ESTIMATING DISTANCES OF ASTEROIDSUsing the Worldwide Internet-Accessible Network of Telescopes

Faculty Information GuideA Global Hands-On UniverseTM Student Research Activity

Lawrence Hall of ScienceUniversity of California, Berkeley

J. Patrick MillerDepartment of MathematicsHardin-Simmons University

Abilene, Texas

Global Hands-On UniverseTM (GHOU) is an education and research program available to students with a keen interest in astronomy and astrophysics.

Using the Internet…

Students are able to access a worldwide network of telescopes to take deep sky images, access professional astronomical databases, and

analyze images and data with a set of user-friendly image processing software tools.

Internet-accessible 10" Meade located in Queen Creek, AZ

(Frank Pino)

Internet-accessible 14" Celestron located in Hawaii

(Ken Archer)

Two Internet-accessible telescopes on the worldwide network.

They are equipped with a digital camera (CCD = charge-coupled device) and color filter wheel

(red, blue, and green bandwidths).

Schmidt-Cassegrain Telescopes

Housing for the 14" Celestron Telescope (Hawaii)

Under faculty supervision, students log onto the Internet and access one of the telescopes on the worldwide network.

To gain access you must have the URL, identification, and password.

Faculty interested in having their students join Global Hands-On UniverseTM programs and using the Internet-accessible telescopes may contact

Dr. Carl Pennypacker at CRPennypacker@lbl.gov for complete information.

On the evening of December 19, 2005, students from Hardin-Simmons University used the

Internet-accessible telescope in Queen Creek, AZ (Ironwood North Observatory).

The purpose of this project was to take images of asteroids and estimate their distances from the Sun.

The Main Asteroid Belt consists of millions of rock boulders located between the orbits of Mars and Jupiter. The largest is named Ceres, which is ~900 km in diameter.

ErosAsteroid in the Main Belt with a long side of 34 km.

PhobosAsteroid in orbit about Mars

with a diameter of 27 km.

TASK #1BUILD AN OBSERVATION LOG

An Organized Plan of the Evening’s Observations

Hardin-Simmons student using an 8" telescope on a field trip.

Hardin-Simmons 14" telescope at a public night.

Lowell Observatory 31" telescope part of NURO.

The students went to Starry Night Pro 5.0®, set it to Queen Creek, AZ at 8:30pm CST, and used its extensive database of asteroids and comets to identify which ones were above the horizon and visible to the telescope.

To find objects visible to the telescope it is best to choose them within a few degrees of the zenith (i.e., Airmass = ~1)1, and preferably with no Moon light.

1Airmass = sec(z) where z is the angle of the object off the zenith

• Build a list of visible asteroids and comets

• Look up the celestial coordinates (J2000.0)

Starry Night Pro 5.0®

Queen Creek, AZDecember 19, 20058:30pm CST

• Determine the color filters to use

• Determine the exposure times

2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 40

0.4

0.8

1.2

1.6

2

2.4

2.8

3.2

3.6

4

Semi-Major Axis (AU)

% o

f Ast

eroi

ds

HISTOGRAM OF SEMI-MAJOR AXES

Distribution of the average distances (semi-major axes) of the asteroids in the Main Belt.

The gaps in the distribution are called the Kirkwood Gaps.

To complete the Observation Log:

The Ironwood Observatory telescope has a color filter wheel with red (R), green (G), and blue (B) bandwidths. The clear filter is called luminescence (L).

For the asteroids and comets, the clear filter (L) is chosen. Two images of these objects are taken 1h apart. During that hour, the objects move more pixels along their orbital paths than the size of their individual images in pixels (i.e., their motion along their orbital paths can be seen).

Color Filters

Exposure Times

Based on the apparent magnitudes of the objects to be imaged, an exposure time can be estimated. The time is also affected by diffuse objects (e.g., dust and gas clouds).

It is possible to estimate the exposure time by taking test images and looking for pixel saturation. If there is saturation then the time can be reduced with a second round of test images.

For asteroids and comets, those with a magnitude greater than ~10, the exposure time of Δt = 120s was used. For brighter objects Δt = 90s was used.

