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ASTR 2020
Space Astronomy
Week 3:Tuesday
Review: EM waves,
Structure of matter
Announcements:
Observing at SBO tonight
Review of Electro-magnetic (EM) Waves:
[wavelength][frequency = [speed of light]
Energy of Photons (particles of light)
Momentum:
ln=c
E(photon) = hn = hc / l
P=h/l
Blackbody radiation:
lpeak
= 0.29 / T(K)
Luminosity of a sphere, Radius R:
L = 4 p R2 s T4
s = 5.67 x 10-5 (Stephan-Boltzmann constant)
Flux at distance D:
F = L / 4 p D2
Doppler Effect:
f / f = l / l = V / c
Diffraction: Resolution of a telescope with diameter D:
qradian = l / D
Telescopes: refraction (refractors) vs. reflectors
Spectra: Interaction of light (EM waves) with matter
Spectrographs
Detection of EM waves: At short l, treat as particles
At long l, treat as waves
Observing in the Radio
i.e. The NRAO GBT (D ~ 100 m)
qradian = l / D
at 21 cm = 1.420 GHz
l
21cm
q= »
= 7.2'
D 10000cm
at 0.3 cm = 100 GHz
l
0.3cm
q= »
= 0.10' = 6.2' '
D 10000cm
Planetary Radar imaging: Doppler shift + time delay = 2D map
Beating the diffraction limit
Redshift
Blueshift
Radar Pulse
Early echo
Late echo
UV
Venus
Radar
Radar
Venus
Radar
Introduction to Geometric optics:
Fermat’s Principle:
Variation in photon time-of-flight is minimum
 (Optical Path) =  (time-of-flight)= 0
Snell’s law of Refraction: V = c / n n = refractive index
Focal-Length: 1 / f = 1 / Dobject + 1 / Dimage
f/ = f / D
Aberrations:
Chromatic, Spherical, Coma, Astigmatism,
Field Curvature, Distortion
Properties of simple optical systems:
Microscopes
Telescopes: refractor vs. reflector
Newtonian, Cassegrain, Gregorian, Catadioptric
Schmidt, Schmidt-Cassegrain, Maksutov, ….
Magnification, resolution, light gathering power
https://en.wikipedia.org/wiki/Optical_telescope
Chabot 8” refractor
European Southern Observatory
VISTA 4-meter reflector
Refraction:
Snell’s Law:
n1 sin(2) = n2 sin(1)
1
n1 = refractive index in region 1
n1
n2
n2 = refractive index in region 2
n = c / v = lvacuum / lmedium
2
l1
1
n1
sin 1
=
n2
sin 2
2
l2
Refraction:
Magnification:
Telescope types
Functions of a Telescope:
- Gather light (as much as possible)
- Resolve small angles 7 detail
- If used visually, to magnify
Spectrographs
Focal Plane collimator
camera
detector
Dispersing element
Slit
Telescope
Spectrograph
Spectra of Galaxies:
(Calcium H+K lines)
Spectrum of
Comparison lamp
(He + Ne + Ar)
Spectrum of galaxy
Spectral lines:
Specific wavelengths & Frequencies
Emitted or absorbed by atoms & molecules.
Spectral lines:
Specific wavelengths & Frequencies
Emitted or absorbed by atoms & molecules.
Spectral lines:
Spectra of elements (in emission)
at visual wavelengths
Absorption Features (lines, bands):
Star emits continuum
- light at energy equal to an atomic
transition is absorbed
- that light is then reemitted in a
random direction
the observer sees all the
wavelengths except those
at the atomic transition energy
an absorption spectrum
The Solar Spectrum (from Kitt Peak’s McMath-Pierce Solar Telescope):
2960 – 8,000 Angstroms (.29 to 0.8 mm)
Spectra of Stars
Spectra of Stars
Spectra of Stars
HerzsprungRussell (HR)
Diagram
Luminosity
vs
Temperature
L= 4p R2 sT4
s = 5.67x10-5
T(K) ~ 0.29 / lpeak
Why do atoms only emit certain
frequencies & wavelengths (spectral lines)?
