Download History and Philosophy of Western Astronomy

History and Philosophy of Western Astronomy
This write-up covers the development of western astronomy and modern science. The focus
is on the rise of modern science in Europe, from the ancient Greeks to Newton to Einstein. Other
cultures were also quite interested and skilled in astronomy (the Mayans, Egyptians, peoples of India,
American Indians, China, Australia, Mesopotamia, Stonehenge builders, etc), but the Greeks were
the first ones to try to explain how the universe worked in a logical, systematic manner using models
and observations. Modern astronomy has its roots in the Greek tradition.
A. 7th Century B.C.
By the 7th Century B.C. a common viewpoint had arisen in Greece that the Universe is a
rational place following universal, natural laws and we are able to figure out those laws. Open
inquiry and critical evaluation was highly valued. The emphasis was on the process of learning about
the universe rather than attaining the goal. But people eventually got tired of learning and wanted
absolute answers. Science is not able to give absolute, certain answers. There was disagreement
among the experts and there came to be a crisis in confidence that led to the rise of the Sophists.
B. Sophists
The Sophists taught that truth and morality are myths; relative to the individual. Since truth
and morality are just cultural inventions, a person should conform to the prevailing views, rather than
resolutely holding to some belief as an absolute one.
C. Thales (624-547)
Predicted a total Solar Eclipse - details unknown
D. Pythagoras & Students (Pythagoras lived 582-500 B.C.).
The Greeks were guided by a paradigm that was first articulated by Pythagoreans. A The
Pythagorean Paradigm had three key points about the movements of celestial objects:
1) Celestial objects and the earth are spheres;
2) The Earth is not at the Center, but rotates around a Central fire that cannot be seen as a counterearth blocks its view;
3) The counter earth, earth, moon, sun and planets move “perfectly circularly” and perfectly
uniformly. The planets produce sounds as they move. This idea is based on the Harmony of the
Musical Scale.
E. Socrates (lived 470-399 B.C.)
Socrates taught that we can attain real truth through collaboration with others. By exploring
together and being skeptical about “common sense” notions about the way things are, we can get a
correct understanding of how our world and society operate.
F. Plato (lived 427-347 B.C., a student of Socrates)
Plato taught that there are absolute truths---mathematics is the key. While statements about
the physical world will be relative to the individual and culture, mathematics is independent of those
influences: 2+2=4 always, here on Earth or on the far side of the galaxy. Plato had four Basic Points:
1. There is certainty.
2. Mathematics gives us the power of perception.
3. Though the physical applications of mathematics may change, the thoughts themselves are
eternal and are in another realm of existence.
4. Mathematics is thought and, therefore, it is eternal and can known by anyone. Mathematical
symmetries are the language of universal design and harmony. [Today we view mathematical
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ideas as free creations of the human mind. They are the tools we use to map the world.
Experience is the key. Although absolute certainty is not possible, we can still attain accurate
knowledge and reasonable beliefs about the world.]
Out of Plato’s teachings grew the belief that when one studies mathematics, one studies the
mind of God. And God is a “perfect” being. Thus his universe is also perfect and unchanging. Plato
gave his students a major problem to work on. Their task was to find a geometric explanation for the
apparent “unordered” motion of the planets, i.e. the retrograde motion using the Pythagorean
Paradigm. This meant that regardless of the scheme they came up with, the Earth should be at the
unmoving center of the planet motions.
G. Eudoxus and his model (408-355 b.c.)
Eudoxus, one of Plato’s students, produced a model of concentrically rotating crystalline
spheres. Four spheres that are somehow connected are needed to explain the motion of each planet.
