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The Solar System
S. Gavin and S. P. Karrer
Physics Department, Wayne State University, Detroit, MI, 48201
[email protected]
I. Introduction
As children we all learned that the Earth is one of many planets circling our Sun. This idea is
so central to our understanding of our place in the Universe – our cosmology – that it’s difficult
to imagine that somebody once had to conceive this idea and prove it correct. This case study
explores where our understanding of the solar system came from.
The idea of a Sun-centered “solar system” followed from the first realization in ancient times
that the movement of stars in the sky was linked with cosmology. Origin myths had existed in
every culture, but the association of cosmology with something you could observe was truly
revolutionary. Things to bear in mind when studying this case:
1. Every generation has had its own cosmology, from Aristotle to Copernicus. We have
always been completely convinced that our model is the correct one. Today, the bigbang model explains the observed expansion of the universe along with many other
observations. But has anybody heard of dark energy?
2. Forget about gravity! Gravity allowed Newton to calculate planetary orbits with a
formula that could be tested in laboratory’s on the Earth. This is proof positive of the
heliocentric system, and makes Aristotle and Ptolemy seem insane to contemporary
students. But that is not the way any of this was discovered. In fact, most details of the
solar system had been discovered earlier, and informed Newton’s work.
3. Cosmological models have implications for the general public that reach far beyond
science. Religion and spirituality has had a profound role in the development and
acceptance of these models.
The role of the scientific method in the development of the heliocentric model is discussed in
The Copernican Revolution by Thomas Kuhn [1]. While understanding the scientific details is
not vital to following this case, ref. [2] is a useful web resource for the related astronomy and
some of the history. We have also used a number of pictures from the Astronomy Picture of
the Day site [3] and other web resources such as the Science U cite, which contains an
explanation of retrograde motion [4].
[1] Thomas Kuhn, The Copernican Revolution, (Harvard University Press, Cambridge, 1957).
[2] Nick Strobel, Astronomy Notes, http://www.astronomynotes.com.
[3] Astronomy Picture of the Day, http://antwrp.gsfc.nasa.gov/apod.
[4] Retrograde Motion, http://www.scienceu.com/observatory/articles/retro/retro.html
[5] Galileo Galilei, Sidereus Nuncius (the Starry Messenger), trans. and annotated by A. Van
Helden, (University of Chicago Press, Chicago, 1989).
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II. Ancient Greece and the Cosmos:
The Sun appears to rise in the east and set in the west. At night, the stars also seem to work
their way east-to-west across the heavens. Some stars rise and set as the Sun does, while
others travel in circular paths, as shown in fig. 1. The stars don’t move relative to one another,
as constellations appear move in fixed formation. This lead the ancient Greeks to imagine that
the stars were fixed to a celestial sphere that rotated daily. Even today, astronomers describe
the position of stars using coordinates that essentially give the longitude and latitude on this
celestial sphere.
Figure 1: Time-lapse image of star trails – the graceful concentric
arcs traced by the stars during the night. Josch Hambsch produced
this composite of star trails around the South Celestial Pole with an
effective "all night" exposure time of almost 11 hours, from [3].
The Greeks believed that the crystalline celestial sphere rotated around a stationary,
spherical Earth. Careful observation of the way the stars move at different latitudes suggest
that the Earth is spherical. In the northern hemisphere, the number of stars that travel in
complete circles (as opposed to rising and setting) decreases the further south you go. Other
observations support the picture of a spherical Earth, such as the `sinking’ of the masts of
ships as they sail into the horizon. Eratosthenes was even able to measure the radius of the
Earth by observing the shadow of the sun at different latitudes.
The Sun and the planets move roughly as the stars do, but with highly important differences.
The daily motion of the Sun is practically indistinguishable from that of any star near its
position on the celestial sphere. The ancients realized that the stars do not disappear during
the day, but that the Sun outshines them when it is above the horizon. However, the Sun’s arc
across the sky changes seasonally, e.g., the position of the noonday Sun is furthest north in
the summer, and the days are longer. This is not so for the stars. This can be explained if the
Sun is fixed to its own transparent sphere inside the celestial sphere. The seasonal variation
is explained if the north pole of the Sun’s crystalline sphere is tilted by 23.5 degrees with
respect to the celestial sphere. The motion of the planets is even more interesting, as we
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discuss shortly. In this picture, each planet requires a crystalline sphere of its own.
