Transcript EM review

Aero 426, Space System
Engineering
Lecture 4
NEA Discoveries (How to
Observe NEAs)
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NEAs are dim but stars are bright – So let’s begin by
considering star light
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Spectral Types, Light Output and Mean Lifetime
Spectral Type
(color)
Mass
(Sun = 1)
Radius
(Sun = 1)
Temp.
(1000 K)
Output of visible
light (Sun = 1)
Approximate
lifetime
(billion years)
O
16 to 100
15
30 – 60
4000 to 15,000
0.003 to 0.03
2.5 to 16
15
10 – 30
50 to 4000
0.03 to 0.4
1.6 to 2.5
2.5
7.5 – 10
8 to 50
0.4 to 2
1.1 to 1.6
1.3
6 – 7.5
1.8 to 8
2 to 8
0.9 to 1.1
1.1
5–6
0.4 to 1.8
8 to 16
0.6 to 0.9
0.9
3.5 – 5
0.02 to 0.4
16 to 80
0.08 to 0.6
0.4
<3.5
10-6 to 0.02
80 to 1000s
(blue)
B
(blue-white)
A
(white)
F
(yellow-white)
G
(yellow)
K
(yelloworange)
M
(red)
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A Hertzsprung-Russell (HR) diagram is a plot of absolute magnitude (luminosity) against
temperature. The majority of stars lie in a band across the middle of the plot, known as the Main
Sequence. This is where stars spend most of their lifetime, during their hydrogen-burning phase.
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The Stellar Pyramid
All other stars
2%
4%
K Dwarfs
Brightness
9%
G-type main-sequence stars,
including the sun
Red Dwarfs
80%
5%
White Dwarfs
5
Measuring the distance to stars

If the angle the star moves through is 2 arcsecond, then the distance to the
star = 1 parsec
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1 pc  3.086  10 m  3.262 ly
6
Measuring the brightness of stars (and NEAS)
The observed brightness of a star is given by its apparent magnitude. (First
devised by Hipparchus who made a catalogue of about 850)
The brightest stars: m=1. Dimmest stars (visible to the naked eye) m=6.
The magnitude scale has been shown to be logarithmic, with a difference of 5
orders of magnitude corresponding to a factor of 100 in actual brightness.
Brightness measured in terms of radiated flux, F. This is the total amount of light
energy emitted per surface area. Assuming that the star is spherical, F=L/4πr2, where
L is the star’s luminosity.
Also defined is the absolute magnitude of a star, M. This is the apparent magnitude
a star would have if it were located ten parsecs away. Comparing apparent and
absolute magnitudes leads to the equation:

m  M  5 log10 r 10

where r is the distance to the star, measured in parsecs.
 The absolute magnitude of a NEA is its magnitude when 1AU distance from the
sun, and at zero phase angle
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Many Stars Are Brighter than 10th Magnitude
Visible to
typical
human eye[1]
Yes
No
Apparent
magnitude
Brightness
relative
to Vega
Number of stars
brighter than
apparent
magnitude[2]
−1.0
250%
1
0.0
100%
4
1.0
40%
15
2.0
16%
48
3.0
6.3%
171
4.0
2.5%
513
5.0
1.0%
1 602
6.0
0.40%
4 800
7.0
0.16%
14 000
8.0
0.063%
42 000
9.0
0.025%
121 000
10.0
0.010%
340 000
[1] ab “Vmag< 6.5”. SIMBAD Astronomical Database 2010-06-25
[2] “Magnitude”. National Solar Observatory – Sacramento Peak. Archived from the original on 2008-02-06. Retrieved 2006-08-23.
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How many stars brighter than a given magnitude?
Approximate Star Light Spectrum
T her m al r adiat ion or blackbody r adiat ion m odel :
 phot ons are modelled as a gas of bosons
 T he gas int eract s wit h at oms t hat randomly emit or absorb phot ons
 T he int eract ing at oms form t he walls of a cavit y cont aining t he gas
 T he most likely dist ribut ion of phot ons among energy levels is t he one t hat is
"most random" - i.e. maximizes t he st at ist ical mechanical ent ropy.
A sea of photons is
surrounded on all sides
by high temperature
plasma and atoms.
These particles
randomly absorb or
emit photons,
permitting all possible
energy transitions
compatible with
conservation of overall
energy
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Approximate Star Light Spectrum: Planck’s Law
B  T   
2hc 2
1
 5 e hc kT   1

W  sr 1  m 3

 
B T
spect r al ir r adiance
 energy per second, per unit wavelengt h,
per unit surface area, per st eradian

wavelengt h
h
T
P lanck's const ant  6.626  10 34W s 2
Absolut e t emperat ure of t he st ar's phot osphere
c
speed of light
k
Bolt zmann's const ant  1.3807  10 23W s / K
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Approximate Star Light Spectrum
Wien’s law
UV & Vis
Infrared
Microwave
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COBE (Cosmic Background Explorer) satellite data
precisely verifies Planck’s radiation law
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Using Planck’s Law: Accuracy of intensity measurement


As given above Planck’s law just gives the rate at which
energy is emitted. But light is composed of discrete packets,
called photons, each having energy hc 
Photon arrivals are a Poisson process for which all statistics
are determined by the average number of photons received in
a given time interval.

