Chapter 2

The key features of this chapter include a discussion of how we obtained our understanding of the solar system over time, and a discussion of how science works. What is science? Sagan described it as way of thinking about the world. We can briefly define it as: Science is a systematic way of inquiry about our world.

It assumes that we can explain phenomena by a restricted set of principles that do not require invoking magic, mysteries, miracles, etc. It assumes there is some sort of logic to how things behave and it tries to discover what that logic is. It tries to simplify the world by discovering the basic principles that operate in many circumstances and that describe phenomena in many different places. Such principles are only considered to be valid or useful if they can make predictions that can be tested, and/or if they help explain past experiments and data. One of the miracles of this process of inquiry has been the realization of the tight connection between our world and mathematics; nature does behave according to mathematical laws, and mathematics is one of the principle tools or languages by which science can operate and advance.

Examples where science has discovered unifying principles:

- Newton's laws of motion
- Newton's law of gravity
- Atoms: building blocks of all elements, and of molecules of life
- Conservation laws in physics, e.g. that of mass/energy

Can you think of others?



Clicker question:

The text above mentions "basic, or unifying, principles" as an integral part of the scientific process. In order to be seen as "science", do those basic principles have to have a clearly understandable scientific foundation?

a. Yes

b. No

c. Not sure

Can you give some examples of principles and how they would fit in?

You have all heard many times how science operates. Here I want to emphasize the most important point that the general public often does not seem to understand. What is a "theory" in science? In every day life we use "theory" as something "dismissive", something that is closer to speculation than truth. In science, when one talks about a particular "theory", it refers a very well established and thought-out system of laws or concepts that explains a lot of observational data. Even today, the difference between these two uses of the word "theory" is not understood, e.g. when people dismiss Darwin's theory of evolution as "just theory".  What others may think of as theory in every day life is what a scientist would call a "guess" at worst, an "educated guess" if it has some plausibility or thinking behind it, or a "hypothesis" if had some scientific thinking behind it to back up the idea. None of these comes close to the meaning of a scientific theory. Even scientists can be guilty in that they may refer to a new framework to explain some phenomena as a "theory" when it hasn't really met the requirements yet to call it that.

Going back to the above clicker question, it is not always true that the "basic principles" we discover must already have a sound scientific basis for them in order to be acceptable. Ultimately, we will insist on finding the basis, but much progress can be made even if we don't yet understand the reason behind the principles. Example: Newton's discovery that gravity decreases as inverse of the distance squared (see below). He didn't know why it was that way, but he did discover that it always works that way.

A scientific theory may not be the "absolute truth", in that it can be modified if new data disagree with the predicted behavior. However, it is usually understood what was wrong with the old theory that makes it necessary to replace it. A better theory is generally not a total new start and rarely involves dismissing the entire old theory. The new theory will build on the old one, and may enlarge the scope of the old theory, or it may replace it while recognizing the strengths and weaknesses of the old theory or theories.

Examples of "paradigm shifts":

Even in some of these cases though, the older theories have played an important role in laying a foundation and providing guidance for ever more detailed and challenging experiments or observations that ultimately led to their demise.

We will come back to Darwin's theory of evolution in this course. It is a scientific theory, with lots of evidence to back it up.

Some examples of phenomena which are distinctly non-scientific claims:

- astrology and horoscopes to predict future events

- UFOs claimed as evidence for alien space craft.
- intelligent design or creationism

They are non-scientific for various reasons:

They do not stand up to scientific scrutiny; if there are any experiments done, they cannot be replicated in controlled conditions or the claims for what was seen or experienced cannot be verified or can be explained in other ways. The last one (intelligent design) mixes religion with science; it assumes we know the answer and tries to fit scientific discoveries within a religious framework and ignores or discredits discoveries or evidence if they don't fit.

Some characteristics of the non-scientific approach include:

Why should you care about such false claims? They may affect your education and future or that of your children. In today's society there is a growing tendency to give equal "credit" or assign equal value to everyone's opinions. But there is a real difference between a validated scientific theory or explanation for certain phenomena versus unsubstantiated or dogmatic claims.

"Opinions" are not all equal when it comes to science. There is no "theory of creation", for example. Creationism is a belief and therefore cannot be and is not intended to be subjected to scientific scrutiny. Likewise, it does not and should not pretend to have input to scientific discoveries or the scientific process.

There are experts in certain subjects that know more about things than others. We don't question this in the world of medicine, for example, but many seem to forget it when it comes too close to their own preconceptions. This is understandable, yet we must subject all such claims to scrutiny with as unbiased a mind as possible.

I think it was Einstein who said that "Anything is possible, but few things actually happen". A scientific model must be as simple as possible (that means invoke as few assumptions or "free parameters" as possible), but "not it should not be simpler than necessary". Theories can grow in complexity over time. E.g. quantum mechanics is decidedly not simple, but it does work better than the simpler classical physics that preceded it.