What really delighted the ancient Greeks was the symmetry of spheres within spheres. In
Aristotle's view the outer celestial sphere was the driving force for the many crystalline
spheres that the Sun, Moon, and the planets rode upon. All of this was centered about the
Earth. But there were many competing views to this `Aristotelian’ cosmology. Atomists
believed that the Earth was just another planet and that no particular place in the universe
was much different from another. The Pythagoreans suggested that the Earth was not the
center of the universe but, rather, an unseen Altar of Zeus was. Heraclides put the Earth back
in the center, but thought that the Earth rotated. He also imagined that Mercury and Venus
orbited the sun. Aristarchus came closest to our modern view. He said that the sun was the
center about which the Earth and the other planets rotated. This system still contained the
sphere of stars, but much farther away. Many of these `alternative’ cosmologies were
dismissed and ridiculed, especially in the Middle Ages.
Q1. How does this picture fit in to the scientific method? What testable predictions does it
suggest?
Q2. What are the similarities and differences from the case of free fall studied earlier?
Q3. The sphere-within-sphere model is very useful for astronomy and navigation. Good
calendars are really useful in farming and other seasonal activities. Of what use are the
distinctions between the ideas of Aristotle and Aristarchus?
Q4. What is the role may spirituality and religious considerations have had in the invention of
this celestial sphere model?
Fig. 2. Venus traces out this S shape on the celestial sphere. Astronomer Tunc
Tezel constructed this composite illustrating Venus' retrograde motion against
the background stars. This picture from [3] combines a series of 29 images
recorded from April 3rd through August 7, 2004.
Copyright 2008 Wayne State University. For educational use only. For permission to use: [email protected]
The motion of the planets presented a challenge for the sphere-within-sphere cosmology.
Like the stars, the Sun and the planets move daily across the night sky from east to west.
Viewed against the background of the fixed stars, careful observation shows that the Sun
slowly drifts from west to east. The planets also drift toward the east – most of the time.
Sometimes, however, they seem to double back and move from east to west on the celestial
sphere. These periods of retrograde motion, shown in fig. 2, were a challenge to understand
or predict.
III. The Standard Model
Claudius Ptolemaeus (90 to 168 AD), or Ptolemy, created the first “standard model” of the
cosmos, a model that lasted 1500 years. He developed a system describing the motion and
placement of all the known major objects in our solar system. Following Aristotle, he placed
the Earth at the center, unmoving, with everything else revolving around it. This worked well
for the Sun, Moon, and stars, but not as well for the wandering planets. To describe
retrograde motion in a Geocentric System, Ptolemy used an idea known as epicycles.
Epicycles are extra orbits that circle an imaginary point called the `eccentric.’ It is the
eccentric that follows a circular orbit around the Earth. Ptolemy’s system is shown in fig. 3.
Prior to Ptolemy, others had used epicycles to describe planetary motion. Ptolemy took the
best of these models and consolidated them. He then used observations and added
refinements of the model to improve agreement. See [1] and [2] for a discussion of some of
the details. What emerged was a messy but effective way to predict the motion of planets and
other astronomical events. Importantly, Ptolemy published his work and made it widely
available – this may have been the secret of his lasting impact!
To be sure, this model conflicted with the fundamental ideas of the Aristotelian sphere-withinsphere cosmology, since there is no way for a planet to follow an epicycle without crashing
through its crystal sphere. Ptolemy’s view was that the model was only a mathematical tool
for predicting planetary motion, the sole justification of which is its agreement of predictions
with future observations. In contemporary physics, we call this a “phenomenological”
approach. Such an approach is typically useful in developing future experiments in research
areas where calculations from first principles are not practical.
It’s worth mentioning that interest in Astrology was one of the major driving forces behind
Ptolemy’s investigations. While he was skeptical of the extent of Astrology’s predictive powers
(he felt other factors such as upbringing also mattered), he wrote the most influential and
popular work on Astrology from the time. His work was very influential in the Islamic world and
parts of Europe.
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Fig. 3. Ptolemy’s Earth-centered system. Planets rotate about certain points, which themselves follow
circular paths about the Earth. From ref. [4]
Q5. What evidence did Ptolemy have for/against his system?
Q6. Introductory physics courses use a number of phenomenological models. Can you name
some? One of these models used in early chapters is later given a more fundamental
explanation in later chapters. Which one?
IV. Copernicus to Galileo
Steady progress in observational astronomy was made throughout the Middle Ages. Islamic
civilization rose in the Arabic countries, while Europe languished in poverty. The works of the
Greek scholars were translated into Arabic. Astronomers thoroughly cataloged the heavens,
giving many of the stars their present Arabic names. Work had continued on developing
Ptolemy’s model to make it more consistent with these improved observations. New cycles
were added and the speed of rotation around these cycles modified. Ptolemy’s work,
presented in his 13 volume series called the “Almagest” was already complex. The improved
models were even more so.