Wave nature of matter:
momentum: p = mV = h/l
E = hf = hn
l = h/p
Atoms: ~10-8 cm
Nuclei: ~ 10-13 cm
Niels Bohr (1885 - 1962, Denmark)
- early quantum physics, “planetary” model of the atom
E = hn = hc/l
p = E/c = h/l
x  p ~ h
=>
Heisenberg Uncertainty
x = l ~ h / mV
ASTR 2020
Space Astronomy
Week 3: Thursday
Review: energy levels, H
Structure of matter
Gravity, energy, momentum
Orbits, escape speed
Homework #2 posted on D2L
Hydrogen spectrum:
g
b
a
b
Balmer
n = R [ 1/nl2 – 1 /nu2]
R = 3.288 x 1015 Hz
Lyman
13.6 eV
a
Spectrum of hydrogen
13.6 eV = 912 Angstroms
10-18
Lyman lines
n-3
Balmer lines
Wavelength (1 / photon energy)
Ultraviolet (UV)
Visual
n
1
2
3
4
Astronomers Periodic Table
Electron “waves”
Copper-oxide lattice
Outline: Gravity and Orbits
- Laws of Motion (Newton’s mechanics)
position, velocity, acceleration
mass, inertia, force, centrifugal force
- The inverse square law: Newton’s law of gravity
falling apples, and the moon
- Escape speed velocity needed to escape
- Orbits
balance between gravity and centrifugal force
- Kepler’s Laws of planetary motions
Motion
- Velocity (or speed):
V = [change in position] / [ time interval]
Example: Car moving. Covers 100 meters in 60 seconds
100 m = 104 cm, V = 104 / 60 = 166 cm/sec = 1.67 m/sec
= 65 ft/sec
= 44.7 mi/hr
- Acceleration:
a = [change in velocity] / [time interval]
Example: Drop a rock in Earth’s gravity ….
Speed increases by 980 cm/sec every second
(until air resistance sets in)
a = 980 cm s-2 (= 32 ft sec-2)
Mass, inertia, force, centrifugal force
- Mass, M: a measure of the amount of material
Example:
Mo = Mass of the Sun = 2 x 1033 grams
Mearth = Mass of the Earth = 6 x 1027 grams
Weight = the downward force a given mass exerts
in the Earth’s gravitational field:
Note: The acceleration of gravity at the Earth’s surface is
a = 980 cm s-2
g = 980 cm s-2
This is used so often we call it little ‘g’
acceleration at Earth’s surface
- Force = [mass] x [acceleration]
Weight = m g
F = ma
Forces
- Acceleration in presence of a force, F
a=F/m
- The four (known) fundamental Forces:
- Gravity (planets, stars, galaxies, …)
FG = - GmM / r2
- Electro-magnetism (atoms, molecules)
FEM = - q1q2 / r2 + q1 VxB / c
Isaac Newton
- Strong nuclear force (binds atomic nuclei)
- Weak nuclear force (radioactive decay, binds electrons to protons)
Gravity
Falling objects on Earth
most motions in astronomy
F = G Mm / r2
inverse square law!
Force pulls together objects with MASS
(mass has TWO roles - inertia AND creating gravity)
Force is weaker when the distance between them is greater
Force is stronger when the distance between them is smaller
This formulation of FORCE predicts motions of planets
accurately!
Mass, inertia, force, centrifugal force
- Inertia, M: a measure of the resistance to a force
In a vacuum (space) object in motion stay in motion
those at rest, stay at rest (unless there is a force).
- Centrifugal Force - actually a consequence of inertia
When tethered to a string, a rock is forced by the
string to move in a circle … but inertia wants to
make it move in a straight line. The resulting
force on the string is:
Fcent = [mass] x [ Velocity2] / [ radius ]
Fcent = mV2 / r
Example: m = 100 g, radius r = 100 cm, velocity = 100 cm/sec
F = 100 1002 / 100 = 104 (g cm sec-2)
Orbits:
Balance of opposing forces
Gravity <=> Centrifugal force
G M m / R2 =
m V2orbit / R
Solve for Vorbit:
M
m
Vorbit = (GM / R)1/2
Newton’s constant:
Vorbit
G = 6.67 x 10-8 c.g.s.
Reaching Orbit:
Vorbit = {GM / (R+H)}1/2
Mearth ~ 5.97 x 1027 g
G = 6.67 x 10-8 c.g.s.
R = 6,371 km
H = 300 km
Vorbit = {[6.67 x 10-8][5.97 x 1027 g]/[6.371e8 +3e7]}1/2
= 7.73 x 105 cm/sec = 7.73 km/s
Rockets: Tsiolkovsky’s equn.
V = Vejecta ln (Minitial/Mfinal)
M
Minitial = Mfinal exp (Vorbit / Vejecta)
~ Mfinal exp (7.7/3) ~ 13 Mfinal
Vorbit
De Laval Nozzle:
Hydrazine: N2H4
Vejecta ~ 1.7 - 2.9 km/s
Liquid: O2 + H2
Vejecta ~ 2.9 - 4.5 km/s
Solid:
Vejecta ~ 2.1 - 3.2 km/s
Echo (1960 - 1964)
Telstar-1 (1962)
Relay 1
Andover, Main
Crawford Hill
A. Penzias
R. W. Wilson
signal
Mixers
LO
mixed
signal
0 Hz
original
signal
frequency
Mixers
signal
The negative
frequencies in the
difference appear the
same as a positive
frequency.
LO
mixed
signal
0 Hz
original
signal
frequency
To avoid this, we can
use “Single Sideband
Mixers” (SSBs) which
eliminate the negative
frequency components.
Amplification
Amplification is in units of deciBells (dB)
logarithmic scale
3 dB = x2
5 dB = x3
10 dB = x10
20 dB = x100
30 dB = x1000
V1
dB = 10 log10 ( )
V2