TASK #1BUILD AN OBSERVATION LOG

An Organized Plan of the Evening’s Observations

• Build a list of visible asteroids and comets

• Look up the celestial coordinates (J2000.0)

• Determine the color filters to use

• Determine the exposure times

OBSERVATION LOG IRONWOOD OBSERVATORY NORTH (Queen Creek, AZ)

Site: Hardin-Simmons University Date: December 19, 2005 Time: 8:30pm CST

Object R.A.

hh:mm:ss.s δ

dd:mm:ss.s L

R

G

B

Δt

Notes

Gaspra

02:45:47.9

17:04:01.0

√

120s

Two images 1h apart, asteroid.

Ariadne

01:27:35.0

12:17:59.4

√

120s

Two images 1h apart, asteroid.

Helena

23:24:52.3

02:59:10.4

√

120s

Two images 1h apart, asteroid.

Julia

01:03:28.4

31:06:30.8

√

90s

Two images 1h apart, asteroid.

LINEAR Comet 2003 K4

02:41:00.1

-11:33:38.3

√

120s

Two images 1h apart, comet.

M 74

N/A

N/A

√

√

√

90s

Three color images, spiral galaxy.

M 79

N/A

N/A

√

√

√

90s

Three color images, globular cluster.

M 31

N/A

N/A

√

10s

Shut down. Point telescope to the west.

Filters

M 74 (spiral galaxy), M 79 (globular cluster), and M 31 (spiral galaxy) were also included in the Observation Log.

These images are not shown in this presentation.

TASK #2TAKE THE IMAGES

After the images were taken, Aladin, a free download from the Centre de Données Astronomiques de Strasbourg (2000A&AS..143...33B), was used to view and subsequently analyze the images.

Aladin is available for download at http://aladin.u-strasbg.fr/. It can also be run online from this same site.

Field of View containing Gaspra

Saturation in a star image.

Field of View containing Ardiane

Field of View containing Helena Field of View containing Julia

Fields of View containing LINEAR Comet 2003 K4Taken 1h Apart

LINEAR Comet 2003 K4

TASK #3ANALYZE THE IMAGES

All of the asteroid and comet images were analyzed. In this presentation, only the analysis of the asteroid Helena is given.

Using Aladin the two images of Helena taken 1h apart were superimposed and blinked to find Helena.

Unknown Asteroid

Helena

A surprise was discovered in the images.

Not only does Helena appear near the center of the field of view, a second, but unknown, asteroid appears in the images.

MPCheckerHere are the results of your search(es) in the requested field(s): --------------------------------------------------------------------------------------------------------------------The following objects, brighter than V = 20.0, were found in the 15.0-arcminute region aroundR.A. = 23 24 52.3, Decl. = +02 59 10.4 (J2000.0) on 2005 12 20.13 UT:

Object R.A. Decl. Vh m s ° ' "

(101) Helena 23 24 51.1 +02 58 5912.7

(123) Brunhild 23 24 29.9 +02 59 1413.8

(80550) 2000 AK89 23 25 37.1 +02 51 1819.2

The unknown asteroid has celestial coordinates of R.A. 23:24:30 and Declination +02:59:15 at the time of the image

December 20, 2005, 3:09:23 UT.

This information was obtained using Aladin.

To determine the unknown asteroid, MPChecker at the Minor Planet Center (Harvard University) was accessed by the Internet. Helena’s celestial coordinates along with the above date and time were used. MPChecker determined all known

asteroids within a 15' radius of Helena with magnitude 20 and brighter.

MPChecker is available for online use at http://scully.harvard.edu/~cgi/CheckMP.

By comparing the celestial coordinates with Aladin, MPChecker shows that the unknown asteroid is Brunhild.

BrunhildHelena

Using Aladin the two images of Helena/Brunhild were stacked, aligned, and subtracted.

The subtraction shows the side-by-side positions of the asteroids.

BrunhildHelena

Line Parallel to the Ecliptic

The number of pixels between the side-by-side positions can be used to calculate the proper motion, which is directly related to the distance of the asteroid from Earth.

(267,267)

(292,279)

(142,273)

(164,280)

Brunhild Helena

Δp=23.1

Δp=27.7

Using Aladin, the pixel coordinates at the center of the images are determined. The length of the line segment Δp is calculated using the distance formula:

212

212 )()( yyxxp

212

212 yyxxp 2

122

12 yyxxp

Using Aladin, the header files on both images are read to get the difference in times of the exposures ΔT (hours) and

the plate scale σ ("/pixel):

ΔT = 04:36:05 UT – 03:09:23 UT = 01:26:42 = 1.445h

σ = 7.106 x 10-4 o/pixel = 2.56 "/pixel

Assuming the asteroids are at opposition (i.e., transit at midnight), the distance from the Sun in AU is found from the following formulas:

T

p

148

2

2

114

d

For a brief explanation of the Opposition Method to calculate the distance of asteroids from the Sun, refer to http://phobos.physics.uiowa.edu/curriculum/asteroids1.html.