Nicolaus Copernicus (1473-1543) brought us the first draft of our current solar system
model. He realized that the daily motion of the stars, Sun, and planets could be explained if
the Earth was a sphere spinning on its axis. He explained the yearly drifting motion of the Sun
from the Earth’s perspective as a consequence of the Earth’s rotation about the Sun. A 23.5
degree tilt of the Earth’s axis relative to the Sun explained the seasons.
Importantly, by placing the planets in the order shown in fig. 4, he could explain their
retrograde motions in a fashion that its much more straightforward than Ptolemy. Figure 5
shows the Earth racing past an outer planet such as Mars. As the Earth passes that planet,
the apparent motion of that planet relative to the Earth seems to reverse direction. Similarly,
as an inner planet such as Venus executes retrograde motion when it passes the Earth [4].
Elements of the heliocentric system had been proposed earlier, and Copernicus was aware of
this. As mentioned before, Heraclides and Aristarchus placed the sun at the center. Later,
Nicholas of Cusa made arguments for the motion of the Earth itself. From the voyages of
Columbus and others, it was well known that there was no end to the Earth. Most people
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were convinced that the Earth was a sphere.
Figure 4: Heliocentric system from ref. [4]
Figure 5: Retrograde motion: as the Earth passes the outer
planet, it image of the planet against the fixed stars appears to
form a loop. From ref. [2].
Philosophical and religious considerations guided Copernicus’ thinking. He believed that God
should the center about which everything revolved, so he followed Aristarchus and placed the
Sun at the center. He argued that the natural motion of a sphere was to move in a circle, so
the orbits of the planets were circular. His universe, too, was spherical, because it contains
the most volume and is the most perfect of all shapes.
But there was also an element of physics in Copernicus’ thinking. Those that argued against a
spinning Earth claimed that it would fly apart. Copernicus argued that a spinning celestial
sphere, being much larger in size, would experience an outward force that was much larger. It
was much easier for the Earth to withstand this, being made of solid, earthy stuff.
Nevertheless, it is important to realize that Copernicus was firmly rooted in the Ptolemaic
tradition, even as he was breaking with it. His own writings were every bit as mathematical
and technical as Ptolemy’s, and ware intended for the same select audience of learned
astronomers. Moreover, since Copernicus believed the planets followed spherical orbits at
uniform speeds, there were small discrepancies with detailed observations. To account for
these discrepancies, he added small epicycles of his own. But he could achieve a comparable
accuracy to Ptolemaic model with far fewer epicycles. (We now know that the orbits are
ellipses with speeds following Kepler’s laws.)
Copernicus felt that the most convincing aspect of his heliocentric picture was its relative
mathematical and scientific simplicity. The epicycles and eccentrics of Ptolemy are reduced in
complexity if you put the sun in the center. It is also more natural, as the speeds of the
planetary orbits decrease as they move farther from the Sun. In contrast, their speeds and
other characteristics were less systematic the Ptolemaic system. With Copernicus, planetary
distances could be determined in terms of the distance from the Earth to the Sun using
trigonometry and observations. In the geocentric system, a change in one epicycle meant
nothing to other planets. But despite its simplicity and natural feel, Copernicus’ model was still
only as accurate as the Ptolemaic model.
Knowledge of Copernicus’ work was limited to refined circles because of the difficulty of his
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writings. Opponents to the Copernican picture did, however, raise troublesome questions.
Why did we not feel the Earth’s motion? It would be centuries before the underlying
mechanics became clear and the Coriolis effect would be demonstrated. If the Earth is circling
the Sun, why didn’t the stars move throughout the year? Very refined telescopes were
needed to demonstrate the parallax effect, because the stars are so very far away. But the
truly profound questions about our place in the universe did not come up until much later.
Q7. Occam's razor states that the simplest explanation is best. Is this a valid scientific
principle? Can you give an example of a modern day theory where simplicity and elegance
are the primary justifications?
Q8. It is also a valid scientific principle to stick to tried-but-true models that explain all
observations. Nobody wants to waste effort on wrong theories. Can you name a few exciting
scientific ideas that turned out to be wrong?
Erasmus Reinhold lived at about the same time as Copernicus and was the first to create
astronomical tables using Copernican methods. His Prutenic Tables, named for the Prussian
sponsor, were more accurate than the formerly used (and very old) tables. The new methods
gave higher accuracy on many important fronts (for example the positions of the planets).
