What is the Scientific Method?

- It is a way of learning about Nature based on direct observations.

- A hypothesis or a set of hypotheses are put forth to explain

the observations.

Testing is Crucial

- These hypotheses are tested through more observation, and through experiment. Testing is a crucial step: observation and experiments are used to decide whether a hypothesis is in agreement with what is seen.

- If the hypothesis is confirmed, repeatedly, it can be considered as a principle or law.

- A set of principles or laws, coherently connected, provide framework for understanding a segment of reality. This set of coherent principles or laws is called a “scientific theory”.

The Scientific Method- Rational thought and logic are used to arrive at tests for a theory, both through the prediction of new observations and through the explanation of existing observations.

Predictions are logical inferences derived from a theory that state what the results of an observation that has yet to be made will be. If a prediction is confirmed by experiment, the theory that made it is strengthened. - A scientific statement must be testable, i.e., there must be the possibility of comparing it to Nature to decide whether it is correct or not.

- Scientific theories cannot be “proven” correct in an absolute sense.

TESTING IS CRUCIALThrough experiments reality tells the scientist whether a hypothesis is in agreement with facts.

The Meaning of “Theory”“Theory” means something very different in science and in everyday language.

In everyday language, if something is “just a theory” it is a possible suggestion that may or may not be a correct description of reality.

In science a theory is a well-established, repeatedly tested, coherent group of ideas.

3000 B.C.: Babylonians & Egyptians become aware of heavens and its regularities…

500 B.C: Pythagorean group (simple geocentric system).

In the simple geocentric view, what motion should be observed for the motion of the planets across the celestial sphere background?

To see how science developed let us look, over time, at how people have analyzed the motion of stars and planets.

A Bit of History….

[1] Early Greek Model: (500 B.C., Pythagoreans) The seven objects (sun, 5 planets, and the moon) are attached to seven concentric transparent spheres (that move at slightly different uniform rate once a day around a static earth).

The imaginary celestial sphere

The early Greek Model predicted a uniform motion of the planets.

But some observations contradicted this prediction…

The Retrograde Motion of the planets.

Testing the Greek Hypothesis

A new theory was required to account for retrograde motion:

[2] Plato’s Theory: (~ 400 B.C.) Multiple transparent sphere theory: Several earth-centered spheres for each planet! Very complicated, but could roughly account for retrograde motion.

[3] Aristarchus’ Theory: (~ 300 B.C.) Planets follow circular orbits around the sun. This theory was shot down because (a) Aristarchus did not have scientific “status” and (b) people had a hard time believing that the earth could move at all since it is so large.

Experimental Testing Failed the Greek Theory

Even though Plato’s theory [2] could roughly explain retrograde motion, there was one observation that it could NOT explain:

It was noticed that during the retrograde motion of a planet, the planet seemed BRIGHTER. What would cause that?

The planet would be brighter if it were CLOSER TO EARTH during its retrograde motion!

A new theory was required ….

Another Experimental Observation…

[4] Simple Epicycle Theory: (~ 100 B.C.)

[5] Ptolemy’s Epicycle Theory: (~ 100 A.D.) In order to describe these finer details, more than 80 epicycles were required!!!!! Also, Earth had to be slightly off center….even if this “lost” the perfect spheres.

The simple epicycle theory [4] could not account for the finer details of planetary motion. It had to be modified, and this was done by Ptolemy…

This theory lasted 1500 years!!!

The Epicycle Theory

A simplified Ptolemy’s System

In the year A.D. 1543, on his deathbed, a Polish astronomer, Nicolaus Copernicus signed his book,

On the Revolutions of Heavenly Spheres

The year A.D. 1543 is often taken as the “birth of modern science”.

Copernicus agreed with the Pythagoreans that a theory of the physical world should be elegant—not complicated like Ptolemy’s epicycle theory.

The Copernicus’ theory was not new (first was Aristarchus), but he (Copernicus) was able to describe retrograde motion …

A Revolutionary Thought!

[6] Copernican Heliocentric theory: sun centered, everything tracked on circular orbits.

The heliocentric theory correctly described retrograde motion!

We now have TWO theories that were capable of describing all of the currently observable phenomena:

Ptolemy’s Epicycle Theory [5]

Copernicus’ Heliocentric Theory [6]

The test was the observation of the phases of the planet Venus.

To give you an understanding of the meaning of phase, let’s look at the phases of the moon...

Which theory is WRONG?

We need an experiment (in the form of an observation) that would show contrast between the theories.

The Phases of the Moon

If Venus followed the epicycle path as formulated by Ptolemy, we would never see the “full Venus” but we would see a “new Venus” twice:

But if Venus went around the Sun instead of the Earth, we would see a “full Venus” whenever Venus and Earth are in opposites sides of the Sun:

Why didn’t they just check this immediately to decide which theory was correct??

Ans: They couldn’t see the phases of Venus with the bare eye --they needed the experimentalists: they needed a TELESCOPE!

Galileo Galilei observed a “Full Venus” in the 1600’s, thereby eliminating the geocentric epicycle theory.

Theory and Experiment: The Importance of Observation

Copernicus himself admitted that his theory did not agree with all of the known data/measurements.

DEFINITIONS:

Qualitative: general behavior not directly compared to actual measurements (numbers).

Quantitative: quantitative measurements compare numbers calculated from a theory to numbers measured through experiment.

So the Copernican theory could describe qualitative features such as retrograde motion and the phases of Venus, but did NOT compare well with quantitative measurements of orbits.

Quantitative measurements: Tycho Brahe (1546 -1601)

He developed very accurate instruments to measure the angular positions of the stars and planets. Not with a telescope but sighting along sticks (see Fig. 1.18).

He cataloged the positions of the planets for over 20 years!

Johannes Kepler joined Brahe in 1600, about a year before Brahe’s death.

Kepler could not be an observational astronomer due to bad eyesight, but he was a good mathematician. He analyzed Brahe’s data in detail.

At the time (still before the observations of Venus by Galileo), Kepler was stuck on the Epicycle and Copernican theories. He favored the Copernican theory, but could not make the theory match the observations!

After much work, Kepler came up with a new theory:

Circle: the set of all points equidistant from a center point.

Ellipse:

The two points used to draw the ellipse are called the foci.

All the points on the ellipse are such the sum of the distances from each of the two foci to any point on the ellipse is a constant.

The largest distance across the ellipse is the major axis of the ellipse

Kepler’s Theory [7]: Kepler’s Laws

Kepler’s 1st Law: Each planet moves in an elliptical orbit around the sun with the sun occupying one foci of the ellipse (the other one is empty).

Kepler’s 2nd Law: The imaginary line connecting the planet to the sun sweeps out equal areas in equal times

Keplers 3rd Law: The square of a planet’s period of revolution is proportional to the cube of its semi-major axis.

Kepler’s 1st Law: Each planet move in an elliptical orbit around the sun with the sun occupying one focus of the ellipse (and the other one is empty).

Kepler’s 2nd Law: The imaginary line connecting the planet to the sun sweeps out equal areas in equal times.

[T2] is proportional to [a3]

Keplers 3rd Law: The square of a planet’s period of revolution, T, is proportional to the cube of its semi-major axis, a.

… Galileo was forced by the church, under threat of TORTURE, to retract his claim that Earth revolved around the sun, and he was place under house arrest in 1633. He was imprisoned for the rest of his life.

“ E pur si muove…”

Homework #1

From Chapter One, Review Questions #’s 5, 6, 11, 18, 19 and 21