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Determining the Orbit of Near-Earth Asteroid2102 Tantalus

Congwen (Nancy) Xu, Westmont SSP 2014, Nehal Rawat, Westmont SSP 2014, and Anthony Flores, Westmont SSP2014

Abstract—Discovered in 1975, 2102 Tantalus is a PotentiallyHazardous Asteroid (PHA) with an eccentric orbit affected by thegravitational fields of nearby planets and the Sun. Using four setsof CCD images taken near solar opposition from ground-basedtelescopes, the orbital elements and trajectory of 2102 Tantaluswere determined. The FITS files were analyzed to centroid theasteroid, and the right ascension (RA) and declination (Dec)of the asteroid at each observation were determined througha Least Squares Plate Reduction (LSPR) program. Photometryperformed on the images reveals apparent magnitudes on theorder of 16.0-17.5, and the orbital elements of the asteroidwere computed. Statistical uncertainty was accounted for byfitting jackknifed data from seven observations to a Gaussiandistribution. The research indicates an eccentricity of 0.301, asemimajor axis of 1.438 AU, an inclination of 63.602, longitudeof the ascending node of 94.477, an argument of perihelion of61.425, and a time of last perihelion of JD 2456738.18.

Keywords—2102 Tantalus, NEO, Orbital Elements, PHA

I. INTRODUCTION

Potentially Hazardous Asteroids (PHA) are celestial objectswith a minimum orbit intersection distance of 0.05AU and amaximum absolute magnitude of 22.0 [1]. They are hazardousto inner solar system planets due to their eccentric orbits. PHAssuch as 2102 Tantalus (1975 YA) have the potential to collidewith the Earth as a result of gravitational perturbations fromnearby planets and stars. At the time of discovery in December1975, 2102 Tantalus approached the Earth at a distance of0.047AU [4]. The most recent close approach was observedon June 28, 2014 as seen in Figure 1. Measuring the orbitsof such asteroids is necessary for refining previous modelsof the asteroid’s orbit to determine the time, trajectory, andprobability of an Earth collision.

Fig. 1. Most Recent Close Approach of 2102 Tantalus on June 28, 2014 [5]

This paper studies the orbital dynamics of 2102 Tantalusthrough local observations from the 14-inch Meade and 0.6-mKeck telescopes in Santa Barbara, California. Remote obser-vations were also taken from the Prompt 1, Prompt 2, andPrompt 8 telescopes at the Cerro Tololo Observatory in LaSerena, Chile. The CCD images were processed to centroidthe asteroid in each of the FITS file arrays, and a LeastSquares Plate Reduction (LSPR) program determined the rightascension (RA) and declination (Dec) of 2102 Tantalus whileaccounting for statistical uncertainty. The orbital elements ofthe asteroid were computed with the Method of Gauss throughmultiple computational iterations. Our results advance thecurrent understanding of 2102 Tantalus’ long-term trajectoryas well as provide an improved model of its orbit.

II. METHODS FOR DATA COLLECTION AND ANALYSIS

A. Observation SpecificationsTh CCD images were taken from two observatories with five

different telescopes. The specifications of each observatory areshown in Table I.

TABLE I. OBSERVATORY AND TELESCOPE SPECIFICATIONS

Observatory Location LatitudeLongitude

Telescope Field of View

WestmontCollege

G60 N 34 26’ 59.24”W 119 39’ 33.59”

0.6m Keck 17’ x 17’

WestmontCollege

G60 N 34 26’ 59.24”W 119 39’ 33.59”

14in Meade 20’ x 16’

Cerro TololoObservatory

807 S 30 10’ 03.50”W 70 48’ 19.40”

Prompt 1 10’ x 10’

Cerro TololoObservatory

807 S 30 10’ 03.50”W 70 48’ 19.40”

Prompt 2 21’ x 16’

Cerro TololoObservatory

807 S 30 10’ 03.50”W 70 48’ 19.40”

Prompt 8 22.6’ x 22.6’