H. Aristotle’s Realism (lived 384-322 B.C.)
Aristotle was also a student of Plato and had probably the most significant influence on many
fields of studies (science, theology, philosophy, etc.) of any single person in history. He improved
Eudoxus’ model crystalline spheres and used 55 concentric spheres, with nine prime spheres which
were: moon, mercury, venus, sun, mars, jupiter, saturn, the stars and finally God. He could explain
rectograde motion, although he was still using the Platonian principle that the heavens were perfect
and that the orbits of the sphere were perfectly circular.Aristotle further showed that the earth is
spherical by arguing that the earth’s shadow during a lunar eclipse is always round, not flat.
I. Aristarchus (310-230)
Aristarchus, another of Plato’s students, violated Plato’s rule and developed a model with the
Sun at the center. His model was not accepted because of the apparently “obvious” observations
against a moving Earth:
1. The Earth is not part of the heavens.
2. The celestial objects are bright points of light while the Earth is an immense, non-luminous
sphere of mud and rock.
3. There is little change in the heavens---stars are the same night after night. In contrast to this, the
Earth is home of birth, change, and destruction. The celestial bodies have an immutable
regularity that is never achieved on the corruptible Earth.
4. Our senses show Earth is stationary: (a) Air, clouds, birds, and other things unattached to Earth
are not left behind as they would be if the Earth was moving. There would be a strong wind if the
Earth were spinning as suggested by some radicals. (b) If the Earth were moving, then anyone
jumping from a high point would hit the Earth far behind from the point where the leap began.
Today we have the understanding of inertia and forces that explains why this does not happen
even though the Earth is spinning and orbiting the Sun. (c) Rocks, trees, and people would be
hurled from a rotating Earth. They knew about centrifugal force, but they did not know about the
force of gravity and inertia.
5. The most convincing argument was that if the earth orbited the sun, the brightness of the stars
would change when the earth gets “closer” to certain stars. Also the stars would then appear to be
more widely separated.
J. Eratosthenes (276-195 B.C.)
Eratosthenes used geometry to calculate the size of the Earth. He used the relationship
between latitude and the altitude of the midday sun to find the difference in the difference in latitude
between Syene and Alexandria. He found that this is 7.2o and calculated that the circumference of the
Earth is 50 times as large as the distance between Syene and Alexandria. The error was ~15%.
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K. Hipparchus
He started making an atlas for bright stars and measured the stellar positions very accurately.
He compared his measurements to those from 170 years ago, and found that all positions
systematically differed by 2o. Thus he discovered precession. His value was accurate to 10%.
L. Ptolemy’s Geocentric Universe (lived 85-165 C.E)
Ptolemy devised a model that used epicycles (a planet had a smaller circular motion--an
epicycle--around a point that was itself in a circular orbit around the Earth) rather than spheres.
Epicycles also explained why the planets are brighter as they retrogress. He added some refinements
to explain the details of the observations: Eccentrics which did not put the earth at the true center of
planet; and Equants which cause the planets motion not to be uniform as it moves around the earth.
These refinements are incompatible with Aristotle’s model and the Pythagorean paradigm: a planet
on an epicycle would crash into its crystalline sphere, and the motion is not truly centered on the
Earth. Since this model could predict the planets motions (accurate to ~5o) it was believed.
Renaissance
A. Rebirth of Astronomy
If it had not been for the Arabs, most of the Greek Astronomy would have gotten lost. They
continued making accurate observations of stars and planets, but they believed in Ptolemy’s
cosmological model. In Europe the following paradigm had developed: Man is God’s special
creation of the physical universe; the Earth is the center of a mathematically planned universe and we
are given the gift of reading this harmony. A vivid description of the Universe can be found in
Dante’s Divine Comedy, written around 1300. However, universities started forming, the Arabic
texts were translated, some old Greek manuscripts were rediscovered, and the Greek’s ideal of
finding logical, systematic explanations to physical events was rediscovered and celebrated. Along
with this came an unbounded faith in the power of reason to solve physical problems. Even Aristotle
was questioned.
