2. Ancient Greek Astronomers
• Ancient Greece (800 BC – 600 AD)
• First preserved written documents
about ancient astronomy are from
ancient Greek philosophy.
• Greeks tried to understand the motions
of the sky and describe them in terms
of mathematical (not physical!) models.
3. Ancient Greek Astronomers
Models were generally wrong because
they were based on wrong “first
principles”, believed to be “obvious” and
not questioned:
1. Geocentric Universe: Earth at the
Center of the Universe.
2. “Perfect Heavens”: Motions of all
celestial bodies described by motions
involving objects of “perfect” shape, i.e.,
spheres or circles.
4. Ancient Greek Astronomers
• Eudoxus (409 – 356 B.C.):
Model of 27 nested spheres
• Aristotle (384 – 322 B.C.),
major authority of philosophy
until the late middle ages:
Universe can be divided in 2
parts:
1. Imperfect, changeable Earth,
2. Perfect Heavens (described
by spheres)
• He expanded Eudoxus’ Model to use 55 spheres.
5. Later refinements (2nd century B.C.)
• Hipparchus: Placing the Earth away from the centers of the
“perfect spheres”
• Ptolemy: Further refinements, including epicycles
6. Epicycles
Introduced to explain
retrograde (westward)
motion of planets
The Ptolemaic system was considered
the “standard model” of the Universe
until the Copernican Revolution.
7. The Copernican Revolution
Nicolaus Copernicus (1473 – 1543):
Heliocentric Universe (Sun in the Center)
8. Copernicus’ New (and Correct) Explanation
for the Retrograde Motion of the Planets
Retrograde
(westward)
motion of a
planet occurs
when the
Earth passes
the planet.
This made Ptolemy’s epicycles unnecessary.
9. Galileo Galilei (1594 – 1642)
• Invented the modern view of science:
Transition from a faith-based “science” to
an observation-based science.
• Greatly improved on the newly invented
telescope technology. (But Galileo did
NOT invent the telescope!)
• Was the first to meticulously report
telescope observations of the sky to
support the Copernican Model of the
Universe.
10. Major Discoveries of Galileo
• Moons of Jupiter (4 Galilean moons)
• Rings of Saturn
(What he really saw)
11. Major Discoveries of Galileo
• Surface structures on the moon; first estimates
of the height of mountains on the moon
13. Major Discoveries of Galileo
• Phases of Venus (including “full Venus”),
proving that Venus orbits the sun, not the Earth!
14. Tycho Brahe’s (1546-1601) Legacy
New World model
• Still geocentric (Earth in the center of
sphere of the stars)
• Sun and Moon orbit Earth;
Planets orbit the sun.
15. Johannes Kepler (1571 – 1630)
• Used the precise observational tables of
Tycho Brahe to study planetary motion
mathematically.
• Found a consistent description by
abandoning both
1. Circular motion and
2. Uniform motion.
• Planets move around the sun on elliptical
paths, with non-uniform velocities.
16. Kepler’s Laws of Planetary Motion
1. The orbits of the planets are ellipses with the
sun at one focus.
c
Eccentricity e = c/a
18. Eccentricities of Planetary Orbits
Orbits of planets are virtually
indistinguishable from circles:
Most extreme example:
Earth: e = 0.0167 Pluto: e = 0.248
19. Planetary Orbits
2. A line from a planet to the sun sweeps
over equal areas in equal intervals of time.
20. Planetary Orbits
3. A planet’s orbital period (P) squared is
proportional to its average distance from the
sun (a) cubed:
(Py = period in years;
Py2 = aAU3 aAU = distance in AU)
21. Medial Conclusion
• Greek Astronomers believed in a
heliocentric model with the Earth in
the center of many crystalline
spheres.
• Copernicus proposed a heliocentric
model.
• Galileo’s telescope helped confirm the
heliocentric model
• The works of Tycho Brahe and
Johannes Kepler helped confirm the
heliocentric model.
23. A New Era of Science
Mathematics as a tool for
understanding physics
24. Isaac Newton (1642 - 1727)
• Building on the results of Galileo and Kepler
• Adding physics interpretations to the
mathematical descriptions of astronomy by
Copernicus, Galileo and Kepler
Major achievements:
1. Invented Calculus as a necessary tool to solve
mathematical problems related to motion
2. Discovered the three laws of motion
3. Discovered the universal law of mutual gravitation
26. Isaac Newton (1642 - 1727)
• The falling apple…
• Newton was inspired by a falling apple to
think about the invisible force that pulled
it down.