The STL-1001E Charge-coupled Device (CCD) used at themain 0.6m Keck telescope in Westmont College has a 1024 x1024 pixel array (24.6 mm x 24.6 mm). The device was usedwith a pixel scale of 1 arcsecond/pixel. The STL-1301E CCDused at the 14” Meade telescope at the Westmont Campushas a 1280 x 1024 pixel array (20.5mm x 16.4 mm) thatencompasses 1.3 million pixels 16 x 16 microns in size [3].Both types of CCD cameras allow for 1x1, 2x2, and 3x3

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binning, which were experimented with throughout differentobservation sessions for the best quality images.

Three telescopes in Chile were also available for use throughthe Cerro Tololo Observatory(CTIO). Proposals were sent tothe Prompt 1, Prompt 2, and Prompt 8 telescopes for remoteimage collection. Of the three telescopes, Prompt 8 has thelargest pixel scale at 0.663 arcseconds/pixel compared to the0.59 arcsecond/pixel scale of both Prompt 1 and Prompt 2 [6].Default binning is 1x1 binning. All three of these telescopeshave a diameter of 16” [7].

B. Observation PreparationFor each observation, the approximate Right Ascen-

sion (RA), Declination (Dec), and Apparent Magnitude ofthe asteroid were found through the JPL Horizons web-site(http://ssd.jpl.nasa.gov/horizons.cgi) from the beginningtime of observation to the end time with 10 minute intervals.The Hour Angle (HA) at the beginning of observation wascalculated using the Local Sidereal Time (LST) and RightAscension.

HA = LST −RA (1)

Star Finder Charts were also included according to thetelescopes’ field of view to help locate the asteroid relativeto nearby stars used as references. These charts were foundfrom the USNO Database [2].

C. Asteroid LocationUsing the Hour Angle and Declination estimates, the rough

position of the asteroid in the sky was determined. A bright starwithin 30of the asteroid’s position was located in order to do apointing calibration of the telescope. The telescope was slewedto the reference star and the star was centered in the telescope’sfield of view. Images were taken and focused using CCDSoft’sfocusing tools. After the telescope pointing calibration wasset, the telescope was moved to the target asteroid’s field ofview. A subframe of the field of view was selected, continuousimages were taken with a 2-5 second exposure time, and thefocus was adjusted using the DFM control paddle. Fine focuswas achieved when the stars in the subframe were as smalland radially symmetric as possible. The subframe option wasthen dechecked to view the entire image selection, which wasmatched with the star patterns on the Sky6 chart and comparedto the star finder charts to determine the exact location of theasteroid.

D. CCD ImagesA total of four independent measurable observations were

made from June 15, 2014 to July 30, 2014. For each obser-vation, multiple sets of images were taken, with at least 3sets of 5 images each. There was a 5-10 minute time spanbetween successive image sets, which was used to identify thelocation of the asteroid in the imageby tracking the asteroid’smovement. Five images were taken in rapid succession ineach set to ensure that temporary disturbances such as cosmic

rays could be eliminated through median combination of theimages. Only one of the three sets from each observation wasused in the final measurements to determine RA and Dec.

The exposure time and binning of the image sets variedbased on the magnitude and rate of the asteroid at the timeof observation. Small exposure time reduced the likelihoodof streaking in the images but also led to fainter images.Likewise, a large binning (3x3) prevented streaking but alsogreatly increased the uncertainty of the measurements. Theexposure time and binning of the images are shown in TableII.

TABLE II. EXPOSURE TIME AND BINNING FOR OBSERVATIONS

Observation Exposure Time Binning

Keck1 30.0 seconds 2 x 2

Keck2 10.0 seconds 1 x 1

Keck3 30.0 seconds 2 x 2

Chile1 20.0 seconds 1 x 1

III. DATA ANALYSIS

A. Centroid

After the images were taken, they were edited and analyzedin MaxIm DL imaging software. Once the asteroid was located,its brightest pixel was taken for centroid calculation. A centroidprogram took this brightest pixel and constructed a squareaperture of count values around it. From the aperture, aweighted average of all the counts was taken to determinethe center of the object in question based on the brightness ofthe surrounding pixels.