B. Occam’s Razor
Scientists use a guiding principle called Occam’s Razor to choose between two or models
that accurately explained the observations. This principle, named after the English philosopher,
William of Occam, who stated this principle in the mid-1300’s, says: the best model is the simplest
one---the one requiring the fewest assumptions and modifications in order to fit the observations.
Guided by Occam’s Razor some scientists began to have serious doubts about Ptolemy’s geocentric
model in the early days of the Renaissance.
C. Copernicus (lived 1473--1543 A.D.)
Nicolaus Copernicus found many deficiencies in the Ptolemaic model. He felt that any model
of the planet motions must account for the observations and have circular, uniform motion. The
Ptolemaic model did not do that. Also, the Ptolemaic model was not elegant and, therefore, unGodlike. During the years between Ptolemy and Copernicus, many small epicycles had been added to
the main epicycles to make Ptolemy’s model agree with the observations. By Copernicus’ time, the
numerous sub-epicycles and offsets had made the Ptolemaic model very complicated. Surely, God
would have made a cleaner more elegant universe!
Copernicus was strongly influenced by neoplatonism (beliefs that combined elements of
Christianity and Platonism) in developing a model to replace Ptolemy’s. This led him to: (a) believe
that the Sun is a material copy of God---God is the creative force sustaining life and the Sun gives us
warmth and light; (b) adopt Aristarchus’ heliocentric (Sun-centered) model because God should be at
the center. Copernicus’ model had same accuracy as the revised Ptolemaic one but was more elegant.
Copernicus retained the Aristotelian notion that planets were striving to fulfill the goal of
perfect (circular) motion. His model still used small epicycles to get the details of the retrograde
loops correct, though they were only a minor feature. He used trigonometry to describe the distances
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of the planets from the Sun relative to the astronomical unit, (AU = average Earth-Sun distance), but
he did not know the numerical value of the AU. He found that the planets farther from the Sun move
slower. The different speeds of the planets around the Sun provided a very simple explanation for the
observed retrograde motion. He explained retrograde motion by projecting the position of a planet on
the background stars. Copernicus thought his model was reality but other people accepted his model
as a more convenient calculation device.
D. Tycho Brahe (lived 1546-1601 A.D.)
Brahe was not a neoplatonist. He argued that if the Earth were moving around the Sun, then
the stars should appear to shift due to our looking at them from different vantage points in our orbit
(a “parallactic shift”). Tycho calculated that if the Earth moved, then the stars are at least 700 times
farther away from Saturn than Saturn is from Sun. Since Tycho believed that God would not waste
that much space in a harmonious, elegant universe, he believed that the Earth was at the center of the
universe. (We now know that the nearest star is over 28,500 times farther away than Saturn is from
the Sun!) Tycho Brahe thus revived Heroclides’ model that had the all of the planets, except the
stationary Earth, revolving around the Sun. The Sun, Moon, and stars revolve around the Earth.
Tycho’s model was mathematically equivalent to Copernicus’ model but did not violate Scripture
and the basic understanding of common sense.
Though Tycho’s beliefs of the universe did not have that much of an effect on those who
followed him, his exquisite observations came to play a key role in determining the true motion of
the planets by Johannes Kepler. Tycho was one of the most thorough observational astronomers to
have ever lived. Without using a telescope, he was able to measure the positions of the planets to
within a few arc minutes.
Battle with the Church
A. Church’s Structure
In the 16th century the hierarchical structure of the Church’s authority was inextricably
bound with the geocentric cosmology.
1. ”Up” meant ascension to greater perfection and greater control.
2. God and heaven existed outside the celestial sphere. There was a gradation of existence and
control from perfect existence to the central imperfect Earth.
3. God delegated power to angels to control planet movements and guide various earthly events.
4. Plants and animals existed to serve humans and humans were to serve God through the
ecclesiastical hierarchy of the Church.
