SIERRA COLLEGE OBSERVATIONAL ASTRONOMY

LABORATORY EXERCISE

NUMBER III.F.a. TITLE: ASTROMETRY OF ASTEROIDS COMPUTER

EXERCISE FROM C.L.E.A. PROJECT, Section I

DATE- PRINT NAME/S AND INITIAL BELOW: GROUP

DAY-

LOCATION

OBJECTIVE:

Use CCD images and a computer to determine:

· The presence of an asteroid.

· Review equatorial coordinates and determine precise RA and Dec of asteroid utilizing reference stars in the Hubble Space Telescope Guide Star Catalog (GSC)

· Distance to an asteroid via its parallax.

· The angular and tangential velocity of an asteroid.

Observe an asteroid with a small telescope if conditions permit.

DESCRIPTION:

Asteroids or minor planets are celestial bodies which orbit the sun much like planets. They are quite small, most of them kilometer size or smaller, and appear as a starlike objects through a telescope or on a photographic or electronic image. They are detected by their motion against a 'fixed' star background. Comparing photographs taken of the same region of sky over a few hours can reveal the presence of these lesser bodies of the solar system. In this exercise you will be given CCD (Charged Coupled Device) digital images of a small region of sky containing the asteroid 1992JB. These images were made at the National Undergraduate Research Observatory using the Lowell Observatory O.8m f/15 telescope.

Asteroids are of popular importance in that some of them have orbits which carry them very close to Earth. Although such an event is unlikely, Earth collisions with larger asteroids (km size) could have devastating effects. Therefore it would be wise to monitor them whenever possible and keep track of their whereabouts. For more information check your lecture textbook.

PROCEDURE -COMPUTER OPERATION AND MEASUREMENTS

The essential parts of this exercise (computer, software, calculations) to accomplish the above objectives are found in the steps below. Instructor will explain. Take Notes!

I. Detecting the asteroid 1992JB & determining RA and DEC

a. Open CLEA-Asteroids (double click 'cc' mouse on proper icon)

c-File, Login

c-x (close student accounting, you don't need to log in)

b. Load Images to Blink

c-File, Load, Image 1

cc-92jb05

c-File, Load, Image 2

cc-92jb07

c. Set up images to blink

c-lmage, Blink

Select stars for image positioning by following instructions in dialog boxes for both images 1 and 2.

d. To Blink

c-Blink

Notice the position change of the asteroid. Use the space provided below to make an accurate sketch of the star field with the asteroid plotted in both positions.

Label asteroid in image 1 and 2 as '05' and '07' respectively on your sketch. North is up and East is to the left.

e. Stop Blink and Measure RA and Dec

c-Stop

c-Identify Target

A dialog box will appear to identify 'Target' which is the asteroid.

Do this for image 1 and 2.

f. Measure and Record RA and DEC of asteroid in images 92jb05 and 92jb07

c-Image, Measure, Image 1.

A 'observation parameter” dialog box will appear.

Enter 92jb05 as the Obs. Name/ID of image 1

c-OK

A 'field parameter' dialog box will appear.

Enter the RA and DEC of the image center (verify values if fields are not blank, compare with the values at the top of the ASTROMETRIC DATA TABLE.)

This coordinate for all images containing the asteroid is given in the ASTROMETRIC DATA TABLE.

Enter '8' in the Field size box (should be the default).

This tells the computer to access a field map 8' arc on a side from the Guide Star Catalog (GSC). A Mag. limit of 20 is ok.

c-OK

A small star field segment of the GSC will appear on the left. Image

1 will appear on the right. Although the scale of both star field and image are not the same, identify a pattern of stars that is recognized in both.

Find at least three stars and follow instructions in dialog boxes.

There may be a greater number of stars in the CCD image on right since it contains stars dimmer than the GSC displays for that region.

After completing the matching process, the computer will determine the RA and DEC of the asteroid "Target" for image 1.

c-OK to accept solution.

c-YES to record measurement.

c-OK until you close window and return to main display

Now, carefully, repeat procedure 'f' for image 2 to determine RA and DEC of asteroid's new position and record coordinate for '92jb07’ under 'Report'.

g. Repeat the above steps (b - f) for the rest of the images of asteroid 1992 JB.

Allow image 1 to remain as 92jb05 and replace image 2 (one at a time) with 92jb08, 09, 10, 12, & 14. This is done by c-File c-Load Image Files c-Image2 and selecting the appropriate file. You will not only have to mark the alignment stars on the right side image, but also the Target asteroid.

Carefully plot each new position of the asteroid on your sketch. Be sure each position of the asteroid is labeled appropriately as 05,07,08,09,10,12,14.

In BlueBook: Notice the asteroid does not appear to move as much in some intervals. Why do you suppose this is so?

SKETCH OF STARFIELD AND ASTEROID MOVEMENT

h. When you have completed blinking and measuring all images, open 'Report' and download (via pencil) all the astrometric results to complete table below.

