ORIGINS OF MODERN ASTRONOMY

ROOTS OF ASTRONOMY

 Astronomy has its origin in a noble human trait: curiosity.

 Archaeoastronomy - The study of the astronomy of ancient peoples, called archaeoastronomy (a combination of
“archaeology” and “astronomy”), yields abundant evidence that seeking to understand the heavens is part of human nature.
 Some have claimed that the Stone Age people who built Stonehenge were using it as a device to predict lunar eclipses.
 The roots of astronomy lie not in sophisticated science and mathematics but in human curiosity and awe.
 Some alignments may have served purposes related to keeping annual calendar. The 2000-year-old Temple of Isis in
Dendera, Egypt, was built to align with the rising point of the bright star Sirius. Each year, the first appearance of this star in
the dawn twilight marked the flooding of the Nile, so it was an important date indicator.
 An intriguing American site in New Mexico, known as the Sun Dagger, unfortunately has no surviving mythology to tell its
story. At noon on the day of the summer solstice, a narrow dagger of sunlight shines across the center of a spiral carved on a
cliff face high above the desert floor.
 Some archaeoastronomers study small artifacts made thousands of years ago rather than large structures. Scratches on certain
bone and stone implements follow a pattern that may record the phases of the Moon.

THE ASTRONOMY OF CLASSICAL GREECE

 Greek astronomy was derived from Babylon and Egypt, but the Greek philosophers took a new approach. Rather than relying
on religion and astrology, the Greeks proposed a rational universe whose secrets could be understood through logic and
reason.
 In most cases, they believed we inhabit a geocentric universe, with Earth at the center. You will see in this chapter that a
small number of astronomers proposed a heliocentric universe with the Sun at the center.

CLASSICAL GREEK ASTRONOMERS

 Thales of Miletus (c. 624–c. 546 bce) - taught that the Universe is rational and that the human mind can understand why the
Universe works the way it does. To Thales and his followers, the mysteries of the Universe were mysteries only because they
were unknown, not because they were unknowable.
 Pythagoras (c. 570–c. 495 bce) - he and his students noticed that many things in nature seem to be governed by geometrical
or mathematical relations.
 Philolaus (5th century bce) - hypothesized that Earth moved in a circular path around a central fire (not the Sun), which was
always hidden behind a counter-Earth located between the fire and Earth. This was the earliest known example of a
hypothesis that Earth is in motion.
 Plato (c. 424–347 bce) was not an astronomer, but his teachings influenced astronomy for 2000 years. Plato agreed with
other philosophers on a principle known as the perfection of the heavens. Consequently, later astronomers tried to describe
the motions of the heavens by imagining multiple rotating spheres. This became known as the principle of uniform circular
motion.
 Eudoxus of Cnidus (408–355 bce) - a student of Plato, applied this principle when he devised a system of 27 nested spheres
that rotated at different rates about different axes to produce a mathematical description of the motions of the Universe.
 Aristotle (384–322 bce), another of Plato’s students, made his own unique contributions to philosophy, history, politics,
ethics, poetry, drama, and other subjects. Aristotle believed that the Universe was divided into two parts: Earth, imperfect
and changeable, and the heavens, perfect and unchanging. Like most of his predecessors, he believed that Earth was the
center of the Universe, so his model is a geocentric universe.
 Aristarchus - philosopher Aristarchus proposed that Earth rotates on its axis and revolves around the Sun.
 Hipparchus - he is usually credited with the invention of trigonometry, the creation of the first star catalog, and the
discovery of precession. Hipparchus also described the motion of the Sun, Moon, and planets as following circular paths
with Earth near—but not at—their centers. These off center circles are now known as eccentrics.
 Ptolemy - was one of the great astronomer–mathematicians of antiquity. He ensured the continued acceptance of Aristotle’s
universe by transforming it into a sophisticated mathematical model.