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The key steps in developing our understanding of the solar system and universe

Let us now move to the early discoveries on the solar system leading to the laws of planetary motion and ultimately Newton's laws of motion and law of gravity.

- Early Greek models (Ptolemy and the work of others) of the solar system had the Earth at the center and the Sun, Moon, planets and "fixed stars" orbiting Earth. These are called "geocentric models". The Greeks were among the first to use scientific principles to develop models. That is, they tested their predictions against observations of the positions of objects in the sky. They were not right, but very brilliant in many ways and they did not have telescopes to improve their observations. These theories were developed from 500 to 100 B.C.

The Greeks made several important contributions to science:

a. They developed a tradition of thinking and reasoning independent of preconceived beliefs; they made thereby the first real attempt to understand nature on its own terms.

b. They developed and applied mathematics, in particular geometry, to interpret and analyze nature (e.g. the motions of objects in the sky).

c. They saw the power of reasoning from observations. So, they realized that if observations contradicted their models, they would have to improve the models.


A model of the sky and the objects in it, needs to explain several phenomena that can be easily observed with the naked eye:

1. daily rising and setting of sun, moon, stars, and planets
2. phases of the moon: Phases of the Moon explained.
3. motion of moon with respect to the stars, about 13 degrees per day
4. motion of the sun with respect to the stars, about 1 degree per day
5. Seasons on earth
6. eclipses of the sun and eclipses of the moon
7. motion of planets with respect to the stars
8. Apparently fixed position of the stars on the sky with respect to each other.

Clicker question:

The Moon is visible:

a. Only at night

b. Anytime

c. Day or night but not all times

d. Not during last quarter phase


Clicker question:

The Moon rises ...... each successive day.

a. earlier

b. later

c. at the same time



Example of daily stellar motion due to Earth's rotation: star trails.

Quick check: What you do you know about Polaris?

Useful: In another browser window, do a search for "celestial sphere animation", images. You will see many diagrams that will be useful to visualize the sky as a sphere around the earth on which the objects appear to move as the Earth rotates on its axis, and orbits the Sun.

Quick check: Do you understand the phases of the moon?

What happens during eclipses?
- eclipses of the Sun (Solar eclipse Geometry)
- eclipse of the Moon (lunar eclipse geometry)

Total solar eclipses are quite spectacular (picture1, picture2).


Quick check: Do you understand eclipses?


The significance of eclipses for the Search for Life

Eclipses are like transits: one object passing in front of another. In a solar eclipse, the Moon transits across the Sun from our perspective. In a lunar eclipse, the Earth transits across the Sun, from the Moon's perspective. A transit offers the opportunity to learn about the transiting object. Venus and Mercury also can transit across the Sun from Earth's perspective. Click here: Venus transits across the Sun; what we can learn from it.

The Sun's light will be dimmed a bit when Venus or Mercury moves across it. How fast the dimming happens can tell us if e.g. a planet has an atmosphere. We will use this later in our study of extra-solar planets.


Point 8 above leads to dividing the sky into "constellations" which are groupings of stars that suggest some symbol or shape and therefore was given a name. We now know that the stars in one constellation are not at all physically connected with each other, but that it is just a chance superposition in the sky (the actual distances to the stars in any one constellation are generally very different).

Here are a few constellations you can look for:

Orion
Big Dipper, Cassiopeia, the star Polaris, and the Northern lights

The Greeks had all these observational clues to help them develop their model of the universe (remember, this was more than 1500 years before telescopes were invented). Their "final" model is called the Ptolomaic Model for the solar system, which is a geocentric model. Here is a sketch of what that looked like: Ptolomaic model

The Greeks also made the critical discovery that the Earth is round, from several lines of reasoning. So, no, it was not Columbus who discovered that, although his and others' voyages helped prove the point.


Ptolemy's model was not perfectly in agreement with the observed positions of planets, but it survived for centuries without dispute. Europe was still in the dark ages, observational tools to get much better data were lacking, and the Christian Church, which started after the Greeks developed their models, surely advocated a view in which Earth was the center of the universe.

- Nevertheless, without new data, Copernicus (1473-1543) developed the "heliocentric model", which showed the plausibility of a model in which we, with the other planets, orbit the Sun. The Moon is the only object that orbits the Earth; together we orbit the Sun. Copernicus published his revolutionary theory in 1543 A.D. The Greeks had thought about such a model, but ruled it out for good scientific reasons. Copernicus had no proof or better data that his model was right, but that soon followed through observations of the planet Mars by Tycho Brahe (1546-1601), and a correct model of planetary orbits by Johannes Kepler (1571-1630).  Another key figure was Galileo (1564-1642), make sure to study in the book what he contributed.  Copernicus's model was much simpler than the Ptolemaic model, but he still assumed the wrong shape for the planetary orbits (circles instead of ellipses).