B. Giordano Bruno (lived 1548--1600 A.D.)
Giordano Bruno revived Democritus’ view that the Sun was one of an infinite number of
stars. This infinite sphere was consistent with the greatness of God. Bruno believed in a heliocentric
universe. Also he believed that God gives each of us an inner source of power equal to all others, so
there was no justification for domination and servitude. His model had definite political ramifications
that threatened the church’s political authority.
C. Galileo Galilei(1564-1642 A.D.):
In 1609, Galileo Galilei, points the telescope to the sky (the telescope was originally used as
a naval tool to assess the strength of the opponent’s fleet from a great distance). He finds new things:
1. New stars never seen before (makes Bruno’s argument more plausible but counteract the
Ptolemaic model where the heavens are apparently unchanging).
2. Pits and craters on the Moon and spots on the Sun which imply that the Earth is not only the
place of change and decay. Again, this violated the Ptolemaic model that states that the heavenly
bodies are perfect.
3. Four moons orbiting Jupiter. These four moons (Io, Europa, Ganymede, and Callisto) are called
the Galilean satellites in his honor. In this system Galileo saw a mini-model of the heliocentric
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system. The moons are not moving around the Earth but are centered on Jupiter. Perhaps other
objects, including the planets, do not move around the Earth.
4. Venus goes through a complete set of phases. The gibbous and full phases of Venus are
impossible in the Ptolemaic model but possible in Copernican model (and Tychonic model too!).
In the Ptolemaic model Venus was always approximately between us and the Sun and was never
found further away from the Earth than the Sun. Because of this geometry, Venus should always
be in a crescent, new, or quarter phase. The only way to arrange Venus to make a gibbous or full
phase is to have it further away from us than the Sun. This was possible only if Venus orbited the
Sun. For Galileo the clear observations of a heliocentric universe was a powerful weapon against
the hierarchical structure.
Galileo argued that the heliocentric model is not a mere instrument but is reality. His
experiments showed that. His ideas were not only derived from thought and reason alone, but used
the guidance of nature (shown from experiments). Thus, Galileo is often considered the father of
modern science because his ideas were supported by experiments and observations. He was to first to
introduce “scientific methodology”. This marked a revolutionary change in science---observational
experience became the key method for discovering nature’s rules.
The struggle between Galileo and the Church was not just a battle between science and
religion but was part of a larger battle over different conceptions of the proper routes to knowledge,
God, and world view. Galileo loved to debate and had the bad habit of ridiculing those he disagreed
with. Some of those were powerful political figures in the Church. He wrote a book detailing the
arguments for and against his model of the universe in a way that ridiculed the official view of the
Church. It was written in Italian (the language of everyday discourse) rather than the scholarly Latin
so even non-scholars were exposed to his scathing arguments against the geocentric universe. He
may have had more success in getting greater acceptance of his different views of God and research
if his style was different but perhaps his ideas needed just such a champion at that time.
Kepler’s Laws of Planetary Motion
Johannes Kepler (1571--1630 A.D.) was hired by Tycho Brahe to work out the mathematical
details of Tycho’s version of the geocentric universe. Although Kepler believed in God, he was also
an individualist and did not go along with the Roman Catholic Church or the Lutherans. He has an
ardent mystical neoplatonic faith. He wanted to work with the best observational data available
because he felt that elegant, mathematically harmonious theories must match reality. Kepler,
motivated by his faith in God, then tried to discover God’s plan in the universe or in his words “read
the mind of God.” Kepler shared the Greek view that mathematics was the language of God. He
knew that all previous models were inaccurate. Although he was hired on Tycho’s geocentric model,
Kepler did not believe in either Tycho’s model or Ptolemy’s model (he thought Ptolemy’s model was
mathematically ugly). His neoplatonic faith led him to choose Copernicus’ heliocentric model. He
discovered three laws, based on empirical findings, not on a physical theory.
Kepler’s First LawKepler refined Copernicus’ model. He claimed that God uses a different
mathematical shape than the circle. Planetary orbits are ellipses with the Sun at one focus. This idea
went against the 2,000 year old Pythagorean paradigm of the perfect shape being a circle! Kepler had
a hard time convincing his contemporaries, including Galileo.
