles
The motion of the planets could be described with perfect circles if epicycles were used.
Epicycle: The circular orbit of a planet in the Ptolemaic model, the center of which revolves around the Earth in another circle.
This could explain retrograde motion.

14. The centers of the epicycles for Mercury and Venus were between the Earth and the Sun. This accounts for the fact that they are never seen far from the Sun.

15. The Ptolemaic model met some criteria for a scientific model:
It fit the data and observations and provided an explanation for their motion.
It made testable predictions about positions and motions.
With epicycles the model was not very simple, but matching the data and making verifiable predictions are stronger criteria when evaluating a model.

16. 2-4 Aristarchus' Heliocentric Model
Aristarchus developed a heliocentric model 400 years before Ptolemy. This model had:
The Sun at the center of the solar system because it was the largest object.
The Earth and other planets moved around the Sun.
The Moon moved around the Earth.
But this could not explain the lack of stellar parallax.

17. Aristarchus estimated the relative sizes of the Earth, Moon, and Sun and their relative distances.
He had good arguments. Some of his measurements were accurate for his time although others were not.
He made a map of the solar system but did not know its scale.

18. Measuring the Size of the Earth
Eratosthenes (276–195 BC) measured the Earth's size.
He measured the angles to the Sun at two cities. The difference in angles was due to the curvature of the Earth. The ratio of that difference to 360o was the same as the ratio of the distance between the cities to the Earth's circumference.

19. 2-5 The Marriage of Aristotle and Christianity
St. Thomas Aquinas (13th century) incorporated the geocentric model in Christian beliefs.
The central, unmoving Earth fit well with literal biblical interpretation.
There was a great reliance on the authority of the Bible and authorities from the past.
© Photos.com

20. 2-6 Nicolaus Copernicus and the Heliocentric Model
Copernicus sought a new model of the solar system:
Predictions based on the Ptolemaic model were inaccurate over time and required corrections.
Placing the Sun at the center was more aesthetically pleasing, and it was the source of light and life.
The Ptolemaic model did not explain the changing brightnesses of the planets very well.

21. The Copernican System Copernicus revived many ideas from Aristarchus.
The Earth was just another planet moving around the Sun. Only the Moon circled the Earth.

22. Copernicus' model could explain retrograde motion without epicycles.
The model also explained why Venus and Mercury are always close the Sun.
Copernicus made very accurate estimates of the relative distances between planets.
Courtesy of NASA/JPL-Caltech.

23. 2-7 Comparing the Two Models
Accuracy in fitting the data: To make accurate predictions Copernicus still included small epicycles because he assumed the planets moved at constant speeds. Both models had similar errors in matching the observations.
Predictive power: Both models made predictions about stellar parallax. The Ptolemaic model predicted none, but the Copernican model predicted it would exist. The Copernican model was later shown to make the correct prediction.

24. 2-7 Comparing the Two Models
3. Simplicity: Both models made the same predictions, but Copernicus' model treated all planets the same rather than using special cases for Mercury and Venus.

25. 2-8 Tycho Brahe: The Importance of Accurate Observatons
Brahe decided more accurate observations were needed to decide between the two solar system models.
He built an observatory with the largest naked eye instruments yet constructed. (The telescope had not yet been invented.)
His observations were accurate to the limit of the human eye. He carefully recorded the uncertainty in the measurements. This is standard practice in science today.

26. Tycho's Model
Because he couldn't measure any stellar parallax, he concluded that the Earth was not moving.
His model was a mix of Ptolemy's and Copernicus'.
Brahe placed the Sun moving about the Earth, but all other planets moved around the Sun.

27. 2-9 Johannes Kepler and the Laws of Planetary Motion
Kepler was hired by Brahe to work on models of planetary motion using Brahe's accurate observations.
After 4 years and 70 combinations of circles and epicycles, Kepler could match the observations of Mars to within 0.13o. This was still larger than the accuracy of the observations.
He gave up on circles and found an ellipse matched the Mars observations and also those of all other planets.

28. PF1 + PF2 = constant = the major axis
The Ellipse
Ellipse: A geometrical shape of which every point is the same total distance from two fixed points called the foci.
PF1 + PF2 = constant = the major axis
Eccentricity: The result obtained by dividing the distance between the foci by the longest distance across the ellipse.
It can vary from 0 to 1.

29. Kepler's First Two Laws of Planetary Motion
First Law: Each planet's path around the Sun is an ellipse, with the Sun at one focus of the ellipse.

30. Second Law: A planet moves along its elliptical path with a speed that changes in such a way that a line from the planet to the Sun sweeps out equal areas in equal intervals of time.
This means it moves slowest at the farthest point from the Sun (aphelion) and fastest at the closest point (perihelion).

31. Kepler's Third Law
Third Law: The ratio of the cube of the semimajor axis of a planet's orbit to the square of its orbital period around the Sun is the same for each planet.
a 3 / P 2 = C
a = semimajor axis = average distance of a planet from the Sun.
P = planet's orbital period around the Sun relative to the stars. This the sidereal period, which is different from the synodic period as seen from the Earth.

32. Testing Kepler's Third Law
a 3 / P 2 = 1 (AU) 3 / (year) 2

33. 2-10 Kepler's Contribution
With Kepler's work the heliocentric theory worked better than the geocentric theory.
To achieve this, he had to abandon perfect circles for ellipses. The reason for this was simply that it worked.