ASTROMETRIC DATA TABLE

Astrometric Data for Asteroid 1992JB								All Images Taken on 5/23/1992
Image UT at mid exposure All images centered at RA = 15h 30m 44.3s											DEC = 11d 15' 10.4"
Image	Obs. U.T. (h, m, s)				RA				DEC			App. Mag.
92jb05	04	53	00	15 h	30 m	38.70 s	º		′	″
92jb07	05	03	00
92jb08	05	09	00
92jb09	06	37	30
92jb10	06	49	00
92jb12	06	57	00
92jb14	07	16	00

SIERRA COLLEGE OBSERVATIONAL ASTRONOMY

LABORATORY EXERCISE

NUMBER III.F.b. TITLE: ASTROMETRY OF ASTEROIDS COMPUTER

EXERCISE FROM C.L.E.A. PROJECT, Section II

DATE- PRINT NAME/S AND INITIAL BELOW: GROUP

DAY-

LOCATION

Section I of this lab exercise begins 4 pages back

II. Detecting the parallax of an asteroid.

On May 23, 1992 at 06:57 UT, two images were recorded of Asteroid 1992JB, one from Hamilton, NY (Colgate Univ.) and the other from Flagstaff, AZ (Lowell Observatory). The projected baseline between these two sites is 3172 km.

Using techniques learned earlier in this exercise, load 'Asteast' as image 1 and 'Astwest' as image 2. Blink image 1 and 2 to detect any parallax of the asteroid. Notice as you blink from 1 to 2, which way (east, west, north, south)

the asteroid appears to shift.

Measure the RA and DEC of the asteroid in both images and record results below:

Image 1 (Asteast) RA = 15 h 30 m _37.72 s DEC = _11_º _15_′ _36.1_″

Image 2 (Astwest) RA = 15 h 30 m _38.69_ s DEC = _11_º _15_′ _41.2_″

Except for rechecking some of your results, you are finished with the computer.

Leave it on so that you may refer back to your REPORT file. Use the 'WORKSHEET' for calculations and analysis.

III. CALCULATE THE ANGULAR VELOCITY μ of the asteroid, where Δθ is the change in position in seconds of arc, and Δt is the elapsed time in seconds.

μ = Δθ/Δt

Enter the RA, DEC, and UT of 92jb05 and 92jb14 found in the

Astrometric Data Table (above) on the worksheet in Table 1.

Calculate the differences in time (in seconds), DEC

(in seconds of arc) and RA (in seconds of time).

Convert RA seconds of time to seconds of arc by multiplying by 15. Adjust the RA arc angle for declination by multiplying the arc second difference by cosine (DEC), in this case the DEC for the CCD image field center or approximately 11.25 degrees.

Noting that the displacement in RA and DEC represent two legs of a right triangle, calculating the length of the hypotenuse will yield the change in position (Δθ). This can be accomplished by using the Pythagorean theorem. However, if you notice a very small or negligible change in either RA or DEC, the 'theorem' may not be necessary. So check it out before you beat yourself up with the arithmetic!

IV. DETERMINE THE PARALLAX of the asteroid by noting the displacement of target in images Asteast and Astwest using a method similar to that used above. Enter information in Table 2, of WORKSHEET. Express baseline in km and parallax in arc seconds. Calculate the distance to the asteroid.

V. CALCULATE THE TANGENTIAL VELOCITY using calculations in Table 1 & 2.

This is the velocity of the asteroid across (perpendicular) our line of site.

NAME/S _______________________________________________ GROUP

CALCULATIONS AND ANALYSIS WORKSHEET

TABLE 1 – CALCULATING ANGULAR VELOCITY ‘μ’

SELECTED FROM ASTROMETRIC DATA TABLE
Image		RA			DEC			UT
	h	m	s	º	′	"	h	m	s
Differences in RA and DEC and UT
Differences in RA (seconds of RA)			s	ΔDEC (")		"	Δt(s)		s
RA Difference x 15"/s			"	Δθ =		μ =
x cos 11.25° =		ΔRA	"

cos 11.25° = ______________

_______________

Δθ = √ ΔRA² + ΔDEC²

ΔDEC Δθ

ΔRA

TABLE 2 – CALCULATING PARALLAX AND DISTANCE

Parallax Images Astwest and Asteast
image	RA			DEC
	h	m	s	°	′	"
Difference in RA and Dec
Difference in RA (sec)			s	ΔDEC (")		"
RA x 15^″^/^s			"	Δt = 0
Corrected for DEC ΔRA			"	Baseline = 3172km

_______________

parallax = √ΔRA² + ΔDEC² = ________″

Distance to Asteroid = ______________ km. (Show work on previous page)

Tangent Velocity V_t = _______________ km/sec. (Show work on previous page)

QUESTIONS AND ANALYSIS

1. What constellation did 1992JB occupy on May 23, 1992, and what direction was it traveling across the celestial sphere? Is this asteroid visible to the unaided eye? How about in small telescope or binoculars?

2. Given the date and times of the images, was 1992JB near the Flagstaff, AZ local meridian around midnight? Flagstaff is in the MST zone or UT - 7hours.

3. What does this imply about its celestial motion (direct or retrograde)? Check out the RA progression in images 92jb05 - 14. Does this fit? Does this place the object near opposition?

4. If the asteroid is near opposition, where would its computed distance put it relative to the orbit of Mars? The average Earth-Sun distance is 149,600,000 km and the average Mars-Sun distance is 227,900,000 km.

5. Given the computed distance to the asteroid, do you think 1992JB is a 'belt' asteroid?

6. What factor are we neglecting if we interpret the asteroid’s tangential velocity as its orbital velocity?