Kepler’s Second Law: To account for the planets’ motion (particularly Mars’) among the
stars, Kepler found that the planets must move around the Sun at a variable speed. When the planet
was close to perihelion, it moved quickly; when it was close to aphelion, it moved slowly. This was
another break with the Pythagorean paradigm of uniform motion! The Sun-planet radius vector
sweeps out equal areas in equal times. [Later, scientists found that this is a consequence of the
conservation of angular momentum. The angular momentum of a planet is a measure of the amount
of orbital motion it has and does NOT change as the planet orbits the Sun. It equals the (planet mass)
x (planet speed) x (distance from the Sun). If the distance decreases, then the speed must increase to
compensate; if the distance increases, then the speed. This effect is also known by “Conservation of
Angular Momentum].
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Kepler’s Third Law: Finally, after several more years of calculations, Kepler found a simple,
elegant equation relating the distance of a planet from the Sun to how long it takes to orbit the Sun
(the planet’s orbital period). (sidereal period in years)2 = (semi-major axis of orbit in A.U.)3 or more
generally for other stars: (sidereal period)2 α (semi-major axis)3
Newton
A. Newton’s Questions
Kepler’s three law of planetary motion provided an accurate description of the orbits,
however, they did not explain why the planets move as they do. Isaac Newton (lived 1641--1727
A.D.) studied the works of Copernicus, Kepler, Galileo and Descarts. His concerns were: What keeps
the planets in their elliptical orbits? On our spinning Earth what prevents objects from flying away
when they are thrown in the air? What keeps us from being hurled off the spinning Earth?
B. René Descartes, Hooke, Kepler and Newton’s Laws
The notion of a greater God and an infinite universe with no special places leads to René
Descartes’ (lived 1596-1650 A.D.) idea of inertia: a body at rest remains at rest, and one moving in a
straight line maintains constant speed and same direction unless deflected by a “force”. This is
known as Newton’s 1st law of motion. As far as planets are concerned they do not move in straight
lines, so a force must act of them. In fact Robert Hooke (1635-1703) who analyzed the pendulum
(and the spring) and argued that this involved a centripetal force, and that the planets must also be
exposed to this centrifugal force which acts towards the center of motion. Another important property
of a body is its mass, which is a measure of the inertia of the body. The momentum of any body is
defined as the product of its mass times its velocity (p=mv) .
Newton’s first law. Rewording the above statement: Unless a force acts on an object its
momentum remains constant (both mass and velocity stay the same).
Newton’s 2nd law: F = m a. If a force does act, it causes in a change in momentum. Since the
mass of an object does not change, this means that there is a change in velocity (either by changing
the speed or the direction). And the change of velocity is the acceleration. The force needed to
accelerate any object of a given mass is: force = mass x acceleration. Newton’s 1st law is qualitative--it tells us when something will accelerate. His 2nd law quantifies the amount of change produced
from a given force---it enables us to calculate the amount of acceleration there will be.
Newton’s 3rd Law: Action Equals Reaction. Newton completes his theory of dynamics with
his third law of motion: every force ON a body by some object has an equal and opposite force
exerted BY that body. For example, if you jump out of a boat into a lake, you will push on the boat
and it will move backward. At the same time, the boat pushes you forward.
