Models of the Solar System
Dr. Pamela Gore
Georgia Perimeter College
- Outline the basics of the Scientific Method.
- Compare and contrast the geocentric and heliocentric models for the solar system.
- Describe the revolution in scientific thought that occurred as a result of the work of Copernicus.
- Discuss how the heliocentric theory eventually received acceptance.
- Explain Tycho's contributions to the models for the solar system.
- Describe what Galileo saw, and how this contributed to the models for the solar system.
- Discuss Kepler's three laws and how they contributed to the models for the solar system.
- Discuss the evidence that must be considered with any model for the origin of the solar system.
- Duscuss the basics of the nebular hypothesis for the origin of the solar system, including the hot and cold accretion models.
- Outline the evidence for the Big Bang Theory of the origin of the Universe.
- Discuss the possible age of the Universe.
This section addresses, in whole or in part, the following Georgia GPS standard(s):
- S6E1. Students will explore current scientific views of the universe and how those views evolved.
- S6E1a. Relate the Nature of Science to the progression of basic historical scientific models (geocentric, heliocentric, Big Bang)
as they describe the formation of our solar system with the sun at its center.
- S6CS8a. When similar investigations give different results, the scientific challenge is to judge whether the differences are trivial or significant, which often requires further study.
Even with similar results, scientists may wait until an investigation has been repeated many times before accepting the results as meaningful.
- S6CS8b. When new experimental results are inconsistent with an existing, well-established theory, scientists may require further experimentation to decide whether
the results are flawed or the theory requires modification.
- S6CS8c. As prevailing theories are challenged by new information, scientific knowledge may change and grow.
This section addresses, in whole or in part, the following Benchmarks for Scientific Literacy:
- The motion of an object is always judged with respect to some other object or point and so the idea of absolute motion or rest is misleading.
- Telescopes reveal that there are many more stars in the night sky than are evident to the unaided eye, the surface of the moon has many craters and mountains, the sun has dark spots, and Jupiter and some other planets have their own moons.
- When similar investigations give different results, the scientific challenge is to judge whether the differences are trivial or significant, and it often takes further studies to decide. Even with similar results, scientists may wait until an investigation has been repeated many times before accepting the results as correct.
- Scientific knowledge is subject to modification as new information challenges prevailing theories and as a new theory leads to looking at old observations in a new way.
- Some scientific knowledge is very old and yet is still applicable today.
Grades 9-12 standards that relate to the Georgia standard
- People perceive that the earth is large and stationary and that all other objects in the sky orbit around it. That perception was the basis for theories of how the universe is organized that prevailed for over 2,000 years.
- Ptolemy, an Egyptian astronomer living in the second century A.D., devised a powerful mathematical model of the universe based on constant motion in perfect circles, and circles on circles. With the model, he was able to predict the motions of the sun, moon, and stars, and even of the irregular "wandering stars" now called planets.
- In the 16th century, a Polish astronomer named Copernicus suggested that all those same motions could be explained by imagining that the earth was turning around once a day and orbiting around the sun once a year. This explanation was rejected by nearly everyone because it violated common sense and required the universe to be unbelievably large. Worse, it flew in the face of the belief, universally held at the time, that the earth was at the center of the universe.
- Johannes Kepler, a German astronomer who lived at about the same time as Galileo, showed mathematically that Copernicus' idea of a sun-centered system worked well if uniform circular motion was replaced with uneven (but predictable) motion along off-center ellipses.
- Using the newly invented telescope to study the sky, Galileo made many discoveries that supported the ideas of Copernicus. It was Galileo who found the moons of Jupiter, sunspots, craters and mountains on the moon, and many more stars than were visible to the unaided eye.
- Writing in Italian rather than in Latin (the language of scholars at the time), Galileo presented arguments for and against the two main views of the universe in a way that favored the newer view. That brought the issue to the educated people of the time and created political, religious, and scientific controversy.
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This section addresses, in whole or in part, the following National Science Education Standards:
- The sun, the earth, and the rest of the solar system formed from a nebular cloud of dust and gas 4.6 billion years ago. The early earth was very different from the planet we live on today.
- The origin of the universe remains one of the greatest questions in science. The "big bang" theory places the origin between 10 and 20 billion years ago, when the universe began in a hot dense state; according to this theory, the universe has been expanding ever since.
- Early in the history of the universe, matter, primarily the light atoms hydrogen and helium, clumped together by gravitational attraction to form countless trillions of stars. Billions of galaxies, each of which is a gravitationally bound cluster of billions of stars, now form most of the visible mass in the universe.