B. Least Squares Plate Reduction

In order to calculate the RA and Dec of the asteroid, itscentroid in the CCD images was compared to 8 surroundingreference stars in the same field of view. Using TheSkyXsoftware, each reference star was located in the UCAC3database and the known right ascension and declination wasrecorded. Afterwards, the centroid of each reference star wastaken from the original image in order to calculate the platecoefficients needed to solve for the RA and Dec of a particularobject in the same image, given by the formulas:

α = b1 + a11X + a12Y (2)

δ = b2 + a21X + a22Y (3)

where[Σαi

Σαi ∗ xiΣαi ∗ yi

]=

N Σxi ΣyiΣxi Σx2

i Σxi ∗ yiΣyi Σxi ∗ yi Σy2

i

∗ [ b1a11

b12

](4)

and

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[Σδi

Σδi ∗ xiΣδi ∗ yi

]=

N Σxi ΣyiΣxi Σx2

i Σxi ∗ yiΣyi Σxi ∗ yi Σy2

i

∗ [ b2a21

b22

](5)

When the x and y coordinates of the asteroid’s centroidwere entered into the transformation equation, its RA and decwere returned, as well as the residuals in the RA and Dec ofeach individual star and the uncertainty of the overall platecoefficients.

C. Method of GaussIn this research, the Method of Gauss was used to determine

the orbit of the asteroid. First the position and velocity of theasteroid in Ecliptic coordinates were calculated.

To determine the position vector of the asteroid, the fun-damental vector triangle for objects orbiting the Sun is used(Fig2):

Fig. 2. Vector Triangle

whereρρ = r + R (6)

Once the Right Ascension and Declination of the asteroidat each observation time (i= 1, 2, 3) were calculated, the valueof ρi was determined through Equation 7.

ρi =

[cosαicosδisinαicosδisinδi

](7)

The position of the asteroid can be determined at any timeusing the f and g series, where time is in modified time(Equation 8):

r(τ) = fr2 + gr2 (8)

Once the position vector is determined, the velocity vectorcan also be calculated using Equation 9:

r2 =f3

(g1f3 − g3f1)r1 −

f1

(g1f3 − g3f1r3 (9)

Using several iterations of the Method of Gauss until ρ2

converged, more accurate values of the position vector and the

velocity vector were calculated, resulting in the vector orbitalelements for the time of the second observation. These resultsare in equatorial coordinates 1 and need to be converted toecliptic coordinates before the classical orbital elements canbe calculated.

D. Classical Orbital Element CalculationsThe classical orbital elements used to determine the orbit

of the asteroid are as follows:

a - Semimajor axise - Eccentricity of the orbiti - InclinationΩ - Longitude of the ascending nodeω- Argument of the perihelionT - Time of perihelion passage

The values of the orbital elements were calculated basedon Kepler’s Equations, gravitational motion, and classicalNewtonian mechanics. The semimajor axis was calculatedusing the vis-viva equation (Eq 10):

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a=

2

r− v2

µ(10)

The eccentricity was calculated as the magnitude of the eccen-tricity vector (Eq 11):

~e = (~r0x~h

µ− ~r0

|r0|) (11)

The inclination was calculated as(Eq 12):

cosi =~h · zh

(12)

where ~h is given by (Eq 13):~h = ~r0 × ~r0 (13)

The longitude of the ascending node was given by (Eq 14):

cosΩ =Nx

| ~N |(14)

where ~N is given by Eq. 15

~N = z × ~h (15)

The argument of the perihelion can be computed as (Eq 16):

cosω =Nx

| ~N |(16)

The time of perihelion passage was computed using themean anomaly (M) and the eccentric anomaly (E) throughEuler’s method.

1Equatorial coordinates are 3-dimensional Cartesian coordinates where thexy plane is an extension of the equatorial plane of the earth and the z-axis isan extension of the North pole. The x-axis points in the direction of the sunslocation on the celestial sphere at vernal equinox.