Newton’s Universal Law of GravitySo the apple fell from the tree and Gravity was
discovered… Well, it was not quite as easy. As the apple falls down the tree, it accelerates, thus a
force must be acting on it. Newton extended this argument to more distant things, namely the moon
and the planets. He wondered if this same force could make the planets go around the sun in circles
because otherwise they would move away in a straight line. So Newton performed the following
thought experiment: The falling apple experiences an acceleration where F=mg, where g is the
gravitational acceleration at the surface of the Earth. How, then, did this force change if you
considered an object as far away as the moon? Did it vary with the inverse square of the distance, i.e.,
Force ∝ (moon mass) / (d to moon)2? Since he knew the moons distance, which is ~60 times the
Earth’s radius, he concluded that the moons acceleration should by 602=3600 times smaller than the
acceleration observed for bodies close to the Earth’s surface. Since the moon goes around the earth in
circles, it must also, according to Newton’s first law, experience an acceleration. This acceleration
must be a centripetal acceleration. This acceleration can be calculated since the moon’s orbital
velocity and distance were known (a=v2/r). He found that, indeed, this acceleration was ~3600 times
less than the acceleration experienced by the apple. Thus Newton’s Universal law of Gravitation
states that: F = G x (Sun mass) x (planet mass) / (distance between them)2, where G is a constant.
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C. A Note on Newtonism
Newton’s development of the unifying law of gravity is also the culmination of a process of
Occam’s Razor in action. From Ptolemy to Newton, the theories of how the planets move got simpler
and more powerful as time went on. Ptolemy’s model had become extremely complicated by the time
of the Renaissance and Copernicus reduced the number of circular motions to around 50 so that it
was simpler. Kepler vastly simplified the theory of planet motion by reducing the number of essential
parts to just three laws. Newton unified all of those laws to the ONE unifying law of gravity. This
law was so simple and elegant that it could also explain motions on the Earth. With Newton, there
was no longer a hierarchical-teleological universe (one designed by God for some purpose with man
playing a crucial role in the plan). The universe was now a perfect machine, based on mathematics,
set in motion by God long ago. God is the reference point for absolute space and time. Reality was
now completely reduced to material objects. Ideas, thought, feelings, and values were secondary.
Newtonism undercut the role of God and religion and the validity of science: science became just a
subjective perspective of the machine universe. Descartes saw the need to rescue thoughts, ideas and
values. He developed a mind-body dualism: a world of thought and spirit exists independent of, but
parallel to, the material world. There is a correspondence between the God, mathematical thought,
and motions in the physical world. Descartes said that mathematical ideas work so well because there
is a pre-established parallelism between the physical world and the human mind. What is real does
not depend on our view---this is probably the actual completion of the Copernican revolution and is
thereafter called “common sense” (how about that for a paradigm shift!).
Closer Look at Gravity
A. Fundamental Forces of Nature
Gravity is one of four fundamental forces in nature---forces that cannot be described in terms
of any other forces and are responsible for every physical interaction in the universe. The four
fundamental forces in nature are:
1. Strong nuclear---short range (only within the atomic nucleus) and the strongest of the forces. It
holds the atomic nucleus together. It is 1042 times stronger than gravity.
2. Weak nuclear---weaker and also short range (nucleus range). It is responsible for the decay of
nuclei (radioactivity). It is 1029 times stronger than gravity.
3. Electromagnetic---electric and magnetic fields are aspects of the same thing (first shown by
James Maxwell who lived 1831-1879 A.D.). It can be attractive or repulsive, it has an infinite
range, it only works for things with charge and it is much stronger than gravity: 1040 times
stronger than gravity.
4. Gravity---weakest of all of the forces but is important for astronomy because: a. All atoms feel it
whether they are charged or not (most of the material in the universe is neutral overall, so the
electromagnetic force does not affect it); b. It is always attractive, never repulsive; c. It does not
depend on the chemical composition of the material only on the mass and distance---it is additive
(more mass means more gravity) and it has an infinite range.
B. Force Unification
Science reduces observations to the fundamental processes and unifies the observations into
an overarching theory. The goal of science is to unify seemingly disjoint facts into a coherent whole
or framework. Might the four fundamental forces be manifestations of one super force? James
Maxwell showed that electricity and magnetism are manifestations of the electromagnetic force.