Note that a theory must be testable, and verifiable by others. If it can't be subsequently verified, it will have to be rejected. You can never PROVE a theory. Theories simply stand until disproved, or until they are seen to have limits.
- Observations (collect data)
- Try to explain observations - HYPOTHESIS
- TEST the hypothesis (with experiments) and as a result:
- Devise a better explanation in accordance with the tests - THEORY
Aristotle (384-322 BC) performed one of the first known uses of the scientific method.
Measuring the Size of the Earth
About 200 BC, Eratosthenes, a Greek mathemetician, geographer and astronomer, used Aristotle's ideas to calculate the size of the Earth.
On a certain day of the year (noon on the summer solstice), observers at Syene, Egypt saw the sun directly overhead.
It shone to the bottom of a deep well.
Observers at other locations (Alexandria, Egypt) saw the sun at an angle on that day.
This was recognized because a vertical pole cast a shadow.
The angle of the shadow was measured (7.2°).
Knowing the distance from Alexandria to Syene (5000 stadia), and using simple geometry,
Eratosthenes calculated the circumference and the radius of the Earth.
He knew from geometry that the angle he measured was equal to the angle between Alexandria and Syene, as measured from the Earth's center.
Because the arc of the angle he measured was 1/50 of a circle, he multiplied 5000 stadia by 50.
His result, 250,000 stadia (or about 46,250 km), is surprisingly close to modern measurements of the circumference of the Earth (about 40,024 km).
The result was within 1 percent accuracy of the figure known today.
His calculation was based on two assumptions - that the Earth is round and that the sun's rays are essentially parallel.
Models of the Universe
Our modern view of astronomy in which the Earth rotates on its axis and revolves around the sun evolved during a time called the scientific revolution. This was in the 16th and 17th centuries (1500's and 1600's), and followed the Renaissance (1275-1475 AD). This period in time provides a transition between the medieval and the modern world.
In the Mid 16th Century (mid-1500's) there were 2 models to describe the structure of the universe:
Both were good models because they:
- Geocentric (earth-centered) model
- Heliocentric (sun-centered) model
- Accounted for all observations of the movement of the sun and the moon, and the planets, and the stars
- Were good predictors of future positions of celestial bodies; models were verifiable
- Simplicity (Occam's Razor or the Principle of Parsimony) - as few assumptions or rules as possible; no contradictions.
Both were complex models.
A. Geocentric Model - Ptolemy
Probably originated with the Greeks or Egyptians prior to 300 BC. Was summarized by Ptolemy (about 100 - 200 AD), a Greek philosopher who studied in Egypt.
As observations become more detailed, the model became more complex (more spheres).
- The Earth is still; motionless
- Earth at center of Universe
- Celestial bodies move in perfect circles at uniform speeds
- Stars were set in a rotating sphere that turned E to W once a day
- Planets, moon, sun also set in separate spheres that moved slower
Planets moved in circles (called epicycles) centered on the Earth.
The ancient Greeks were aware of 5 bodies in the sky that did not behave in a regular, predictable pattern. They were called "wanderers", planetes.
Quality of observations was fairly poor, and model worked fairly well. (With more precise observations, it did not hold up; many corrections had to be added.) It did not explain some things, such as changes in brightness of planets.
These planets are all on (or very close to) the ecliptic.
Planets rise in the east and set in the west (due to the Earth's rotation), but normally appear farther east each night. Occasionally, however, they seem to slow down and move backwards (westward) for a month or two. This reversal in direction is called RETROGRADE MOTION.
This motion is easily explained by a model in which the Earth and the planets orbit the sun at different distances and at different speeds (faster closest to the sun). However, it was a problem for the early astronomers who did not use a sun-centered model for the solar system.
The Ptolemaic model required 80 circles. Complex. A simple model would be better.
Aristotle had a strong influence, and his teachings carried great weight. He promoted the geocentric model.
The Ptolemaic "Earth-centered" model survived for almost 1300 years.
B. Heliocentric Model of Copernicus - A Revolution in Scientific Thought
The heliocentric or sun-centered model was proposed by Nicholaus Copernicus, a Polish cleric (1473-1543), around 1500.
Copernicus was dissatisfied with the complexity of the geocentric model.
He stated that the motions of the objects in the sky could be explained by imagining that the Earth revolved around the sun once a year,
and that the Earth rotated on its axis once a day.