They were less accurate, however, on determining the length of the year. Despite this
shortcoming, the new tables were used by many astronomers. This helped the heliocentric
system gain a foothold.
Q9. What does the lowered accuracy of the year say about the Copernican system?
Q10. What does this show about scientific consensus and community?
Tycho Brahé (1546-1601) is remarkable more for his observations than his theories. With
only his naked eye and what was essentially a million-dollar protractor, he was able to make
extremely accurate measurements of planetary motion (to within one arc-minute for stars and
four arc-minutes for planets). This laid the groundwork for Kepler to design his famous laws.
He also developed a hybrid geo-heliocentric system in which the Earth was still at the center.
The sun revolved around the Earth but all the other planets revolved around the sun. Brahé
also made two key observations: a nova and comets. A new star appeared in the
constellation Cassiopeia and gave evidence against the perfection of the heavens. The
measurement of parallax of comets showed they were part of the heavens and provided more
evidence. The comets also showed that the planets did not ride on crystalline spheres. If
there were such spheres, the comets would have smashed through them, but they moved
unhindered as the stars or planets.
Q11. How do Brahé's measurements stand out in that era of science?
Johannes Kepler (1571-1630) systematized Brahé's observations in the framework of the
heliocentric solar system. His three laws of planetary motion greatly simplified Copernicus’
model and rid the world of epicycles. Kepler's First Law states that planetary orbits are
ellipses and the sun is at one of the foci of this ellipse. In particular, Brahé's observations of
the orbit of Mars were described to high accuracy by an elliptical orbit. His Second Law states
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that in a given time of orbit, the sector created by the arc that the planet has traveled will
always have the same area. This law took the function of equant point from Ptolemy's system.
Kepler's Third Law states that the square of the period of orbit (the “year”) is proportional to
the cube of the orbital radius.
Q12. Kepler’s observation that planetary orbits where ellipses put the final nail through
Aristotle’s crystalline spheres. But there was no fundamental justification for elliptical orbits. Is
this any better than Ptolemy’s description?
Galileo Galilei (1564-1642) brought the heliocentric solar system to the world stage with
striking new discoveries. The key to his success was the telescope. He hand-built one of the
first telescopes and used it to investigate the other planets. It is worth noting that his
telescope was about as good as a pair of binoculars with modern optics.
First, on looking at supposedly “blank space” in the sky he observed countless (and before,
invisible) stars. Though not considered a scientific argument today, for the philosophically
oriented renaissance audience, this was evidence that the heavens were not perfect as
assumed. Next, he observed the moon and other objects and found them to be “imperfect,”
with surface features similar to the Earth. This put all the planets on equal footing, instead of
the other planets being perfect, heavenly spheres. Galileo also discovered that Jupiter had
moons. He argued that the moons orbiting Jupiter was a microcosm of the solar system – a
large body with smaller bodies orbiting around it.
He discovered that Venus has a complete set of phases, as does the moon. Copernicus had
suggested that an observation of Venus’ phases would provide direct evidence on the nature
of its orbit. In the Ptolemaic system, Venus orbits within the sphere of the Sun. Copernicus
argued that in Ptolemy’s model, Venus would exhibit only “crescent” or “new” phases when
facing the Sun as shown in fig. 7. It would therefore not be possible to see a “full” or “gibbous”
Venus. One might imagine an alternative geocentric model with Venus outside the Sun’s
sphere, but in that case only gibbous and full phases would be possible. Galileo saw all the
phases and sizes of Venus in the sequence predicted using the heliocentric model, see fig. 6.
Galileo had a very high profile and wrote for the public in plain language. This brought his
revolutionary ideas to the public, and he was criticized from all quarters. In particular, the New
Testament states that "the world is firmly established, it cannot be moved," which is at least
superficially at odds its rotation and orbiting in the heliocentric model. There were many
powerful people who did not like Galileo's new arguments, in particular Cardinal Bellarmine.
There were trials and questions, and eventually Galileo was given a life sentence of house
arrest.
Q13. How is each piece of evidence credible/not credible?
Q14. Do any of these arguments specifically prove the Copernican system?
Discussion question: If you were an astronomer in Copernicus’ day, which model would you
use? At what point in history would you start using the heliocentric model. Bear in mind that in
science the easiest discoveries with the greatest impact are often made first. On the other
hand, your colleagues will laugh at you if you work on something they consider crazy.
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Figure 6. Sequence of Venus’ sizes and phases
according to Copernicus from ref. [5], pg 107.
Figure 7. Sequence of Venus’ sizes and phases
according to Ptolemy from ref. [5], pg 108.
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