Download Objectives for grade E - Particle and Astroparticle Physics

Lecture 2
Examination
The course is assessed in three parts:
•Problem sets. The problem sets and the peer reviews. One of the sets
will randomly be corrected by me
•Observational labs. The laborative exercises + a lab report.
•Written Exam. It consists of two parts. Part I is needed for grade E:
at least 75% needs to be correct. It is also needed to be able to go on to
Part II, which is used to assess for grades A-D. The grade is set
according to the score.
To pass the course, all three of the above assessments must be ready.
Objectives for grade E: For passing the course with grade E you need to know
the fundamentals of the course.
Objectives for grades A-D: Be able to solve problems on topics covered in the
course, that need a well developped and mature understanding its content.
Pedagogical background for peer review:
- See other solutions, comparing solutions.
- The understanding gets deeper, when applying criteria for good/bad solutions; ”Is it
really the correct solution for this problem?
- Select good evidence to be able to convince others.
- Learn to judge a good performance. You are included in the critique process.
- All this leads to increased self-supervision capabilities.
Other positive effects of this is that the feedback is prompt, and is relevant. In addition,
learning from errors is very powerful. The possibility of erroneous thinking without the
risk of being negatively judged by the teacher is important.
Repetition
Declination
Vernal equinox
”Vårdagsjämningspunkten”
Right ascension
• The Sun appears to
trace out a circular path
called the ecliptic on
the celestial sphere
tilted at 23 ½ degrees to
the equator
Sept
21
June
21
Dec
21
March
31
• The ecliptic and the
celestial equator
intersect at only two
points
• Each point is called an
equinox
• The point on the ecliptic
farthest north of the
celestial equator that
marks the location of
the Sun at the beginning
of summer in the
northern hemisphere is
called the summer
solstice
• At the beginning of the
northern hemisphere’s
winter the Sun is
farthest south of the
celestial equator at a
point called the winter
solstice
Stellar Motions: Proper motion m
Nature of Light - Cnt’d
Spectral Lines
Kirchhoff’s Laws
Bohr’s formula for hydrogen wavelengths
1/l = R x [ 1/N2 – 1/n2 ]
N = number of inner orbit
n = number of outer orbit
R = Rydberg constant
(1.097 X 107 m-1)
l = wavelength of emitted or
absorbed photon
Ha H
b
Lya Ly
b
Balmer Lines in Star Spectrum
Photons’ interaction with matter:
Extinction
Absorption:
Interstellar grains and gas
Scattering:
Scattering
Rayleigh scattering is responsible for the
scattering of visible light in the daytime sky
*
Scattering on electrons
* Proportional to 1/l4
Gravitation
Ancient astronomers invented geocentric models
to explain planetary motions
• Like the Sun and Moon, the planets move on the celestial sphere
with respect to the background of stars
• Most of the time a planet moves eastward in direct motion, in the
same direction as the Sun and the Moon, but from time to time it
moves westward in retrograde motion
A planet undergoes retrograde motion as seen from
Earth when the Earth and the planet pass each other
Johannes Kepler proposed elliptical paths
for the planets about the Sun
•
Using data collected by
Tycho Brahe, Kepler
deduced three laws of
planetary motion:
1. the orbits are ellipses
2. a planet’s speed
varies as it moves
around its elliptical
orbit
3. the orbital period of a
planet is related to the
size of its orbit
Kepler’s First Law:
A planet orbits the Sun in an ellipse, with the Sun at
one focus of the ellipse
0
r + r = 2a
Semiminor axis
Eccentricity
Focal point
2
Semimajor axis
Actually, the center-of-mass is at the focus
2
2
à
=
(1
b
a
e)
Kepler’s Second Law:
A line connecting a planet to the Sun sweeps out equal areas in equal
time intervals
Orbital speed depends
on location
Angular momentum of a system is a constant
for a central force law
dL
=
0
dt
1L
dA
=
2ö
dt
ö=
m 1m 2
m 1+ m 2
The time rate of change of the area swept out by a line connecting
a planet to the focus of an ellipse is a constant =
one-half of the orbital angular momentum per unit mass
Kepler’s Third Law (harmonic law):
Relates the average orbital distance of a planet from the Sun to its period
P2 = a3
P = planet’s sidereal period, in years
a = planet’s semimajor axis, in AU
Kepler’s Third Law
Simple derivation using Newtonian mechanics gives that
Kepler’s third law is
2
P =
2
4ù
3
a
G( m 1+ m 2)
Galileo’s discoveries with a telescope strongly
supported a heliocentric model
• The invention of the
telescope led Galileo
to new discoveries
that supported a
heliocentric model
• These included his
observations of the
phases of Venus and
of the motions of four
moons around Jupiter
• One of Galileo’s most important discoveries with the telescope was
that Venus exhibits phases like those of the Moon
• Galileo also noticed that the apparent size of Venus as seen through
his telescope was related to the planet’s phase
• Venus appears small at gibbous phase and largest at crescent
phase
Geocentric
• To explain why Venus is never
seen very far from the Sun,
the Ptolemaic model had to
assume that the deferents of
Venus and of the Sun move
together in lockstep, with the
epicycle of Venus centered on