This explanation was rejected by nearly everyone at the time because it violated common sense.
It also required the universe to be unbelievably large.
More seriously, it flew in the face of the universally-held philosophical and religious beliefs that Man (and the Earth)
was at the center of the universe. Man was believed to be superior, and not just a part of nature.
The heliocentric theory ran against the theories of the politically powerful churchmen of the time.
Two Italian scientists of the day, Galileo (see below) and Bruno, accepted the Copernican theory,
and as a result suffered much personal injury at the hands of the powerful church inquisitors.
Giordano Bruno dared to suggest that space was boundless and that the sun, with its planets, was but one of many similar systems.
In fact, there even might be other inhabited worlds with intelligent beings equal (or possibly superior to) ourselves.
For such blasphemy, Bruno was tried before the powerful church inquisitors, condemned and burned at the stake in 1600.
In 1633, Galileo was forced to give a public denial of the Copernican theories, under the threat of torture and death,
and was thereafter sentenced to imprisonment for the rest of his life.
Revolutions in scientific thought, or paradigm shifts, do not come easily.
It is important to note that scientific knowledge is subject to modification as new information challenges prevailing theories.
Basics of the Heliocentric Model
- Sun is at the center of the universe, motionless; stars are motionless around the edge
- Planets all revolve around the sun (6 total including Earth)
- Moon revolves around Earth
- Earth rotates on axis causing apparent daily motion of the heavens
- Earth revolves around sun causing sun's annual movements
- Retrograde motion of planets is due to relative planetary motions
- Planetary orbits are perfect circles
We know that some parts of this model have been modified - the planetary orbits are actually elliptical; the sun rotates on its axis, for example.
Copernicus was the first to determine the relative distances of planets from the sun.
The Benchmarks for Scientific Literacy state: The great cosmological revolution usually associated with the name of Nicolaus Copernicus was one of the episodes in history that was truly transforming. It changed, ultimately, the sense most people have of their relation to the physical universe, and it raised difficult questions of human existence that for many people have yet to be resolved satisfactorily.
The Copernican Revolution merits study by all students because it illustrates many aspects of the way science works, especially the way in which science, mathematics, and technology are intertwined and the way in which international efforts in science come together.
Interestingly, Aristarchus of Samos, a Greek about 310-230 BC, had a heliocentric model.
He proposed that all of the planets, including Earth revolved around the Sun,
and that the Earth rotates on its axis once a day. His ideas did not gain widespread acceptance during his lifetime because the geocentric model was favored.
Tycho Brahe (1546-1601)
In trying to decide between the geocentric and heliocentric models, Tycho was disappointed with the predictive capability of both models. Much of the reason was the crudeness of the available instruments. Tycho felt that he needed better instruments to make more accurate measurements. He hoped that better observations would allow him to choose between the models.
Tycho Brahe's Contributions to Astronomy:
- Tycho was the first to suggest a non-circular orbit for a celestial body (a comet).
- Used calibrated and bigger instruments, new techniques to measure angles (similar to a sextant).
- Built an observatory (remember - no telescopes yet) and made accurate and continuous measurements for 20 years.
His measurements helped to prove that planets orbited the sun.
- Accurate map of the stars with 777 stars.
- Measured length of the year to within 1 second.
- Was still unable to choose between the geocentric and heliocentric model.
He had his own model with the Earth at the center, orbited by the sun and the moon, with planets orbiting the sun.
Never worked out the mathematical details, and his model was never accepted.
- Using Tycho's data, a German astronomer (Kepler) was able to refute the geocentric model.
Johannes Kepler (1571-1630)
Was interested in two questions:
- Why are there only 6 planets? (Remember that this was back around 1600. The other planets had not been discovered yet.)
- How are their orbital periods related to their distance from the sun?
To answer the first question, Kepler hypothesized that the spheres supporting the planets were separated by invisible regular solids
(only 5 are possible - cube, tetrahedron, octahedron, etc.).
Astronomers knew that the outer planets took longer to orbit the sun, and moved slower in their orbits.
Kepler hypothesized that a physical force moved the planets, and that the force diminished with distance.
Planets closer to the sun feel a stronger force and move faster.
The concept of a physical force was a monumental step. Kepler was on the verge of assigning physical causes to celestial motions.
In 1600, Kepler began working as Tycho's assistant.
They recognized that neither the Ptolemaic (geocentric) or Copernican (heliocentric) models could predict positions of Mars as accurately as they could measure them. Kepler tried to calculate an orbit that would fit the data.