Proper Motion

Object Δp (pixels) ΔT (hours) σ ("/pixel) β (pixels/hr) ω ("/hr) α d (AU)

Brunhild 23.1 1.445 2.56 16.0 41.0 3.6 2.1

Helena 27.7 1.445 2.56 19.2 49.2 3.0 1.7

In AU from the Sun, the distance estimates of Brunhild and Helena are given by:

Both Brunhild and Helena are known to be Main Belt asteroids. According to Starry Night Pro 5.0®, Brunhild was at 2.5 AU and

Helena at 2.3 AU from the Sun on December 19, 2005, 8:30pm CST.

In fact at the time of the observation, Brunhild and Helena were not at opposition.

The Sun and the two asteroids were separated by 85o instead of 180o at opposition.

For an explanation of the Kolena method to calculate the distance asteroids are from the Sun, refer to http://www.phy.duke.edu/~kolena/asteroid.html.

To improve the distance calculations of Helena and Brunhild given that they are not at opposition, the Kolena method is available instead:

This method assumes Earth and the asteroids have circular orbits in the same plane centered about the Sun, and the asteroids’ orbit are outside Earth’s.

The proper motion ω must be in radians/second.

λSun and λAsteroid are the celestial longitudes of the Sun and asteroid.

f(d) = 0 is a non-linear equation in d that must be solved implicitly.

T

p

AsteroidSun

)cos(

)sin(1

1)(cos)cos(

10991.1)(

2

22

7

dd

ddf

To find the celestial longitudes of the Sun and asteroid1:

1The Celestial Longitude is measured along the Ecliptic starting at the Vernal Equinox and going east. This compares to Right Ascension, which is measured along the Celestial Equator starting at the Vernal Equinox and going east.

Find the celestial coordinates (J2000.0) of the Sun and asteroid at the time of the observation.

Go to the NED Coordinate Calculator located athttp://nedwww.ipac.caltech.edu/forms/calculator.html

Set the input parameters to Equatorial and J2000.0

Set the output parameters to Ecliptic and J2000.0

Input the celestial coordinates then calculate

On December 19, 2005, at 8:30pm CST:

Starry Night Pro 5.0® gives the following celestial coordinates.

NED Coordinate Calculator gives the following celestial longitudes.

The Kolena method gives the following distances from the Sun.

Note: It is possible to use Starry Night Pro 5.0® instead of the NED Coordinate Calculator to find the angular separation between the Sun and the asteroids.

ObjectR.A.

hh:mm:ss.sδ

dd:mm:ss.s λ (o) |Δλ| d (AU)Starry Night Pro 5.0®

d (AU)

Sun 17:52:14.8 -23:24:38.3 268.2 ---- ---- ----

Brunhild 23:24:30.0 02:59:15.0 353.0 84.8 2.5 2.5

Helena 23:24:52.3 02:59:10.4 353.3 85.1 2.2 2.3

Build an Observation Log

Take the Images

Build a list of asteroidsLook up the celestial coordinates (J2000.0)Assign the luminescence filterDetermine the exposure times

Use MPChecker to Identify Unknown Asteroids (If Any)http://scully.harvard.edu/~cgi/CheckMP

Two images of each asteroid taken 1h apart

Use Aladin to Determine Δp, ΔT, σhttp://aladin.u-strasbg.fr/

Use Starry Night Pro 5.0® to Determine R.A. and δ of the Sun

Use NED Coordinate Checker to Determine Δλ http://nedwww.ipac.caltech.edu/forms/calculator.html

Calculate the Proper Motion ω

Use the Kolena Method to Calculate the Distance of the Asteroid from the Sunhttp://www.phy.duke.edu/~kolena/asteroid.html

Analyze the Images

To calculate the distances that asteroids are from the Sun:

Lawrence Hall of ScienceUniversity of California, Berkeley

Global Hands-On UniverseTM (GHOU) is an education and research program available to students with a keen interest in astronomy and astrophysics.

J. Patrick MillerDepartment of MathematicsHardin-Simmons University

Abilene, Texas