1

NEAs are dim but stars are bright – So let’s begin by considering star light
2

Spectral Types, Light Output and Mean Lifetime
Spectral Type
(color)
Mass
(Sun = 1)
O
(blue)
B
(blue-white)
A
(white)
F
(yellow-white)
G
(yellow)
K
(yelloworange)
M
(red)
16 to 100
2.5 to 16
1.6 to 2.5
1.1 to 1.6
0.9 to 1.1
0.6 to 0.9
0.08 to 0.6
Radius
(Sun = 1)
15
15
2.5
1.3
1.1
0.9
0.4
Temp.
(1000 K)
Output of visible light (Sun = 1)
Approximate lifetime
(billion years)
30 – 60 4000 to 15,000 0.003 to 0.03
10 – 30
7.5 – 10
6 – 7.5
5 – 6
3.5 – 5
<3.5
50 to 4000
8 to 50
1.8 to 8
0.4 to 1.8
0.02 to 0.4
10 -6 to 0.02
0.03 to 0.4
0.4 to 2
2 to 8
8 to 16
16 to 80
80 to 1000s
3

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.
4

The Stellar Pyramid
2%
4%
All other stars
9%
G-type main-sequence stars, including the sun
K Dwarfs
80%
Red Dwarfs
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
1 pc
  16 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/4πr 2 , 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 log
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
7

Many Stars Are Brighter than 10 th Magnitude
Visible to typical human eye [1]
Yes
No
Apparent magnitude
3.0
4.0
5.0
6.0
7.0
−1.0
0.0
1.0
2.0
8.0
9.0
10.0
Brightness relative to Vega
250%
100%
40%
16%
6.3%
2.5%
1.0%
0.40%
0.16%
0.063%
0.025%
0.010%
Number of stars brighter than apparent magnitude [2]
1
4
15
48
171
513
1 602
4 800
14 000
42 000
121 000
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.
8

How many stars brighter than a given magnitude?

Approximate Star Light Spectrum
T her m a l r a d ia t io n or bla ckbo d y r a d ia t io n m o d el :

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 c avit 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
 
 2 hc

5
2 e
1

B

 


1 s p ect r a l ir r a d ia n ce

W
 sr

1
 m

3
energy per second, per unit wavelengt h,

per unit surface area, per st eradian
 wavelengt h h P lanck's const ant
  
34
W s
2
T
 c k
Absolut e t emperat ure of t he st ar's phot osphere
speed of light
Bolt zmann's const ant

1.3807

10

23
W s / K
11

Approximate Star Light Spectrum
Wien’s law
UV & Vis Infrared Microwave
12

COBE (Cosmic Background Explorer) satellite data precisely verifies Planck’s radiation law
13

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:
SNR

Average number of phot ons received
St andard deviat ion of fluct uat ion about t he average

Average number of phot ons received
 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
 
  
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
 



4

1 L h c d 2
  
10
0.4
m

 10

0.4
m 
    

1

2 d

1

4 where : m
1 e hc
 kT


1

0
 d

1

5

Solar magnitude
 
26.73
1 e hc
 kT


1 d

Solar distance

1.58 10

5 lyr
L

Solar luminosity
  26
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
 10
This formula is what we'll use for the design calculations

 You have a simple model for the number of stars brighter than a given magnitude (see slide 16):
 
3

1
 m


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

0.4
m
10  , N
0
 10
This is essential to evaluate the “goodness” of the intensity data.
The next lecture shows how to compute the SNR from this.

 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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




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/TargetNEO-
Session2-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
19

















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.
20

 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."
21

22

Diameter(m) >1000 1000-140 140-40 40-1
Distance (km) for which
F>100
(

=0.5
 m)
H (mag)
>20 million < 20 million,
> 400,000
17.75
17.75-22.0
<400,000
(Lunar orbit)
>32,000
(GEO orbit)
22.0-24.75
N estimated 966
N observed 899
O/E 93%
`14,000
4,557
~33%
~285,000
2,259
~1%
<32,000
>20
>24.75
??
1,685
??
Only 1% detected, and if you wait for sharp shadows, it’s probably too late

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