a straight line between the
Earth and the Sun
• In this model, Venus was
never on the opposite side of
the Sun from the Earth, and so
it could never have shown the
gibbous phases that Galileo
observed
• In 1610 Galileo
discovered four
moons, now called
the Galilean
satellites, orbiting
Jupiter
Isaac Newton formulated three laws that describe
fundamental properties of physical reality
•
•
Isaac Newton developed three
principles, called the laws of
motion, that apply to the
motions of objects on Earth as
well as in space
These are
1. the law of inertia: a body
remains at rest, or moves in a
straight line at a constant
speed, unless acted upon by a
net outside force
2. F = m x a (the force on an
object is directly proportional to
its mass and acceleration)
3. the principle of action and
reaction: whenever one body
exerts a force on a second
body, the second body exerts
an equal and opposite force on
the first body
Newton’s Law of Universal Gravitation
F = gravitational force between two objects
m1 = mass of first object
m2 = mass of second object
r = distance between objects
G = universal constant of gravitation
• If the masses are measured in kilograms and the distance between
them in meters, then the force is measured in newtons
• Laboratory experiments have yielded a value for G of
G = 6.67 × 10–11 newton • m2/kg2
Kepler’s First Law:
A planet orbits the Sun in an ellipse, with the Sun at
one focus of the ellipse
-2
Elliptical
orbits
Semiminor
axis result from an attractive r central
force law such as gravity, when the total energy of
the system is less than zero (a bound system).
0
r + r = 2a
Eccentricity
Parabolic path is obtained when E=0.
Hyperbolic
path in an unbound system E>0
Focal
point
Semimajor axis
2
2
à
=
(1
b
a
e)
Actually, the center-of-mass is at the focus
2
Orbits may be any of a family of curves
called conic sections
Orbits
• The law of universal
gravitation accounts for
planets not falling into the
Sun nor the Moon
crashing into the Earth
• Paths A, B, and C do not
have enough horizontal
velocity to escape Earth’s
surface whereas Paths D,
E, and F do.
• Path E is where the
horizontal velocity is
exactly what is needed so
its orbit matches the
circular curve of the Earth
FIN
Tidal force
Gravitational forces between two objects
produce tides
The Origin of Tidal Forces
Light has properties of both waves and
particles
• Newton thought light was in the form of little packets of energy
called photons and subsequent experiments with blackbody
radiation indicate it has particle-like properties
• Young’s Double-Slit Experiment indicated light behaved as a
wave
• Light has a dual personality; it behaves as a stream of particle
like photons, but each photon has wavelike properties
Determining the Speed of Light
• Galileo tried
unsuccessfully to
determine the speed
of light using an
assistant with a
lantern on a distant
hilltop
Light travels through empty space at a speed
of 300,000 km/s
• In 1676, Danish astronomer
Olaus Rømer discovered
that the exact time of
eclipses of Jupiter’s moons
depended on the distance
of Jupiter to Earth
• This happens because it
takes varying times for light
to travel the varying
distance between Earth and
Jupiter
• Using d=rt with a known
distance and a measured
time gave the speed (rate)
of the light
• In 1850 Fizeau and Foucalt also experimented with light
by bouncing it off a rotating mirror and measuring time
• The light returned to its source at a slightly different
position because the mirror has moved during the time
light was traveling
• d=rt again gave c
• The number of protons in an atom’s nucleus is the atomic number for
that particular element
• The same element may have different numbers of neutrons in its
nucleus
• These three slightly different kinds of elements are called isotopes
Spectral lines are produced when an electron jumps
from one energy level to another within an atom
• The nucleus of an atom is
surrounded by electrons that
occupy only certain orbits or
energy levels
• When an electron jumps from one
energy level to another, it emits or
absorbs a photon of appropriate
energy (and hence of a specific
wavelength).
• The spectral lines of a particular
element correspond to the various
electron transitions between
energy levels in atoms of that
element.
• Bohr’s model of the atom correctly
predicts the wavelengths of
hydrogen’s spectral lines.
A planet’s synodic period is measured with respect
to the Earth and the Sun (for example, from one
opposition to the next)
Tycho Brahe’s astronomical observations
disproved ancient ideas about the heavens
Parallax Shift
There is a correlation between the phases of Venus and
the planet’s angular distance from the Sun
Newton’s description of gravity accounts for Kepler’s
laws and explains the motions of the planets and
other orbiting bodies
Each chemical element produces its own
unique set of spectral lines
Bohr’s Model of the Hydrogen atom
Spectral line series of the hydrogen atom
Doppler Shifts
• Red Shift: The object is moving away from the observer
• Blue Shift: The object is moving towards the observer
õ obsà õ r est
õ r est
=
4õ
õ r est
=
vr
c
Dl = wavelength shift
lrest = wavelength if source is not moving
v = velocity of source
c = speed of light
The wavelength of a spectral line is affected by the
relative motion between the source and the observer