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E. Statistical Analysis

In order to calculate the true values and uncertainty ofthe data, the data from the observations were used in thejackknife method along with three sets of observations fromanother team to find the mean value and standard deviationof the classical orbital elements. The seven observations usedfor the jackknife method are shown in Table III. The orbitalelements were computed for each possible subgroup of threeobservations. The resulting values were then fit to a Gaussiandistribution. The mean and standard deviation were computedfor each value from the 35 observation combinations. Sevenobservations were used to provide a larger sample set for bettermeasurement uncertainty and precision.

TABLE III. SEVEN OBSERVATIONS USED FOR THE JACKKNIFEMETHOD AND COMPUTING THE CLASSICAL ORBITAL ELEMENTS

Observation JD Time RA(decimalhours)

Dec(decimaldegrees)

Latitude(decimaldegrees)

Longitude(decimaldegrees)

1 2456834.80 16.096 37.381 34.448 -119.663

2 2456850.78 15.308 1.778 34.448 -119.663

3 2456861.71 15.124 -14.501 34.448 -119.663

4 2456863.54 15.110 -16.570 -30.168 -70.805

5 2456841.85 15.642 20.679 34.448 -119.663

6 2456855.72 15.201 6.482 34.448 -119.663

7 2456859.72 15.144 -12.055 34.448 -119.663

F. Photometry

The images for each observation were used to calculate theapparent magnitude of the asteroid. For each image, TheSkyXsoftware was used to determine the apparent magnitude of areference star within the field of view of the asteroid. Thesoftware used the selected star as a calibration point fordetermining apparent magnitude of the asteroid. This wasperformed by summing the counts within the aperture of thestar. An annulus around the star was used to determine thebackground count, which was then subtracted from the sumof the star and background count to give the star count.

IV. RESULTS

A. Images

Four groups of measurable CCD images were obtainedthrough the individual observations. Each group of CCDimages was composed of at least 3 sets with at least 5images per set. The image set used for processing was chosenbased on the number of available reference stars near theasteroid. Other considerations included the image set qualityand the presence of potentially disturbing nearby objects.When possible, the median combined image of a given set wasused for measurements, although single images from sets wereused when streaking was present in the median combined ones.This phenomenon occurred for long exposure times, which wasgenerally avoided. Table IV categorizes the images that wereused from each set for measurement.

TABLE IV. IMAGES USED FOR MEASUREMENT

Observation Time Set # Image #

Keck1 2014-06-26 07:12:56.962 UT 3 5

Keck2 2014-07-12 06:44:15.00 UT 2 Median Combined

Keck3 2014-07-23 05:14:43.16 UT 2 Median Combined

Chile1 2014-07-25 01:01:55 UT 5 Median Combined

The corresponding inverted CD images are displayed inFigures 1-4.

Fig. 3. Keck 1 Image

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Fig. 4. Keck 2 Image

Fig. 5. Keck 3 Image

Fig. 6. Chile 1 Image

B. Image ProcessingAfter determining the centroid of the asteroid in each of

the four image sets, a Least Squares Plate Reduction wasperformed on the asteroid and eight surrounding stars. Byminimizing the value of the chi-squared sum of a linearregression, the RA and Dec of the asteroid was determined.All images used had an RA and Dec residual on the order ofless than or equal to 10−4 degrees for the asteroid. This cutoffwas used to ensure the precision of the measurements 2. Theresults are shown in Table V.

TABLE V. CENTROID AND LSPR RESULTS

Observation Centroid pixel RA Dec

Keck 1 (326.01, 396.99) 16h 05m 43.62s +3722’ 51.23”

Keck 2 (550.99, 776.00) 15h 18m 30.09s +0146’ 41.08”

Keck 3 (289.01, 227.00) 15h 07m 25.43s -1430’ 04.32”

Chile 1 (494.91, 148.26) 15h 06m 34.50s -1634’ 13.50”

C. Classical Orbital ElementsThe classical orbital elements were computed based on the

RA and Dec of the asteroid in seven observations. The finalcomputed orbital elements are the mean value of the orbitalelements from 35 jackknifed sets of three observations each.Table VI displays computed orbital elements.