Three important ideas and five new terms that show how first principles influenced early descriptions of the Universe and its
motions:

1. Ancient philosophers and astronomers accepted as first principles that the heavens were geocentric with Earth located at the
center and the Sun, Moon, and planets moving in uniform circular motion. It seemed clear to them that Earth was not moving
because they saw no parallax in the positions of the stars.

2. The observed motion of the planets did not fit the theory very well. The apparent retrograde motion of the planets was difficult
to explain with a model of an unmoving Earth at the center of the Universe plus uniform circular motion of celestial objects.
3. In his book that later came to be known as the Almagest, Ptolemy attempted to explain the motion of the planets by devising a
small circle, an epicycle, that rotated along the edge of a larger circle, the deferent, which enclosed a slightly off-center Earth. An
equant was a point from which the center of an epicycle appeared to move at a constant rate. That meant the speed of the planets
would vary slightly as viewed from Earth.

THE COPERNICAN REVOLUTION

Nicolaus Copernicus (1473-1543)

Copernicus and the Heliocentric Hypothesis

 Sometime before 1514, he wrote an essay proposing a heliocentric universe model in which the Sun, not Earth, is the
center of the Universe. To explain the daily and annual cycles of the sky, Copernicus proposed that Earth rotates on
its axis and revolves around the Sun.
 Although his early essay discussed every major aspect of his later work, it did not include observations and
calculations. His ideas needed supporting evidence, so Copernicus began gathering observations and making detailed
calculations to be published as a book that would demonstrate the plausibility of his revolutionary idea.

Copernicus’s Book: De Revolutionibus

 Copernicus worked on his book De Revolutionibus Orbium Coelestium (On the Revolutions of the Celestial Spheres)
over a period of many years and was essentially finished by about 1529.
 The most important idea in the book was placing the Sun at the center of the Universe.
Reasons why he hesitated publishing his book:
1. He knew the idea of a heliocentric universe would be highly controversial. This was a time of rebellion in the Church.
2. It was incomplete. His model could not accurately predict planetary positions, so he continued to refine it. Finally in
1540 he allowed the visiting astronomer Joachim Rheticus to publish an account of the Copernican universe in
Rheticus’s book, Narratio Prima (First Narrative). In late 1542, Copernicus sent the manuscript of De Revolutionibus off
to be printed. He died in the spring of 1543 before the printing was completed.

COPERNICUS AND THE HELIOCENTRIC HYPOTHESIS

 PTOLEMAIC MODEL
a detailed version of Aristotle universe. The central location of around the earth was widely accepted, and everyone knew
that the heavens moved in uniform circular motion.

Tycho, Kepler, and Planetary Motion

THYCO BRAHE
• Found that the old Alfonsine Tables, based on the Ptolemaic model, were a full month in error in their prediction of that
event, and the new Prutenic Tables, based on the Copernican, model were in error by several days.
• In 1572, a “new star” (now called Tycho’s supernova) appeared in the sky, shining more brightly than Venus
THYCO’S LEGACY
• Tycho made no direct contribution to astronomical theory. Because he could measure no parallax for the
stars, he concluded that Earth had to be stationary, thus rejecting the Copernican hypothesis.
• He rejected the Ptolemaic model because of its inaccuracy.
• He devised a complex model in which Earth was the unmoving center of the Universe around which the Sun
and the Moon moved while the other planets circled the Sun (Figure 4-11).
• The model thus incorporated part of the Copernican model, but Tycho preserved the central immobile
Earth.
• Tycho did not intend to base the Rudolphine Tables on the Ptolemaic system but rather on his own Tychonic
system, proving once and for all the validity of his hypothesis. To assist him, he hired a few mathematicians and
astronomers, including one Johannes Kepler. Then, in November 1601, Tycho collapsed while visiting a
nobleman’s home in Prague. Before he died 11 days later, he asked Rudolph II to make Kepler imperial
mathematician. The newcomer, not a nobleman at all but a commoner, became Tycho’s replacement (at one-
sixth Tycho’s salary).
JOHANNES KEPLER
• Tycho’s sudden death in 1601 left Kepler, the new imperial mathematician, in a position to use Tycho’s data to
analyze the motions of the planets and complete the Rudolphine Tables.
• He began by studying the motion of Mars, trying to deduce from the observations how the planet moved. By
1606, he had solved the mystery. The orbit of Mars is not a circle but an ellipse. With that, Kepler gave up the
2000-year-old belief in the circular motion of the planets. But even this insight was not enough to explain the
observations. In fact, the planets do not move at uniform speeds along their elliptical orbits.
• Kepler’s analysis showed that they move faster when close to the Sun and slower when farther away. With those
two brilliant discoveries, Kepler abandoned both uniform motion and circular motion, and thereby finally solved
the puzzle of planetary motion. He published his results in 1609 in a book called Astronomia Nova (New
Astronomy).