Tycho died in 1601; Kepler then had full access to Tycho's data, and analyzed the data for 8 years! He tried to calculate an orbit that would fit the data, but was unable to do so.
Kepler later determined that the orbits were not circular but elliptical.
Kepler's Laws of Planetary Motion
Kepler's 3 laws replaced the cumbersome epicycles to explain planetary motion with three mathematical laws that allowed the positions of the planets to be predicted with accuracies ten times better than Ptolemaic or Copernican models.
- The orbits of the planets are elliptical.
eccentricity e = F/A
(When F = 0, then e = 0, A CIRCLE)
(Eccentricity is a maximum at e = 1)
- An imaginary line connecting a planet and the sun sweeps out equal areas during equal time intervals.
The Earth's orbital speed varies at different times of the year.
Moves fastest when closest to the sun; slowest when farthest away.
Terms to know:
- PERIHELION = where a planet is closest to the sun
- APHELION = where a planet is farthest from the sun
Kepler's Second Law of Planetary Motion was calculated for Earth, then the hypothesis was tested using data for Mars, and it worked!
A planet's speed changes with its distance from the sun.
Animation illustrating Kepler's Second Law, by bill Drennon from http://home.cvc.org/science/kepler.htm
NASA Video of Kepler's Second Law
- Kepler's Third Law of Planetary Motion showed the relationship between the size of a planet's orbit and its orbital period, P.
a3 = p2
a3 / p2 is the same for all planets. Constancy of ratio.
The distance of a planet from the sun varies. Its orbital size is defined as a = 1/2 of the major axis A. This is the seim-major axis, a. (a = 1/2 A)
IF THE PERIOD OF A PLANET IS KNOWN IN EARTH YEARS, ITS SEMI-MAJOR AXIS CAN BE CALCULATED IN A.U. (and vice versa) .
Galileo Galilei (1564-1642)
Was the first to report using the telescope to view the heavens.
Telescope invented in 1604 by Hans Lippershay.
Galileo used the telescope in 1609. Built his own. Two lenses in a metal tube about 4 feet long, diameter = 4 cm (1.6 inches). Magnification 3X to 33X.
His observations between 1609 and 1612 changed our ideas about the universe.
What did he see?
- New stars (Milky Way made up of stars)
- Mountains and valleys on the moon
- Four moons orbiting Jupiter (now called Galilean moons)
- Phases of Venus
- Sunspots (rotating around the sun about once a month)
- The rings of Saturn (sketches. was puzzling; not identified as rings until about 50 years later.)
- Planets are disks, not pinpoints of light like the stars
The significance of what he saw:
- Cast doubt on the view of the "perfection of the heavens" (of Aristotle and Plato)
- Showed deficiencies of the geocentric (Ptolemaic) model
- Rotation of sunspots around sun suggested that if the sun could rotate, perhaps the Earth could too.
- Phases of Venus would be a natural consequence of the heliocentric model.
- Jupiter's moons showed that centers of motion other than Earth existed.
Galileo published in Italian, not Latin. Widely read. Language of the people, rather than language of the scholars.
Arguments against the geocentric model were so forceful that he came under fire from the Catholic Church and was forced to give a public denial of the heliocentric/Copernican system, and was placed under house arrest for the last 10 years of his life.
Was not pardoned by the Church until 1992.
Science in Italy was dealt a severe blow. The center of scientific investigation shifted to northern Europe.
Many scholars refused to believe his ideas and a few even refused to look through the telescope. Many clung to old ideas.
Evidence that must be considered for any theory of the origin of the solar system
- Planets revolve around sun in same direction - CCW
- Planets lie roughly within sun's equatorial plane (plane of sun's rotation)
- Solar system is disk-like in shape
- Planets rotate CCW on their axes, except for:
- Venus - slowly CW
- Uranus - on its side
- Pluto - on its side
- Moons go CCW around planets (with a few exceptions)
- Distribution of planet densities and compositions is related to their distance from sun
- Inner, terrestrial planets are rocky, small and have high density
- Outer, jovian planets are gaseous (H, He, CH4), large and have low density
- Age - Moon and meteorites 4.6 by
- Sun lies in the center of the solar system.
Sun is dominantly composed of hydrogen (H) and helium (He).
- Abundances of some elements in the sun:
- H 78.5% percent by mass
- He 19.7%
- O 0.86%
- C 0.40%
- Fe 0.14%
- Si 0.10%
- N 0.09% etc.