2See appendices for LSPR residuals

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TABLE VI. 2102 TANTALUS ORBITAL ELEMENTS

OrbitalElement

Mean Value Standard Deviation

a 1.438 0.342

e 0.301 0.007

i 63.602 2.665

Ω 94.477 1.051

ω 61.425 14.615

T 2456738.18 8.570

TABLE VII. 2102 TANTALUS ORBITAL ELEMENTS COMPARED TOJPL VALUES

OrbitalElement

Mean Value Standard De-viation

JPL Values JPLUncertainty

a 1.4379 0.3417 1.2900 1.04E-09 AU

e 0.3014 0.0067 0.2991 6.24E-08

i 63.6018 2.6647 64.0077 1.69E-05

Ω 94.4769 1.0509 94.3731 6.94E-06

ω 61.4251 14.6153 61.5443 1.79E-05

T 2456738.176 8.5701 2456737.7682 2.20E-05 JED

D. Photometry

TABLE VIII. PHOTOMETRY (APPARENT MAGNITUDEMEASUREMENTS)

Observation Reference Star ApparentMagni-tude ofStar

ApparentMagni-tude ofAsteroid

Keck 1 UCAC3 255:114437 16.22 16.68

Keck 2 UCAC3 184:122929 16.03 16.84

Keck 3 UCAC3 152:152928 14.83 17.58

Chile 1 UCAC3 147:146961 15.59 17.86

E. Ephemeris Generation Check

Unfortunately, the ephemeris generation using calculatedorbital elements produced similar RA values to those expectedbut the generated declination was extremely different fromwhat was originally observed.

TABLE IX. EPHEMERIS GENERATION CHECK COMPARISON:OBSERVED VS. PREDICTED VALUES

Time(JD)

RA Observed DecObserved

RA Calculated DecCalculated

2456861.72 15h 07m 25.43s -14 30’ 4.32 15h 10m 47.4s 2 58’ 6.1”

V. DISCUSSION

In order to calculate the classical orbital elements of 2102Tantalus, sets of images were taken from 4 observationsspanning from June 15, 2014 to July 30, 2014. Unfortunately,due to inclement weather in the middle of this time period,most images were recorded either at the very beginning ofthe period or the very end. As a result of this, some of theobservations used in the jackknife method for determining theclassical orbital elements were close in time. This resulted invalues that greatly differed from those predicted by JPL. On theother hand, data from observations that occurred on oppositeends of the time period resulted in values of classical elementsthat were closer to JPL predictions. The effect of this variationwas mitigated as the sample size of the data increased, allowingthe data to be fit to a Gaussian model more accurately.

Moreover, when using the jackknife method on observationstaken only a few Julian days apart, the orbital determinationprogram failed to converge on a plausible value. Therefore,while the jackknife method should have resulted in 35 datapoints, only 34 could be used because the incorrect conver-gence resulted in a data value. This was not a statistical outlier.

Additionally, due to Tantalus’s speed, not all data were takenfrom combined image sets. For example, when a thirty secondexposure time in the Keck1 set caused 2102 Tantalus to streak,a single image instead of a median combined image had tobe taken for analysis. While this increased the possibility ofa cosmic ray saturating the image, extreme care was taken tochoose an image from the third set where Tantalus was a singledistinguishable point and no cosmic rays or other pollutingsources were present.

VI. CONCLUSION

According to the calculated orbital elements, 2102 Tantalushas a semi-major axis(a) of 1.438AU with a standard deviationof 0.342AU, an eccentricity of orbit of 0.301 with a standarddeviation of 0.007, an angle of inclination of 63.602 with astandard deviation of 2.665, a longitude of the ascending nodeof 94.477 with a standard deviation of 1.051, an argumentof perihelion of 61.425 with a standard deviation of 14.615,and a time of last perihelion of JD 2456738.18 with a standarddeviation of 8.57 Julian days.

