Transcript The History of Astronomy (Professor Powerpoint)

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History of
Astronomy
Eratosthenes ( 276 –194 B.C.) measured
circumference of the Earth
Eratosthenes read of a
well in Syene, Egypt which
at noon on June 21 would
reflect the sun overhead.
A year later, Eratosthenes
in Alexandria observed the
shadow of a stick and
measured the angle to be
7.2 deg,
The distance between
Alexandria and Syene is
about 740 kilometers
X/740 = 360/7.2
X=38,057 km or 22,940 mi
The distance to Mercury & Venus
A
A
90 deg
B
aa
B
When the planet Venus or Mercury are at greatest elongation,
measure the angle between the Sun and the planet at Sunset. The
distance of Earth to Sun is 1 A.U.
Simple Trig: Sin (a)= A/B or A = (B) Sin(a)
Using this method Mercury and Venus were .4 and .7 A.U. from the
Sun respectively.
Claudius Ptolemy ~ 200 A.D.
Born in Alexandria, Egypt.
His model of the Solar system
strived to explain the motion of the
planets.
He presumed that the Earth was at the
center of the Universe (geocentric) a
theory that had been proposed by
Aristotle.
Geocentric
Theory
The planets &
Sun revolve
around the Earth.
The circles are
epicycles, where
the planets appear
to go into a loop
and then continue
onward.
He explained the motion of the planets
this way!
Copernicus proposed
the heliocentric
model, with circular
orbits, and uniform
motion.
The model was less
accurate for
predicting positions,
but more “physically
realistic”
Copernicus:
1473 –1543
He also had a
simple explanation
for retrograde
motion, the planet
moved backwards
for a short period
of time.
Galileo Galilei
1564-1642
•Galileo was among the first to turn a
telescope to the sky.
•He developed the Scientific Method,
and the Law of Inertia.
• Galileo’s earlier work:
– 1590 Masses fall at same rate, heavier
do not fall faster (unless affected by air
resistance). First to experiment
– 1604 He observed a supernova
• Telescopes:
– 1609 He hears of the invention of a
telescope, which uses eyeglass lenses.
– Works out details of better lenses and ,
builds improved ones himself.
Telescope Discoveries
The Moons of Jupiter
Clear example
of four objects
that do not
orbit the Earth.
Telescope
Discoveries
On the Moon he saw
mountains, valleys
and (Earthlike)
features .
Sunspots
He showed they were
really on the Sun.
 But the Sun was made
in the image of God!
Galileo’s Venus Observations
• Detects the phases of Venus
– Phases show that Venus must orbit the
Sun.
From our text: Horizons, by Seeds
Tycho Brahe (1546-1601)
He was of Danish nobility.
Lost his nose in duel (so he
had a metal one made).
He built very accurate instruments
for measuring sky positions.
He hired Kepler to try to understand
the motion of Mars and shortly
thereafter he died.
Johannes Kepler
(1571-1630)
He was born sickly and poor
and, went to work with Tycho
to escape 30 Years War.
Kepler proposed a geometrical
heliocentric model with
imbedded polygons ,but had
to gave up (clever, but not
better).
• He finally determined, that the planets
moved along elliptical paths, with the
sun at one of the foci of the ellipse.
Since the planets’ orbits are close to circular,
nothing is located at the other focus.
Properties of Ellipses
• An ellipse is defined by two constants :
• (1) eccentricity
e
0=circle, 1 = line
e=0
e=0.98
Same focus, at
the sun
Properties of Ellipses
(2)
semi-major axis = a
1/2 length of major axis
b
a
a = Semi-major axis
b = Semi-minor axis ( we will not use)
Planet
Kepler’s Three Laws
•Law I
Sun
–Planets orbit the Sun in ellipses with
the Sun at one focus of the ellipse.
Note: There is
nothing at the
other focus or in
the center.
Kepler’s Law II
2) A line between a planet and the Sun
sweeps out equal areas of the ellipse in
equal amounts of time.
Kepler’s Laws
• Law III
The orbital period of a planet squared
is proportional to the length of the
semi-major axis cubed. P2 a3
If P is measured in earth years, and a is
measured in AU, then the formula
becomes
2
3
P a
Using the Third Law
P2 a3
P must be in earth years, and a in AU.
A planet is located 4 au form the sun,
what is the period of the planet ?
P 2  4 3 , p2  64,
2
3
2
P  4 , p  64,
P