Kepler’s 3 laws of planetary motion

1. The orbits of the planet’s are ellipses with the Sun at one focus
 2. A line from the planet to the Sun sweeps over equal areas in equal intervals of time
3. A planet’s orbital period squared is proportional to its average distance from the Sun cubed:

1. The orbits of the planet’s are ellipses with the Sun at one focus.
Thanks to the precision of Tycho’s observations and the sophistication of Kepler’s mathematics, Kepler was able to
recognize the elliptical shape of the orbits even though they are nearly circular. Mercury has the most elliptical orbit, but even it
deviates only slightly from a circle.

2. A line from the planet to the Sun sweeps over equal areas in equal intervals of time.
This means that when the planet is closer to the Sun and the line connecting it to the Sun is shorter, the planet must move
more rapidly so that the line sweeps over the same area per time interval that it sweeps over when the planet is farther from the
Sun.
3. A planet’s orbital period squared is proportional to its average distance from the Sun cubed:
Kepler’s third law relates a planet’s orbital period to its average distance from the Sun. The orbital period, P, is the time a
planet takes to travel around the Sun once. The average distance of a planet from the Sun around its elliptical path turns out simply
to equal the semimajor axis of its orbit, a. Kepler’s third law says that a planet’s orbital period squared is proportional to the
semimajor axis of its orbit cubed (Figure 4-13c). Measuring P in years and a in astronomical units, you can summarize the third
law as:

Kepler’s Final Book: The Rudolphin Tables

• Kepler continued his mathematical work on the Rudolphine Tables, and at last, in 1627, it was ready. He
financed the printing himself, dedicating the book to the memory of Tycho Brahe.
• The Rudolphine Tables was Kepler’s masterpiece. The tables could predict the positions of the planets 10 to 100
times more accurately than previous tables. Kepler’s tables were the precise model of planetary motion that
Copernicus had sought but failed to find because he could not give up the idea of perfectly circular motions. The
accuracy of the Rudolphine Tables was strong evidence that both Kepler’s laws of planetary motion and the
Copernican hypothesis for the place of Earth were correct.
• Copernicus would have been pleased. Kepler died in 1630. He had solved the problem of planetary motion, and
his Rudolphine Tables demonstrated his solution. Although he did not understand why the planets moved or
why they followed ellipses—insights that had to wait half a century for Isaac Newton—Kepler’s three laws
worked. In science the only test of a hypothesis is, “Does it describe reality?” (In other words, does it match
what is observed?) Kepler’s laws have been used for almost four centuries as a true description of orbital
motion.

Galileo’s conclusive evidence

Who is galileo?
• born in Pisa (Italy)
• the Great Defender of Copernicanism
• Two of Galleo's telescopes, on display in a museum in Florence.
• Studied Medicine, but his true love is mathematics.
• He became Professor of mathemarics at the University in Padua for 18 years.
• Adopted the Copernican model but not supported it publicly.