The standard deviation of the fluctuation from the mean of the
number of photons received is the square root of the average
number received.
 Then the Signal-to-Noise Ratio (SNR) of an intensity
measurement during a given time interval is:
Average number of phot ons received
St andard deviat ion of fluct uat ion about t he average
 Average number of phot ons received
SNR 

The key parameter is the average rate of photons received
per unit area of collecting aperture for light in a given
wavelength band, n

n T   Average number of photons received per second, per square meter,
in the wavelength range 1    2
If m is the star magnitude, and T is its photosphere temperature then:
n
 1 L
0.4 m


T
10



2
4

hc
d

 T  

2
1
d
1
1
 4 e hc  kT  1



0

 100.4 m

d
1
1
 5 ehc  kT  1

where :
m  Solar magnitude  26.73
d  Solar distance  1.58  105 lyr
L  Solar luminosity  3.846  1026 W
This has critical importance for estimating the accuracy of the intensity
measurements (see next lecture)
Most st ars are M-class
n   N 0 10
0.4 m 
N 0  1.46  1010
This formula is what
we'll use for the design
calculations
Summary for Stars

You have a simple model for the number of stars brighter than a
given magnitude (see slide 16):
 
N m
1m  
 23
This helps you figure out what type of star you should choose to
look at.

You also have a simple model for how many photons are received
per sec as a function of magnitude (see slide 9):
n   N 0 10
0.4 m 
, N 0  1.46  1010
This is essential to evaluate the “goodness” of the intensity data.
The next lecture shows how to compute the SNR from this.
NEA Types

An asteroid is coined a Near Earth Asteroid (NEA)
when its trajectory brings it within 1.3 AU [Astronomical
Unit] from the Sun and hence within 0.3 AU of the
Earth's orbit. The largest known NEA is 1036 Ganymede
(1924 TD, H = 9.45 mag, D = 31.7 km).

A NEA is said to be a Potentially Hazardous Asteroid
(PHA) when its orbit comes to within 0.05 AU (= 19.5 LD
[Lunar Distance] = 7.5 million km) of the Earth's orbit, the
so-called Earth Minimum Orbit Intersection Distance
(MOID), and has an absolute magnitude H < 22 mag
(i.e., its diameter D > 140 m). The largest known PHA is
4179 Toutatis (1989 AC, H = 15.3 mag, D = 4.6×2.4×1.9
km).
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Statistics as of December 2012





899 NEAs are known with D* > 1000 m (H** < 17.75 mag), i.e., 93 ±
4 % of an estimated population of 966 ± 45 NEAs
8501 NEAs are known with D < 1000 m
The estimated total population of all NEAs with D > 140 m (H < 22.0
mag) is ~ 15,000; observed: 5456 (~ 37 %)
The estimated total population of all NEAs with D > 100 m (H <
22.75 mag) is ~ 20,000; observed: 6059 (~ 30 %).
The estimated total population of all NEAs with D > 40 m (H < 24.75
mag) is ~ 300,000; observed: 7715 (~ 3%) .
Estimates: <targetneo.jhuapl.edu/pdfs/sessions/TargetNEOSession2-Harris.pdf>.
Further details: <ssd.jpl.nasa.gov/sbdb_query.cgi>.
* D denotes the asteroid mean diameter
** H is the Visible-band magnitude an asteroid would have at 1 AU distance from the
Earth, viewed at opposition
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NEO Search Programs
















Asiago DLR Asteroid Survey (ADAS), Italy/Germany
Campo Imperatore Near Earth Object Survey (CINEOS), Italy
Catalina Sky Survey (CSS), USA
China NEO Survey / NEO Survey Telescope (CNEOS/NEOST)
European NEA Search Observatories (EUNEASO)
EUROpean Near Earth Asteroid Research (EURONEAR)
IMPACTON, Brasil
Japanese Spaceguard Association (JSGA), Japan
La Sagra Sky Survey (LSSS), Spain
Lincoln Near-Earth Asteroid Research (LINEAR), USA
Lowell Observatory Near-Earth Object Search (LONEOS), USA
Near-Earth Asteroid Tracking (NEAT), USA
Panoramic Survey Telescope And Rapid Response System (Pan-STARRS), USA
Spacewatch, USA
Teide Observatory Tenerife Asteroid Survey (TOTAS), Spain
Wide-field Infrared Survey Explorer (WISE), USA.
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Current Surveys

Currently the vast majority of NEA discoveries are being
carried out by the Catalina Sky Survey near Tucson (AZ,
USA), the LINEAR survey near Socorro (NM, USA), the
Pan-STARRS survey on Maui (HI, USA), and, until
recently, the NEO-WISE survey of the Wide-field
Infrared Survey Explorer (WISE).
A review of NEO surveys is given by: Stephen Larson,
2007, in: A. Milani, G.B. Valsecchi & D. Vokrouhlický
(eds.), Proceedings IAU Symposium No. 236, Near
Earth Objects, our Celestial Neighbors: Opportunity and
Risk, Prague (Czech Republic) 14-18 August 2006
(Cambridge: CUP), p. 323, "Current NEO surveys."
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NEA Detection Summary
Diameter(m)
>1000
1000-140
140-40
40-1
Distance (km)
for which
F>100
(=0.5 m)
>20 million
< 20 million,
> 400,000
<400,000
(Lunar orbit)
>32,000
(GEO orbit)
<32,000
>20
H (mag)
17.75
17.75-22.0
22.0-24.75
>24.75
N estimated
966
`14,000
~285,000
??
N observed
899
4,557
2,259
1,685
O/E
93%
~33%
~1%
??
Only 1% detected, and if you wait for sharp shadows,
it’s probably too late
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