Later, in the 1970s, the electromagnetic and weak nuclear forces were found to be manifestations of
the “electroweak force” (they behave in the same way at very high temperatures and energies). Other
attempts unify the strong nuclear force with others. These theories are called Grand Unification
Theories (GUT’s). We are also trying to merge gravity with the rest of the forces (super-GUT’s, a
name that indicates some scientists are watching too many Saturday morning cartoons).
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Einstein
A. Special Relativity
At the beginning of this century, Albert Einstein (lived 1879 - 1955) created a new vision of
the cosmos. This picture emerged in two stages: the Special Theory of Relativity (STR), and the
General Theory of Relativity (GTR). STR deals with the laws of physics as seen by unaccelerated
observes (for example it helps us determine length contraction and time dilation and is used to
explain things like the twin’s paradox, where one twin goes to a distant planet and comes back aged
less than his twin on earth). The GTR is a generalization of this theory and includes accelerated
observers that travel in the fabric of Space-Time. This fabric of Space-Time is altered in the presence
of masses which cause Space-Time to be curved. Light (and also any particles and objects with
masses) travels on geodesics (a geodesic is the shortest distance between two points - for example, a
plane flying from the US to Europe, flies the shortest distance which is via Greenland rather than
along a latitude of, say, 40o). Space-Time gets more curved the closer you are to a massive object.
B. The Principle of Equivalence & Gravity
This is Einstein’s famous thought experiment. He considers himself in an elevator that is at
rest and where he cannot look out. In his hand he is holding Newton’s famous apple. He opens his
hand and the apple drops due to Gravity. However if this elevator is on a spaceship that is
accelerating, the apple would again fall if he opened his hand (this is analogues to you weighing
more if the elevator accelerates up - have you ever tried jumping in an elevator?). So going back to
the spaceship, the apple falls because the spaceship accelerates, not because of Gravity. Thus
Einstein provided us with a new theory of gravity, called the General Theory of Relativity.
Generally, this theory must be applied in the proximity of massive bodies. At large distances from
masses, Newton’s Theory of Gravity is a good approximation to GTR.
C. Proofs of General Relativity
a. Solar eclipses (Eddington 1919): observed star positions close to Sun were shifted by the amount
predicted by G.R. The starlight is bent around the Sun just as Einstein said it should so it appears
to us that the stars have shifted their position compared to when the Sun is not close by.
b. Gravitational lenses: see multiple images of far away quasar lensed by a closer massive galaxy.
c. Clocks high above ground are observed to run faster than those on the ground-time dilation closer
to massive object (the Earth).
d. Gravitational redshift observed in light from white dwarfs (have very strong surface gravity).
e. Mercury’s Pelihelion: as mercury rotates around the sun, its orbit slowly rotates and traces out a
rosette figure. This is explained by GTR. For other planets this effect is minimal, because
Mercury is much closer to the Sun.
References and Acknowledgement
This write-up was compiled with the aid of Nick Strobel’s outline and text books by:
Roland Pine, John Fix, and Kaufmann. Also:
1. Owen Barfield Saving the Appearances pp. 46--54.
2. Paul K. Feyerabend Galileo and the Tyranny of Truth in The Galileo Affair: A Meeting of Faith
and Science ed. Coyne, Heller, Zycinski (Vatican City: 1985), pp. 155-166 and other papers from
that symposium held at the Vatican.
3. George S. Johnston 1995, The Galileo Affair (Scepter Press: Princeton, NJ). HTML version
version available here.
4. Thomas S. Kuhn The Copernican Revolution: Planetary Astronomy in the Development of
Western Thought (Cambridge, Mass: Harvard Univ. Press, 1957).
5. Ronald Pine: Science and the Human Prospect (Wadsworth Publ. Co: Belmont, CA, 1989) esp.
ch. 5: pp. 130-162.
6. A prelude to Copernicus is Owen Gingerich’s Scientific American article Astronomy in the Age
of Columbus Nov. 1992, pp. 100-105.
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