Telescope observations
 Moon- Moon is imperfect. It had mountains and valleys on its surface, and Galileo even used some of the mountains
shadows to calculate their height. (Earth’s like feature.)
 Milky Way- Made up of myriad stars too faint to see with the unaided eye.
 GALILEAN MOONS- Four new "planets" circling Jupiter, objects known today as the Galilean moons of Jupiter. This
used as a strong evidence for the Copernican model.

Discovery of galilean moons

 On the night of January 7, 1610, Galileo saw three small "stars" near the bright disk of Jupiter.
 January 9 was cloudy
 On subsequent nights he saw that the stars were actually four moons orbiting Jupiter.

Additional two discoveries:

 SUNSPOT -He suspected that the Sun, like the Moon, is imperfect.
-He concluded that the Sun is a sphere and that it rotates on its axis.
 VENUS- -In contrast to Ptolemaic model, Galileo said that Venus revolve all the way around the Sun

DIALOGO AND TRIAL

 1610- Sidereus Nuncius is published.
 1611- Galileo visits Rome and engages in friendly discussions with Cardinal Barberini.
  1616- Galileo becomes the center of controversy. Books related to Copernicanism are banned in Catholic lands.
 1621- Pope Paul V, who enforced the 1616 prohibition, passes away.
 1623- Cardinal Barberini becomes Pope Urban VIII. Galileo hopes for the lifting of the 1616 prohibition.
 1629- Galileo works on his Dialogue Concerning the Two Chief World Systems from his home outside Florence.
 1632- The "Dialogo" is published, comparing the Aristotelian/Ptolemaic model with the Copernican model. It becomes
controversial.
 1633- Galileo is summoned by the Inquisition.The trial focuses on his disobedience to the 1616 orders rather than his
belief in Copernicanism.
 1633-1642 --Galileo is sentenced to life imprisonment but is confined to his villa, possibly due to the intervention of the
pope. He dies on January 8, 1642.
 1979-1992--Pope John Paul II appoints a commission to reexamine Galileo's case. In October 1992, the commission
concludes that Galileo's inquisitors made a subjective error in judgment.

99 YEARS: Transition from Ancient to Modern Astronomy

 From De Revolutionibus (1543) to Galileo's Legacy (1642)

Evolution in the methods of science:

1. PARADIGM SHIFT- from Ptolemaic model to Copernican Mode

2. Hypothesis- Heliocentric Hypothesis Impact
3. Theory- The Evolution of Heliocentric Theory
4. Scientific Law- Kepler's Laws - Precision in Motion

Orbital motion and tides

ORBIT - The curved path of one celestial object or spacecraft around another celestial object.
ORBIT VELOCITY - The speed and direction of motion of a moving body.
Orbital VELOCITY It is the velocity at which a body revolves around the other body.

THREE KEY CONCEPTS:

1. An object orbiting Earth is actually “FALLING” (being accelerated) toward Earth's center. The object continuously misses
colliding with Earth because of its lateral ("sideways") orbital velocity. To follow a circular orbit, the object must move at circular
velocity (V). Placed in a circular orbit at the right distance from Earth, it could be an especially useful geosynchronous satellite.
2. Notice that it is more accurate to say that objects orbiting each other are actually revolving around their mutual center of
mass.
3. Finally, notice the difference between closed orbits and open orbits. If you want to leave Earth forever, you need to accelerate
your spaceship at least until it is moving at escape velocity (V), so it will follow an open orbit and never return.

ORBITAL VELOCITY
• M : mass of the central body (Earth in this case) (kg)
• r : radius of the orbit in (meters)
• G: gravitational constant = 6.67 × 10-11 m³/s²/kg.

TIDES AND TIDAL FORCES

TIDES are the rise and fall of sea levels cased by combined effects of the gravitational forces exerted by the moon and are also
caused by earth and moon orbiting one another. Tides are caused by small differences in gravitational forces.

Tidal changes:
At those moon phases, high tides are exceptionally high, and low tides are exceptionally low. Such tides are called spring tides.
Here the word spring does not refer to the season of the year but to the rising up of water. Galileo tried to understand tides, but
it was not until Newton described gravity that astronomers could analyze tidal forces and recognize their surprising effects. For
example, the moving water in tidal bulges experiences friction with the ocean beds and resistance as it rises onto continents.

