Transcript The Roots of Astronomy

The History of Astronomy
When did mankind first become
interested in the science of astronomy?
1. With the advent of modern computer
technology (mid-20th century)
2. With the development of the theory of relativity
(early 20th century)
3. With the invention of the telescope (~ A.D.
1600)
4. During the times of the ancient greeks (~ 400 –
300 B.C.)
5. In the stone and bronze ages (several
thousand years B.C.)
The Roots of Astronomy
• Already in the stone and bronze ages,
human cultures realized the cyclic nature
of motions in the sky.
• Monuments dating back to ~ 3000 B.C.
show alignments with astronomical
significance.
• Those monuments were probably used as
calendars or even to predict eclipses.
Stonehenge
Stonehenge
• Constructed 3000 – 1800
B.C. in Great Britain
• Alignments with locations of
sunset, sunrise, moonset and
moonrise at summer and
winter solstices
• Probably used as calendar.
Why is it so difficult to find out about
the state of astronomical knowledge of
bronze-age civilizations?
1.
2.
3.
4.
5.
Written documents from that time are in languages that
we don’t understand.
There are no written documents documents from that
time.
Different written documents about their astronomical
knowledge often contradict each other.
Due to the Earth’s precession, they had a completely
different view of the sky than we have today.
They didn’t have any astronomical knowledge at all.
Ancient Greek Astronomers
•
Models were based on unproven “first principles”,
believed to be “obvious” and were not questioned:
1. Geocentric “Universe”: The Earth is
at the Center of the “Universe”.
2. “Perfect Heavens”: The motions of all
celestial bodies can be described by
motions involving objects of “perfect”
shape, i.e., spheres or circles.
• Ptolemy: Geocentric model, including epicycles
Central guiding principles:
1. Imperfect, changeable Earth,
2. Perfect Heavens (described by spheres)
What were the epicycles in Ptolemy’s
model supposed to explain?
1.
2.
3.
4.
5.
The fact that planets are moving against the
background of the stars.
The fact that the sun is moving against the background
of the stars.
The fact that planets are moving eastward for a short
amount of time, while they are usually moving
westward.
The fact that planets are moving westward for a short
amount of time, while they are usually moving
eastward.
The fact that planets seem to remain stationary for
substantial amounts of time.
Epicycles
Introduced to explain retrograde
(westward) motion of planets
The ptolemaic system was considered
the “standard model” of the Universe
until the Copernican Revolution.
At the time of Ptolemy, the introduction
of epicycles was considered a very
elegant idea because …
1.
2.
3.
4.
5.
it explained the motion of the planets to the accuracy
observable at the time.
it was consistent with the prevailing geocentric world
view.
it explained the apparently irregular motion of the
planets in the sky with “perfect” circles.
because it did not openly contradict the teaching of the
previous authorities.
All of the above.
The Copernican Revolution
Nicolaus Copernicus (1473 – 1543):
Heliocentric Universe (Sun in the Center)
New (and correct) explanation for
retrograde motion of the planets:
Retrograde
(westward)
motion of a
planet occurs
when the Earth
passes the
planet.
This made
Ptolemy’s
epicycles
unnecessary.
Described in Copernicus’ famous book “De Revolutionibus
Orbium Coelestium” (“About the revolutions of celestial objects”)
Galileo Galilei
(1564 – 1642)
Invented the modern view of
science: Transition from a
faith-based “science” to an
observation-based science.
Was the first to meticulously report
telescope observations of the sky to support
the Copernican Model of the Universe.
Major discoveries of Galileo:
• Moons of Jupiter
(4 Galilean moons)
(What he really saw)
• Rings of Saturn
What he really saw: Two little
“moons” on both sides of Saturn!
Knowing about the nature of Saturn’s rings,
which problem would you anticipate for Galileo
concerning his observations of Saturn?
1.
2.
3.
4.
Nobody would believe it because
everybody knew that Saturn has much
more than just 2 moons.
Nobody would believe it because such a
configuration is physically unstable.
The two little “moons” might seem to
disappear when the rings are viewed edgeon.
All of the above.
Major discoveries of Galileo (II):
• Surface structures on the moon;
first estimates of the height of mountains
on the moon
Major discoveries of Galileo (III):
• Sun spots (proving that the sun is not perfect!)
Which “phases” of Venus would you
expect to see in the Ptolomaic model?
1. All phases, just like the moon: full,
crescent, gibbous, and new.
2. Only full and gibbous.
3. Only new and crescent.
4. Only new and full.
5. Only crescent and gibbous.
Major discoveries of Galileo (IV):
• Phases of Venus,
proving that Venus orbits the sun,
not the Earth!
In the Copernikan “Universe”, the
orbits of planets and moons were …
1.
2.
3.
4.
5.
Perfect Circles
Ellipses
Spirals
Epicycles
None of the above.
Johannes Kepler (1571 – 1630)
• Used the precise observational
tables of Tycho Brahe (1546 –
1601) 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.
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
e = 0  perfect circle
e = 1  straight line
Guess: Which of these Ellipses describes
best Earth’s Orbit around the Sun?
1)
2)
e = 0.02
3)
e = 0.1
e = 0.2
5)
4)
e = 0.4
e = 0.6
Eccentricities of planetary orbits
Orbits of planets are virtually indistinguishable
from circles:
Most extreme example:
Earth: e = 0.0167
Pluto: e = 0.248
Slow
Fast
2. A line from a planet to the sun sweeps over
equal areas in equal intervals of time.
Are all four seasons equally long?
1. Yes.
2. No, summer is the longest; winter is the
shortest.
3. No, fall is the longest; spring is the shortest.
4. No, winter is the longest; summer is the
shortest.