Here is a link with info on the Copernican model development, and a figure showing the arrangement of the planets and stars: Copernican Model (scroll down a bit in the linked page)


Check: Visualize how all observed points listed above are explained with the Copernican model.

Kepler derived the correct laws for planetary motion and the correct shape of the orbits, but did not have an explanation for why the orbits were as they are. He did show conclusively that the Sun is at the center of the solar system. Kepler discovered the 3 laws of planetary motion:

Figure for Kepler's first law and explanation of ellipses
Figure for Kepler's second law
Figure demonstrating accuracy of Kepler's third law


Quick check: How well do you understand Kepler's laws?


Newton (1642-1727) was a genius who discovered the laws of motion and the law of gravity, and together these two sets of laws explained the motions of planets and other objects in the Universe. We still rely today on Newton for most of our general understanding of the laws of motion and the concept of force and acceleration.

Let first check you intuition through a clicker question: How about them forces?

Briefly, Newton's laws of motion:

1. An object that is at rest will stay at rest unless acted upon by a net force. An object that is moving at constant velocity will continue to move at that constant velocity unless acted upon by a net force.

2. Force equals mass times acceleration (hence acceleration equals force divided by mass).

With acceleration we mean the rate of change in velocity with time. This change can be in direction (e.g. for an object in circular motion at constant speed we do need a force to keep changing its direction of motion) and/or in magnitude (increasing or decreasing speed).

3. When an object, A, is exerting a force on another object, B, object B exerts an equally large but opposite force on object A (action = reaction law).

These three simple laws have enormous implications for our understanding of motions and interactions among objects. They define the concept of "inertia", the tendency of objects with mass to not change their speed when they are in motion, and to stay at rest when they are at rest. They describe how much force (and energy) is required to accelerate objects (very relevant to e.g. every day driving, flying airplanes, shooting missiles or guns, rocket flight,  etc).

Newton also discovered the "law of gravity", which describes how strong the force of gravity is between two objects, and in which direction it acts.

Force of gravity between two objects with mass M1 and M2 is equal to a constant named "G" times the product of the masses divided by their distance (called R) squared:

Fg = G * M1 *M2 / R2

Together with the laws of motion, the law of gravity can be used to describe how objects move under gravity; hence how the planets move as they orbit the Sun, and why they move the way they do. How the Moon moves around Earth, how objects fall on Earth, how the Sun moves around in our Galaxy, and how spacecraft move in our solar system, etc. Newton's laws lead to Kepler's laws; he provided the explanation for Kepler's laws that had eluded Kepler.


Some important examples of how Newton's laws explain various phenomena:


- ACTION = REACTION: Newton's third law provides the principle behind rocket flight!


- How to place a satellite in orbit. This is actually related to the question of "Why the moon is falling towards the Earth without ever colliding with it". This is connected to the larger topic of "orbits" for objects in the solar system or other stellar systems. An object that is orbiting around another object is all the time falling towards the other object, but because it also has motion (velocity) in a direction different from the direction in which it falls (which is the direction to the center of the other object), it never crashes but instead orbits in an ellipse or circle.

- Why do objects fall at same rate? Galileo discovered this by experiment, but Newton's laws explain why. By combining the law of the gravity with Newton's second law, we can show that the acceleration of an object as a result of the gravitational force between it and another object is not dependent on the object's mass.
- The relevance of Kepler's and Newton's laws for discovering extra-solar planets. We will learn much more about this later in the course. A consequence of the first and third law of motion is that the sun is not completely at rest when planets orbit it!


- Concepts of weight and mass.

The force of gravity on you when you are standing on a planet or moon is your weight: your weight on Mars or the Moon will be less than it is on Earth. Weight = force of gravity on you by Earth or another planet (while "at rest" on Earth or another planet so when something is supporting you). "Mass" is a conserved quantity, think of it as a measure of the amount of "stuff" in an object. Weight is not a conserved quantity, it depends on where you are and how you are moving.


"Mass" occurs in Newton's 2nd law as "inertial mass" and in the law of gravity as "gravitational mass"; why are these two masses the same quantity? There is no reason for it, necessarily, but it is observed to be the case.

- Being weightless in space. This does NOT require the absence of gravity, but is defined as being in a state of free-fall. That means, being in motion in a place where gravity is the only force that is acting on you (if you could be in a place where there is no gravity, or where the forces of gravity on you cancel, you would also be weightless). For example, an astronaut orbiting the Earth in a space craft that is not operating its engines, is weightless but still very much in the gravitational field of the Earth (or she wouldn't be orbiting the Earth!). Yet, she is weightless, because she and the space craft she is in, are falling continually towards Earth. The orbital speed keeps them in orbit rather than have them crash, but she is still falling. Think also of the example of the elevator we discussed in class.



Quick check: How well do you understand Newton's laws?




Effects of weightlessness: Example 1. Weightlessness and food in space

Example 2. Wringout out a cloth.