• Kepler showed that planets had elliptical
orbits, and
• Galileo shoed that things accelerate at an
even pace as they fall to the ground.
• Was the invisible force that pulled the
apple to the ground the same force that
held the planets in orbit?
27. The Universal Law of Gravity
• Any two bodies are attracting each
other through gravitation, with a force
proportional to the product of their
masses and inversely proportional to
the square of their distance:
Mm
F=-G
r2
(G is the Universal constant of gravity.)
28. The variables involved in gravitational attraction.
The force of attraction (F) is proportional to the
product of the masses (m1, m2) and inversely
proportional to the square of the distance (d)
between the centers of the two masses.
29. Understanding Orbital Motion
The universal law of gravity allows us to
understand orbital motion of planets and
moons: Example:
• Earth and moon attract each other through gravitation.
• Since Earth is much more v
massive than the moon, the moon’s
effect on Earth is small. v v’
• Earth’s gravitational force
constantly accelerates the moon Moon
towards Earth. F
• This acceleration is constantly
changing the moon’s direction of Earth
motion, holding it on its almost
circular orbit.
30. Orbital Motion
In order to stay on a
closed orbit, an object
has to be within a
certain range of
velocities:
Too slow => Object falls
back down to Earth
Too fast => Object escapes
Earth’s gravity
31. Kepler’s Third Law
Explained by Newton
Balancing the force (called
“centripetal force”) necessary to
keep an object in circular motion
with the gravitational force
expression equivalent to
Kepler’s third law,
Py2 = aAU3
32. Einstein and Relativity
Einstein (1879 – 1955) noticed
that Newton’s laws of motion are
only correct in the limit of low
velocities, much less than the
speed of light.
Theory of Special Relativity
Also, revised understanding
of gravity
Theory of General Relativity
33. Two Postulates Leading to Special
Relativity
1. Observers can
never detect their
uniform motion,
except relative to
other objects.
This is equivalent to:
The laws of physics are the same for all
observers, no matter what their motion, as
long as they are not accelerated.
34. Two Postulates Leading to Special
Relativity
2. The velocity of
light, c, is
constant and
will be the
same for all
observers,
independent of
their motion
relative to the
light source.
35. Basics of Special Relativity
The two postulates of special relativity
have some amazing consequences.
Consider thought experiment:
Motion of Assume a light source moving with velocity v
“stationary” relative to a “stationary” observer:
observer
v’ v v
c t’ c t
Light c t’
source
v t
Seen by an observer
moving along with the light Seen by the
source “stationary” observer
36. Basics of Special Relativity (2)
Now, recall that the speed of light, c,
is the same for all observers.
The times t and t’ must be different!
Then, the Pythagorean Theorem gives:
(c t)2 = (c t’)2 + (v t)2
or
t’ = ( t)/ c t’ c t
where = 1/(1 – [v/c]2)1/2
v t
is the Lorentz factor.
This effect is called time dilation.
37. Other Effects of Special Relativity
• Length contraction: Length
scales on a rapidly moving
object appear shortened.
• Relativistic aberration:
Distortion of angles
• The energy of a body
at rest is not 0.
Instead, we find
E0 = m c2
38. General Relativity
A new description of gravity
Postulate:
Equivalence Principle:
“Observers can not
distinguish locally
between inertial forces
due to acceleration and
uniform gravitational
forces due to the
presence of massive
bodies.”
39. Another Thought Experiment
Imagine a light source on board a rapidly
accelerated space ship:
Time Time
a
Light
source
a a a
g
As seen by a As seen by an observer
“stationary” observer on board the space ship
40. Thought Experiment (2)
For the accelerated observer, the light
ray appears to bend downward!
Now, we can’t distinguish between
this inertial effect and the effect of
gravitational forces
Thus, a gravitational force
equivalent to the inertial force
must also be able to bend light!
41. Thought Experiment (Conclusion)
This bending of light by the gravitation of massive
bodies has indeed been observed:
During total solar
eclipses:
The positions of
stars apparently
close to the sun
are shifted away
from the position
of the sun.
New description of gravity as
curvature of space-time!
42. Another manifestation of bending of light:
Gravitational lenses
A massive galaxy cluster is bending and
focusing the light from a background object.
43. Other Effects of General Relativity
• Perihelion advance
(in particular, of
Mercury)
• Gravitational red shift: Light from sources near
massive bodies seems shifted towards longer
wavelengths (red).