Although the values are not entirely consistent with the JPLOrbital Elements, the observations lend greater understandingto the trajectory and orbit of 2102 Tantalus. The uncertaintiesare larger than ideal despite small LSPR residuals. Possibleerror could have derived come from inaccurate convergenceof the OD program for observations that were too close inJulian date. However, the effect of this phenomenon wasminimized by the jackknife method. Some selected reference

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stars radially spread around the asteroid were not used becausethey were unavailable in TheSkyX database. In this case,alternate reference stars were selected instead.

Compared to the JPL ephemerides, the RA and Dec ofthe asteroid as determined by the calculated classical orbitalelements were similar to the values in the database. Thecalculated declination deviated from the JPL value more thanthe RA. This is most likely due to the inconsistency betweenJPL and the calculated values for the semimajor axis. Theother orbital elements were extremely close in value to the JPLvalues and corroborate the database’s predictions (see TableVII).

Furthermore, alternate methods to determine the orbit of theasteroid such as the Method of Laplace or using the Methodof Gauss with higher orders of the f and g series can improvecalculated results.

APPENDIX ALSPR RESIDUALS

TABLE X. KECK 1 RESIDUALS

Target Ob-ject

RA Dec σRA σDec

Asteroid 16h 05m 43.62s +37 22’ 51.23” 0.04337s 0.2623”

Ref 1UCAC3255:114500

16h 06m 18.27s +37 20’ 29.09” -0.01512s 0.1439”

Ref 2UCAC3255:114450

16h 05m 37.45s +37 21’ 31.01” -0.0070s -0.0408”

Ref 3UCAC3255:114483

16h 05m 59.14s +37 23’ 05.86” 0.0575s -0.1692”

Ref 4UCAC3255:114466

16h 05m 46.87s +37 25’ 18.21” -0.0291s 0.1186”

Ref 5UCAC3255:114440

16h 05m 24.48s +37 26’ 32.72” -0.0416s -0.3219”

Ref 6UCAC3255:114430

16h 05m 18.14s +37 26’ 23.70” 0.0331s 0.2733”

Ref 7UCAC3255:114482

16h 05m 58.50s +37 27’ 06.92” 0.0339s 0.2225”

Ref 8UCAC3255:114490

16h 06m 07.83s +37 25’ 52.77” -0.0316s -0.2264”

TABLE XI. KECK 2 RESIDUALS

Target Ob-ject

RA Dec σRA σDec

Asteroid 15h 18m 30.09s +01 46’ 41.08” 0.0191s 0.6042”

Ref 1UCAC3184:122914

15h 18m 31.29s +01 46’ 11.14” 0.0119s -0.2053”

Ref 2UCAC3184:122873

15h 18m 17.18s +01 47’ 55.93” 0.0237s -0.0119”

Ref 3UCAC3184:122867

15h 18m 15.56s +01 48’ 06.53” 0.0178s -0.1383”

Ref 4UCAC3184:122840

15h 18m 06.39s +01 48’ 25.71” -0.0070s 0.0549”

Ref 5UCAC3184:122843

15h 18m 07.38s +01 47’ 25.47” -0.0156s -0.2366”

Ref 6UCAC3184:122856

15h 18m 11.39s +01 42’ 42.74” -0.0066s 0.9933”

Ref 7UCAC3184:122870

15h 18m 16.48s +01 42’ 34.14” -0.0027s -0.7823”

Ref 8UCAC3184:122935

15h 18m 36.00s +01 49’ 35.02” -0.0216s 0.3261”

TABLE XII. KECK 3 RESIDUALS

Target Ob-ject

RA Dec σRA (hr) σDec

(deg)