TIDAL FORCES
Tidal forces can also affect orbital motion. Earth rotates eastward, and friction with the ocean beds drags the tidal
bulges slightly eastward out of a direct EarthMoon line. These tidal bulges are massive, and their gravitational field pulls the
Moon forward in its orbit, as shown in Figure 5-7c. As a result, the Moon's orbit is growing larger by about 3.8 cm a year, an
effect that astronomers can measure by bouncing laser beams off reflectors left on the lunar surface by the Apollo astronauts.
Earth's gravitation exerts tidal forces on the Moon, and, although there are no bodies of water on the Moon, friction
within the flexing rock has slowed the Moon's rotation to the point that it now keeps the same face toward Earth.
Tides are much more than just the cause of oceans rising and falling in daily and monthly rhythms. In later chapters,
you will see how tides can pull gas away from stars to feed black holes, rip galaxies apart, and melt the interiors of small moons
orbiting massive planets. Tidal forces produce some of the most surprising and impressive processes in the Universe.
Astronomy after newton
ISAAC NEWTON
Newton published his work in 1687 in a book titled, in Latin, Philosophiae Naturalis Principia Mathematica (Mathematical
Principles of Natural Philosophy)

PRINCIPIA
After the Principia was published, physicists and astronomers understood that the motions of celestial bodies are governed by
simple, universal rules that describe the motions of everything from orbiting planets to falling apples. Suddenly the Universe was
understandable in simple terms, and astronomers could accurately predict future planetary motions
• The Principia changed astronomy by ushering in a new age.
• The Principia also changed science in general.
• Principia changed the way people thought about nature.
• Newton's work broke the last bonds between science and formal philosophy.

Newton's laws were foundations of astronomy and physics for two centuries. Then, early in the 20th century, a physicist named
Albert Einstein proposed a new way to describe gravity. The new theory did not replace Newton's laws but rather showed that
they were only approximately correct and could be seriously in error under certain special circum- stances. Einstein's theories
further extended the scientific understanding of the nature of gravity. Just as Newton stood on the shoulders of Galileo, Einstein
stood on the shoulders of Newton.

Einstein and Relativity

ALBERT EINSTEIN
Einstein has become a symbol of the brilliant scientist. His fame began when he was a young man and thought deeply
about the nature of motion. That led him to revolutionary insights into the meaning of space and time and a new understanding
of gravity.

SPECIAL RELATIVITY
First postulate (the principle of relativity): Observers can never detect their uniform motion except relative to other objects.
First postulate (more sophisticated version): The laws of physics are the same for all observers, no matter what their motion, so
long as they are not accelerated.
Second postulate: The speed of light in a vacuum is constant and will have the same value for all observers independent of their
motion relative to the light source.

GENERAL THEORY RELATIVITY

In 1916, Einstein published a more general version of the theory of relativity that dealt with accelerated as well
as uniform motion. This general theory of relativity contained a new description of gravity.
Equivalence principle: Observers cannot distinguish locally between inertial forces due to acceleration versus
uniform gravitational forces due to the presence of a massive body.

The importance of the general theory of relativity lies in its description of gravity. Einstein concluded that gravity,
inertia, and acceleration are all associated with the way space and time are connected as a single entity referred to as space-
time. This relation is often referred to as curvature, and a one-line description of general relativity is that it explains a
gravitational field as a curved region of space-time:
Gravity according to general relativity: Mass tells space-time how to curve, and the curvature of spacetime (gravity)
tells mass how to accelerate.
Therefore, you feel gravity because Earth’s mass causes a
curvature of space-time. The mass of your body responds to that curvature by accelerating toward Earth’s center, and that
presses you downward in your chair. According to general relativity, all masses cause curvature of the space around them, and
the larger the mass, the more severe the curvature. That’s gravity