5. No, spring is the longest; fall is the shortest.
Why is the summer longer
than winter?
1.
2.
3.
4.
5.
Because of the precession of the Earth’s axis of
rotation.
Because of the moon’s 5o inclination with respect to
the Ecliptic.
Because the Earth is rotating around its axis more
slowly in the summer (→ longer days!).
Because the Earth is closest to the sun in January and
most distant from the sun in July.
Because the Earth is closest to the sun in July and
most distant from the sun in January.
Autumnal Equinox (beg. of fall)
July
Winter solstice
(beg. of winter)
Fall
Summer
Winter
Spring
Summer
solstice
(beg. of
summer)
January
Vernal equinox
(beg. of spring)
Kepler’s Third Law
3. A planet’s orbital period (P) squared is
proportional to its average distance from the
sun (a) cubed:
Py2 = aAU3
(Py = period in years; aAU = distance in AU)
Orbital period P known → Calculate average distance to the sun, a:
aAU = Py2/3
Average distance to the sun, a, known → Calculate orbital period P.
Py = aAU3/2
It takes 29.46 years for Saturn to orbit
once around the sun. What is its
average distance from the sun?
1.
2.
3.
4.
5.
9.54 AU
19.64 AU
29.46 AU
44.31 AU
160.55 AU
Think critically about Kepler’s Laws:
Would you categorize his achievements
as physics or mathematics?
1. Mathematics
2. Physics
Isaac Newton (1643 - 1727)
• 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
Newton’s Laws of Motion (I)
1. A body continues at
rest or in uniform
motion in a straight
line unless acted
upon by some net
force.
An astronaut floating in
space will float forever in
a straight line unless
some external force is
accelerating him/her.
Velocity and Acceleration
Acceleration (a) is the change of a
body’s velocity (v) with time (t):
a
a = Dv/Dt
Velocity and acceleration are directed
quantities (vectors)!
v
Which of the following involve(s)
a (non-zero) acceleration?
1.
2.
3.
4.
5.
Increasing the speed of an object.
Braking.
Uniform motion on a circular path.
All of the above.
None of the above
Velocity and Acceleration
Acceleration (a) is the change of a
body’s velocity (v) with time (t):
a
a = Dv/Dt
Velocity and acceleration are directed
quantities (vectors)!
v
Different cases of acceleration:
1. Acceleration in the conventional
sense (i.e. increasing speed)
2. Deceleration (i.e. decreasing speed)
3. Change of the direction of motion
(e.g., in circular motion)
A ball attached to a string is in a
circular motion as shown. Which path
will the ball follow if the string breaks at
the marked point?
1)
2)
3)
4)
5) Impossible to
tell from the given
information.
Newton’s Laws of Motion (II)
2. The acceleration a
of a body is
inversely
proportional to its
mass m, directly
proportional to the
net force F, and in
the same direction
as the net force.
a = F/m  F = m a
Newton’s Laws of Motion (III)
3. To every action,
there is an equal
and opposite
reaction.
The same force that is
accelerating the boy
forward, is accelerating
the skateboard backward.
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:
F=-G
Mm
r2
(G is the Universal constant of gravity.)
According to Newton’s universal law of
gravity, the sun is attracting the Earth
with a force of 3.6*1022 N. What is the
gravitational force that the Earth exerts
on the sun?
1.
2.
3.
4.
5.
0
1.75*1018 N
3.6*1022 N
1.95*1029 N.
Depends on the relative speed of the
Earth with respect to the sun.
Einstein and Relativity
Einstein (1879 – 1955): 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 (GR)
Two postulates leading to
Special Relativity (I)
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.
A physicist on a train that moves at 50 mph
throws a ball straight up in the air. Where will
the ball land? (Neglect air resistance.)
4.
1. Far ahead of the train.
2. It will come back to the
same point on the train.
3. It will stay behind.
4. It will never fall back down.
1.
2.
3.
Two postulates leading to
Special Relativity (II)
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.
Effects of Special Relativity
• Time dilation: Fast moving objects
experience less time.
Effects of Special Relativity
• Time dilation: Fast moving objects
experience less time.
• Length contraction: Fast moving objects
appear shortened.
How would the Smiley appear to you if
he/she moved straight towards you with
50 % of the speed of light?
1. His face would appear stretched
vertically
2. His face would appear stretched
horizontally
3. His face would appear bigger overall.
4. His face would appear smaller overall.
5. His face would appear at the same size
and shape it would have if he were not
moving.
Effects of Special Relativity
• Time dilation: Fast moving objects
experience less time.
• Length contraction: Fast moving objects
appear shortened.
• The energy of a body at rest is not 0.
Instead, we find E0 = m c2
• Relativistic aberration: Distortion of angles
n’
Effects of Special Relativity
• Time dilation: Fast moving objects
experience less time.
• Length contraction: Fast moving objects
appear shortened.
• The energy of a body at rest is not 0.
Instead, we find
E0 = m c2
• Relativistic aberration: Distortion of angles
• Relativistic Doppler shift: Change
of wavelength (color) of light.
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.”
A thought experiment:
Imagine a light source on board a
rapidly accelerated space ship:
Time
Light
source
Time
a
a
a
a
g
As seen by a
“stationary” observer
As seen by an observer
on board the space ship
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!
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!
General Relativity Effects
Spatial distortion of light → gravitational lensing
What is the shape of the orbits of the
planets around the sun?
1.
2.
3.
4.
Perfect circles
Ellipses with the sun in the center
Ellipses with the sun in one focus
Ellipses with the sun being a point on the
ellipse.
5. Epicycles (circles whose centers revolve
around a perfect circle around the sun)
The Orbits of Planets
Ellipses with the Sun in one focus
Perihelion Precession