64,
P

8
years
P  64, P  8 years
Summary of Kepler’s Three Laws
• I. The orbits of the planets are
ellipses with the sun at one focus.
• II The orbital path sweeps out
equal areas in equal time.
• III The orbital period squared is
proportional to the average
distance cubed (usually expressed
in earth years and A.U.s).
Isaac Newton (1642-1727)
One of world’s greatest
scientists, co-inventor of calculus.
He discovered the law of Universal
Gravitation, Three Laws of Motion and he
was able to explain Kepler’s Laws.
Personally rather obnoxious. Had poor
relationships with women. Did most of his
work before he turned 25!
Newton’s Laws
The First Law ( Inertia )
A body continues to move as it has been
moving unless acted upon by an external
force.
A body at rest
stays at rest ,
unless acted
upon by some
force .
An astronaut,
floating in
space, will
float in a
straight line ,
unless some
force acts
upon him/her.
The
nd
2
Law
Newton’s Laws
F = (mass) a or a = F/m
Forces acting on a body can produce an
acceleration to a body.
The
rd
3
Law
Newton’s
Laws
For every action there is
an equal and opposite reaction
Newton’s Law of Universal Gravitation
Every object in the universe attracts every other
object with a force that is directly proportional to
the product of its masses, and inversely
proportional to the square of its distance.
d
M1
F
GM 1M 2
d2
M2
More distance less
force - less distance,
more force
2d
F
M1
d/2
M1
GM1M 2 1 GM1M 2

2
(2d )
4 d2
GM 1M 2
GM 1M 2
F
4
2
(d / 2)
d2
M2
M2
d
GM 1M 2
F
d2
M2
M1
d
More mass
more force –
less mass, less
force
G (2 M 1 ) M 2
GM 1M 2
F
2
2
d
d2
M2
2M1
d
2M1
F
2M2
G (2 M 1 )(2M 2 )
GM 1M 2

4
d2
d2
What is mass and weight ?
Weight is the attraction of gravity for an
object. Mass is how much matter an
object contains.
Mass does not depend on gravity. One
kg on Earth is one kg everywhere in the
universe.
Weight would be different for each
planet, due to gravity.
Temperature Scales
Astronomers use the Kelvin scale, because it starts with 0 degrees,
where there is no molecular motion .
•On the microscopic level , the average kinetic
energy of the particles within a substance is
called the temperature.
Three Basic Types of Energy
• Kinetic Energy
– Energy due to motion
• Potential Energy
– Stored energy
• Radiative Energy
– Energy transported by light
Energy can change from one form
to another.
Conservation of Energy
• Energy can be neither created nor
destroyed.
• It merely changes it form or is
exchanged between objects.
• The total energy content of the
Universe was determined in the Big
Bang and remains the same today.
Potential Energy
• gravitational potential energy
is the energy which an object
stores due to its ability to fall.
E=mgh
g
m
• It depends on:
– the object’s mass (m)
– the strength of gravity (g)
– the distance which it falls (d)
d
Energy is stored in matter itself
andthis mass-energy equation is how
much energy would be released if an
amount of mass, m were converted into
energy.
E=
2
mc
[ c = 3 x 108 m/s is the speed of light; m
is in kg, then E is in joules]
The Acceleration of Gravity
Ignoring air friction
• As objects fall, they
accelerate.
• The acceleration due
to Earth’s gravity is
10 m/s each second,
or g = 10 m/s2,or 32
ft/s2.
• The higher you drop
the ball, the greater
its velocity will be at
impact.
Conservation of Angular Momentum
Angular momentum = rotational momentum
– Spinning objects rotate faster when
radius shrinks, and rotate slower when
their radius expands.
Experimental evidence indicates
that angular momentum is
rigorously conserved in our
Universe: it can be transferred,
but it cannot be created or
destroyed.
When an ice skater goes into a spin, if the
skater moves their arms inward, the rate of
spin increases, and if the arms are move
outward, the rate of spin slows down.
This is conservation of angular momentum.
When they bring their arms in, this shortens
the distance from the mass in the arms to the
rotation axis, so the velocity of that mass
must increase accordingly for the product of
the two to remain the same.