- (Data from p. 392 in Flower, Understanding the Universe, first edition)
Interpretation of the Evidence:
Solar Nebula Hypothesis or Nebular Hypothesis
- Cold cloud of gas and dust spins, contracts under gravity, flattens, and rotates to form a flattened disk.
- Concentration of matter in center forming a proto-sun (most of mass, 99.85%)
- Accretion and collisions of particles of dust and gas in the disk of matter around central mass formed protoplanets (cold accretion).
- Continued impacts enlarge protoplanets into planets.
- Cloud condensed, shrank, and heated by gravitational compression to form Sun.
Dense concentration of H and He at center led to fusion of atoms.
Hydrogen burning; He produced. This is the source of the sun's energy
- Solar wind drove lighter elements outward causing observed distribution of masses and densities.
Heat of sun drove off H and He from inner planets (due to their small size and weak gravity.)
H and He accumulated around planets farther out in the solar system (now called Jovian planets).
A. Cold accretion model
Earth was initially unsorted material; but now layered.
Requires a process of differentiation. Heating and at least partial melting.
Iron and nickel sink to form core. Less dense material forms mantle and lighter crust.
Source(s) of heat for melting?
- Accretionary heat from bombardment
- Heat from gravitational compression
- Radioactive decay
B. Hot accretion model
Internal zonation of planets is a result of hot heterogeneous accretion. Hot solar nebula (over 1000 C).
Initial crystallization of iron-rich materials forms planet cores. With continued cooling, lower density silicate materials crystallized.
When did this occur?
4.6 - 5 billion years ago (bya)
Based on dates of meteorites and moon rocks.
What happened or existed before this?
- Iron is the heaviest element that can be created in a star through nuclear reactions.
- Elements heavier than iron are present on the Earth; gold, silver, titanium, uranium (all of these are heavier elements than iron).
- Elements heavier than iron are created by the fusion of atoms and neutron capture under high pressures which occur
during a violent explosion marking the end of a star's life (a supernova).
A supernova (tremendous stellar explosion ejecting most of a star into space).
occurred near the solar nebula at time of its collapse to form our solar system.
Our sun is a second generation star. It is made of "recycled material" left over after a supernova.
There must have been an earlier star/sun that exploded into a supernova in this part of the galaxy,
creating the heavier elements that are present on Earth and in our solar system.
And prior to this?
Movement of galaxies and the Big Bang Theory
- The galaxies are rapidly moving apart. This indicates that the galaxies were closer together in the past.
(This was discovered in 1929 by Edwin P. Hubble and is called Hubble's Law).
- Observed temperature of the universe today (background microwave radiation) is 3 degrees above absolute zero.
- Present abundances of hydrogen and helium.
The universe is expanding. Everything began together at a point,
and a big explosion occurred, causing things to move apart rapidly.
This interpretation is called the Big Bang Theory.
Other theories for the origin of the universe:
- Steady-state cosmology - universe will continue to expand forever;
new matter is formed in the spaces between galaxies at about the same rate that the older material is receeding.
Density of matter in the universe remains relatively constant.
- Oscillating universe cosmology - universe expands (like with the Big Bang) and then contracts. Expansion and contraction alternate.
Formation of stars, galaxies, solar systems, planets
Material begins to clump together as it moves away from the center of the
Molecular clouds form (raw material for new star systems).
How old is the Universe?
Calculations of the age of the universe depend on the calculation of the Hubble Constant, a number which refers to the rate of expansion of the universe.
Controversy arose in Fall 1994
Age of the universe has been calculated to be about 10-15 billion years; calculations show that the age must be less than 20 billion years.
BUT 1994 data from Hubble Space Telescope was interpreted to indicate a high rate of expansion, resulting in an age of only about 8 billion years.
This stirred up a lot of excitement in Astronomy. For details, see the March 6, 1995 issue of TIME Magazine, p. 76-84.
Update: April 7, 1997, front page, New York Times. National Academy of Sciences held a colloquium on the age of the universe in March 1997.
Many cosmologists now think that the age of the universe is likely to be between 12 and 14 billion years. Later observations from the Hubble Space
Telescope observations of Cephids (pulsating stars) have given somewhat lower expansion rates.
Lower expansion rates have been suggested by other recent studies as well. This seems to mean that the age of the universe is most likely 15-20 billion years.
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Page created by Pamela J.W. Gore
Georgia Perimeter College,
Page created March 29, 2005