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Aero 426, Space System Engineering

Lecture 4NEA 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(blue)

16 to 100 15 30 – 60 4000 to 15,000 0.003 to 0.03

B(blue-white)

2.5 to 16 15 10 – 30 50 to 4000 0.03 to 0.4

A(white)

1.6 to 2.5 2.5 7.5 – 10 8 to 50 0.4 to 2

F(yellow-white)

1.1 to 1.6 1.3 6 – 7.5 1.8 to 8 2 to 8

G(yellow)

0.9 to 1.1 1.1 5 – 6 0.4 to 1.8 8 to 16

K(yellow-orange)

0.6 to 0.9 0.9 3.5 – 5 0.02 to 0.4 16 to 80

M(red)

0.08 to 0.6 0.4 <3.5 10-6 to 0.02 80 to 1000s

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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

Brig

htne

ss

5%

80%

9%

4%

2%

White Dwarfs

Red Dwarfs

K Dwarfs

G-type main-sequence stars, including the sun

All other stars

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Measuring the distance to stars

If the angle the star moves through is 2 arcsecond, then the distance to the star = 1 parsec 161 pc 3.086 10 3.262m ly

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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:

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

105log 10m M r

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Many Stars Are Brighter than 10th Magnitude

Visible totypicalhuman eye[1]

Apparentmagnitude

Brightnessrelativeto Vega

Number of starsbrighter thanapparent magnitude[2]

Yes

−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

No

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.

How many stars brighter than a given magnitude?

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Approximate Star Light Spectrum

or

photons are modelled as a gas of bosons

The gas interacts with atoms that randomly emit or absorb photons

The interacting atoms form the walls of a c

Thermal radiation blackbody radiation model :

avity containing the gas

The most likely distribution of photons among energy levels is the one that is

"most random" - i.e. maximizes the statistical mechanical entropy.

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

21 3

5

energy per second, per unit wavelength,

per unit surface area, per steradian

wavelength

2 11hc kT

B T

h

hcB T W sr me

spectral irradiance

34 2

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Planck's constant 6.626 10

Absolute temperature of the star's photosphere

speed of light

Boltzmann's constant 1.3807 10 /

W s

T

c

k W s K

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Approximate Star Light Spectrum

UV & Vis Infrared Microwave

Wien’s law

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

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

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:

The key parameter is the average rate of photons received per unit area of collecting aperture for light in a given wavelength band,

hc

Average number of photons receivedStandard deviation of fluctuation about the average

Average number of photons received

SNR

n

1 2

Average number of photons received per second, per square meter,

in the wavelength range

If is the star magnitude, and is its photosphere temperature then:

n T

m T

2

14 5

0

0.4 0.42

1 1 1 1

1 1:

Solar magnitude 26.73

1 10 104

hc kT hc kT

m m

T d de e

where

m

Ln T

hc d

5

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Solar distance 1.58 10

Solar luminosity 3.846 10

d lyr

L W

This has critical importance for estimating the accuracy of the intensity

measurements (see next lecture)

0.4

010

0

Most stars are M-class

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1.46 10

mn N

N

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):

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):

This is essential to evaluate the “goodness” of the intensity data. The next lecture shows how to compute the SNR from this.

12 3

mN m

0.4 100 0

10 , 1.46 10m

n N N

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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/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

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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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