ASTR 2020
Space Astronomy
Week 2: Wed.
The Winter sky ….
Infrared view of winter sky (10 - 120 mm)
Star
A large, glowing ball of gas that generates heat and light through
nuclear fusion
Visual wavelength
UV & X-ray wavelengths
Properties of Thermal Radiation
1. Hotter objects emit more light at all frequencies per unit
area.
2. Hotter objects emit photons with a higher average
energy.
1 nm
“nano meter”:
= 10-9 m
= 10-7 cm
= 10 Angstroms
= 10-3 mm
Thermal (Black-body) radiation:
[peak wavelength] = 0.3 cm / [Absolute Temperature (Ko )]
Wien
Rayleigh-Jeans
ASTR 2020
Space Astronomy
Week 2: Friday
Electromagnetic (EM) Radiation
• Light:
-
lwavelength,
n = frequency
ln = c = 2.998 x 1010 cm/s (in vacuum)
E = h n
Photon energy (erg)
1 erg sec-1 = 10-7 Watt
h = 6.626 x 10-27 (c.g.s)
1 eV = 1.602 x 10-12 erg
-
p = E / c = h / l Photon momentum
l = h / p = h / mv
Wavelength of a particle
• Black-body Planck Function: Bn(T)
The Planck Function: Black-body radiation
(erg s-1 cm-2 Hz-1 2 p sr-1)
Wien:
B(n,T) = (2 phn3 / c2) e-hn/kT
Rayleigh-Jeans:
B(n,T) = 2 p kT / l2
Review of Some Basics
•
Angular resolution:
q = 1.22 l / D radians
206,265” in a radian
• Flux
F = L / 4 p d2
• Flux density (per Hz) 1 Jansky = 10-26 (W m-2 Hz-1)
= 10-23 (erg s-1 cm-2 Hz-1)
Constants:
c = 3 x 1010 cm/sec,
k = 1.38 x 10-16
h = 6.626 x 10-27
mH ~ mproton = 1.67 x 10-24 grams
me = 0.91 x 10-27 grams
eV = 1.602 x 10-12 erg
Luminosity of Sun = 4 x 1033 erg/sec
Mass of the Sun = 2 x 1033 grams
Luminosity & Flux
- Luminosity: Energy given off each second
energy is measures in ergs
luminosity is an erg/second
1 Watt = 107 erg /sec
- Flux: flow or energy though a unit area.
[erg sec-1 cm-2]
Example: Flux of energy from the Sun:
Sun’s luminosity = 4 x 1033 erg sec-1
Sun’s mass = 2 x 1033 grams)
Distance between Earth & Sun D = 1.5 x 1013 cm
= 1 Astronomical Unit
= 1 A.U.
Flux = L / 4 p D2 = 4 x 1033 / (4 x 3.14 x 1.5x1013*2)
= 1.4 x 106 erg s-1 cm-2 = 1.4 x 1010 erg s-1 m-2
= 1400 Watts m-2 = 1.4 kW m-2
The Doppler Effect
Motion changes wavelength & frequency:
Let:
fobserved - frest = f = “change in frequency”
lobservedlrest = l = “change in wavelength”
f/f = ll V / c
= “velocity in units of speed of light”
Fractional change in frequency & wavelength
= [velocity along line-of-sight] / [speed of light]
Spectra of Galaxies:
(Calcium H+K lines)
Spectrum of
Comparison lamp
(He + Ne + Ar)
Spectrum of galaxy
Example:
Freflect = ftrans +/- f
f = 2 f (V/c)
f = 10 GHz = 1010 Hz
Police
V = 100 km/h = 27.8 m /s = 2.78 x 103 cm/s
Radar: c = 3 x 1010 cm/s = 3 x 105 km/s
f = 2 f V / c
= 2 [1010 Hz][2.78x103 cm/s] / [3x1010 cm/s]
= [2 x 2.78 / 3] [10 10+3-10]
= [5.56 / 3] x 103 Hz = 1.85 x 103 Hz = 1,850 Hz
Picky Clouds
A cloud of particles absorbs
all of one type of light and
transmits all others.
If there are an equal
number of photons of all
types of light hitting the
cloud, which type of cloud
would heat up the fastest.
a)
b)
c)
d)
e)
Absorbs Radio
Absorbs X-Ray
Absorbs Far IR
Absorbs Near UV
Absorbs Visible
Picky Clouds
A cloud of particles absorbs
all of one type of light and
transmits all others.
If there are an equal
number of photons of all
types of light hitting the
cloud, which type of cloud
would heat up the fastest.
a)
b)
c)
d)
e)
Absorbs Radio
Absorbs X-Ray
Absorbs Far IR
Absorbs Near UV
Absorbs Visible
X-Ray photons have the shortest
wavelength/highest frequency, therefore the most
energy per photon
LASERS!!!
 You have a 5mW laser,
which color of laser will
have the highest photon
count per second?
a) Blue
b) Yellow
c) Red
d) Green
e) Cyan
LASERS!!!
 You have a 5mW laser,
which color of laser will
have the highest photon
count per second?
a) Blue
b) Yellow
c) Red
d) Green
e) Cyan
Red photons have the highest wavelength,
therefore the lowest frequency,
and therefore the lowest energy per photon
Freflect = f trans + / - f
f trans
f = 1850 Hz
frequency of `beat wave’ (envelope)
Mixers
signal in
w1
local oscillator
w2
signal out
w1+w2
and
w1w2
LO
A mixer takes two inputs:
the signal and a local
oscillator (LO).
The mixer outputs the sum
and difference frequencies.
In radio astronomy, we
usually filter out the high
frequency (sum) component.
Single sideband mixer:
Local oscillator
Down-converted signal
f = 10 GHz
F + f =
10 GHz + 1850 Hz
1850 Hz
f = fIF
Frequency
Band-pass of amplifier:
Intermediate frequency = IF
Observing in the Radio
i.e. The NRAO GBT (D ~ 100 m)
at 21cm = 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
Redshift
Radar Pulse
Blueshift
Early echo
Late echo
UV
Venus
Radar
Radar
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 log 10 ( )
V2