Asteroid 15h 07m 25.43s -14 30’ 4.32” 1.1764e-05 0.0001307

Ref 1UCAC3152:152928

15h 07m 20.54s -14 29’ 45.57” -1.2437e-05 -0.0001390

Ref 2UCAC3152:152909

15h 07m 11.94s -14 29’ 55.60” 4.1622e-06 -5.1605e-05

Ref 3UCAC3152:152901

15h 07m 06.13s -14 28’ 05.67” -1.2466e-05 0.0002100

Ref 4UCAC3152:152899

15h 07m 05.15s -14 26’ 47.97” 1.2684e-05 -8.8184e-05

Ref 5UCAC3151:157820

15h 07m 14.71s -14 32’ 41.02” -1.1402e-06 -4.4892e-05

Ref 6UCAC3151:157841

15h 07m 27.86s -14 32’ 49.98” 1.2299e-05 9.1443e-05

Ref 7UCAC3151:157854

15h 07m 34.53s -14 31’ 42.27” -6.3594e-06 -4.4953e-06

Ref 8UCAC3152:152962

15h 07m 34.70s -14 27’ 56.05” 3.2587e-06 2.5931e-05

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TABLE XIII. CHILE 1 RESIDUALS

Target Ob-ject

RA Dec σRA (hr) σDec

(deg)

Asteroid 15h 06m 34.50s -16 34’ 13.50” 5.0264e-06 5.5884e-05

Ref 1UCAC3147:146952

15h 06m 33.53s -16 33’ 46.64” 9.162e-06 0.00011

Ref 2UCAC3147:146945

15h 06m 28.96s -16 33’ 36.66” -6.0785e-07 -3.987e-05

Ref 3UCAC3147:146940

15h 06m 26.84s -16 32’ 30.73” 1.9408e-07 -1.237e-05

Ref 4UCAC3147:146950

15h 06m 31.97s -16 35’ 12.74” -1.1353e-07 -1.7407e-05

Ref 5UCAC3147:146933

15h 06m 23.12s -16 35’ 18.45” -4.0644e-06 -7.1762e-06

Ref 6UCAC3147:146970

15h 06m 41.92s -16 33’ 59.17” 9.5395e-07 -1.7507e-05

Ref 7UCAC3147:146978

15h 06m 45.44s -16 33’ 00.09” -4.9148e-06 -1.8593e-05

Ref 8UCAC3148:145844

15h 06m 22.02s -16 29’ 46.13” -6.0978e-07 -4.9114e-07

ACKNOWLEDGMENT

Thank you to the SSP faculty and staff for providing theinstruction, resources, and support necessary for completingthis research report. Special thanks to Dr. Michael Faison, Dr.Cassandra Fallscheer, Ms. Martinez and TAs Andrew, Daksha,Christine, and James.

REFERENCES

[1] National Aeronautics and Space Administration, NEO Groups, Near-Earth Object Program. Web. 26 July 2014. http://neo.jpl.nasa.gov/neo/groups.html

[2] US Naval Observatory, USNO Image and Catalogue Data, USNO Imageand Catalogue Data. Web. 26 July 2014. http://www.nofs.navy.mil/tmp/fch6ScjEQ fch.html

[3] Santa Barbara Instrument Group, Model STL-1301e Typical Specifica-tions, STL-1001E Operating Manual. Web. 26 July 2014.

[4] Jet Propulsion Laboratory, 2102 Tantalus (1975 YA), JPL Small-BodyDatabase Browser. Web. 26 July 2014. http://ssd.jpl.nasa.gov/sbdb.cgi?sstr=2102+Tantalus

[5] Jet Propulsion Laboratory, Orbit Diagram: 2102 Tantalus (1975 YA),JPL Small-Body Database Browser. Web. 26 July 2014.

[6] SKYNET, Our Telescopes, SKYNET: Our Scopes. Web. 26 July 2014.http://skynet.unc.edu/index.php?selection=telescopes

[7] University of North Carolina, Introduction to SKYNET, PromptTelescopes. Web. 26 July 2014. http://user.physics.unc.edu/∼reichart/ASTR101L-1.pdf