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Direct determination of NEO distance by parallax
Monty Robson
John J. McCarthy Observatory, USA
Peter Birtwhistle
Great Shefford Observatory, UK
Kuffner Observatory, Vienna
Friday 12 May 2006
932
McCarthy Observatory
New Milford, Connecticut
USA
J95
Great Shefford Observatory
West Berkshire
England
Dr. Brian Marsden
Director, MPC
Lisa Glukhovsky
Winner 2003 Intel ISEF
Project statistics•From 2004 11 26 until 2006 01 28 there were 24 near simultaneous observation pairs reported to the MPC of 9 different newly discovered Near Earth Asteroids
• 3 NEOCP objects were observed
• Closest NEO range = 0.047 AU
• Most distant range = 0.313 AU
• Mean range error = 0.41% (derived range vs. JPL range)
•Mean residual of reported observations = 0.35"
• Mean timing error = 0.36 s
Observations932 - J95 NEA Ranging Project
Summary of Reported Observations
Object Date Time Derived Range, km JPL Range, km JPL uncert. JPL Range, AU Range Diff. % JPL-Derived, km2004 VB 2004 11 26.957295 8,727,000 8,798,573 175 0.058815 0.813 71,573
2004 11 26.961465 8,748,000 8,797,961 175 0.058811 0.568 49,9612004 11 26.966325 8,747,000 8,797,250 175 0.058806 0.571 50,250
2004 XJ 2004 12 03.03611 7,029,000 7,049,230 36,060 0.047121 0.287 20,2302004 12 03.03993 7,056,000 7,050,016 36,060 0.047126 0.085 -5,9842004 12 03.05590 7,094,000 7,053,312 36,060 0.047148 0.577 -40,688
2004 VD17 2004 12 03.07164 46,392,000 46,783,045 68 0.312725 0.836 391,0452004 12 03.07708 46,411,000 46,791,791 68 0.312784 0.814 380,791
2004 YR 2005 01 02.04063 28,411,000 28,595,515 417 0.191149 0.645 184,5152005 01 02.06563 28,563,000 28,584,975 417 0.191079 0.077 21,9752005 01 02.06986 28,425,000 28,583,195 417 0.191067 0.553 158,195
2005 CC37 2005 02 07.017365 12,760,000 12,680,403 12,986 0.084763 0.628 -79,5972005 02 07.021255 12,650,000 12,683,065 12,986 0.084781 0.261 33,0652005 02 07.025005 12,653,000 12,685,625 12,986 0.084798 0.257 32,625
2005 CR37 2005 02 20.04306 13,482,000 13,444,281 12 0.089869 0.281 -37,7192005 02 20.04653 13,458,000 13,440,715 12 0.089846 0.129 -17,2852005 02 20.05000 13,480,000 13,437,151 12 0.089822 0.319 -42,849
2005 CL7 2005 02 20.091665 33,430,000 33,391,146 328 0.223206 0.116 -38,8542005 02 20.096525 33,528,000 33,395,165 328 0.223233 0.398 -132,8352005 02 20.10288 33,353,000 33,400,418 328 0.223268 0.142 47,418
2005 HN3 2005 04 29.08889 15,388,000 15,371,551 16,500 0.102752 0.107 -16,4492005 04 29.09514 15,326,000 15,374,605 16,500 0.102773 0.316 48,6052005 04 29.09903 15,352,000 15,376,506 16,500 0.102786 0.159 24,506
2006 BN55 2006 01 28.03820 15,155,000 15,274,684 7,086 0.102105 0.784 119,684Correlation with JPL AU Range 1.0000 1.0000 -0.5228 0.2128 0.6019
JJMO Asteroid Range Calulator.xls Computes the distance to an asteroid observed simultaneously at two locations.Enter observation DATA in yellow blocks. Do NOT modify this spreadsheet; duplicate the worksheet for each observation.The RANGE is in the blue cells.
Target: 2004 VD17Date and Time of the observations:
mm/dd/yyyy Excel # Time of day (d) Julian Date time Tu Greenwich Mean Sidereal TimeDate: 3-Dec-04 38324 0.07708 2453342.577 0.049214978 6.670914241 hours = 1.746441264 radians
hours minutes seconds decimal time, hours hours minutes secondsUTC: 1 51 0 1.85 6 40 15.29126837
Observatory data: Geographic Coordinates (use decimal degrees) Cylindrical CoordinatesNumber Observer(s) IAU Code Elevation (m) Longitude East (°) Latitude (°) u(radians) Z ( Dz) km ρ (Dxy) km Long. East
1 PB J95 128.854 358.55321 51.4749 0.896769267 4966.593459 3980.811016 358.553212 MR 932 79.0495 286.5739 41.5259 0.723097038 4206.300597 4782.044187 286.5739
Cartesian Coordinates (km) Unit vector to each observatoryx y z r (km) x y z
1 J95 3979.54195 -100.5097685 4966.593459 6365.053568 0.625217354 -0.015790876 0.780290912 932 1364.086675 -4583.362756 4206.300597 6368.744878 0.214184537 -0.719664996 0.6604599
Separation vector, d -2615.455275 -4482.852987 -760.292861 Baseline dist., d (km) 5245.43825Separation unit vector -0.498615206 -0.854619342 -0.14494363
Asteroid position data:Equatorial Coordinates
------------------- Right Ascension --------------------- ------------------------------------ Declination -------------------------------------hours minutes seconds radians ° ' " decimal deg. radians
J95 4 1 5.21 1.051939756 13 13 28.6 13.22461111 0.23081301932 4 1 6.77 1.052053203 13 13 32.6 13.22572222 0.23083240
Geocentric unit vector to asteroid Transform to Geographical Coordinates at GMST: x y z
J95 -0.694501508 0.230813006 0.747996144 -0.62303009 0.22876904932 -0.694388062 0.230832399 0.74806341 -0.62294239 0.22878792
Calculate distances from each observatory to the asteroid, R1 & R2: Parallax = 0.000112127 radians = 0.006424424 degrees(Law of Sines)
J95 arccos(d·R2/dxR2) = 1.697355382 radians R1 = 46,406,900 km932 arccos(d·R1/dxR1) = 1.444125148 radians R2 = 46,406,300 km
Calculate distance from Center of Earth to asteroid, R:(Law of Cosines)
r2·R2/r2xR2 = 0.7596387 Theta = 139.43 degrees R= 46,411,000 km
JPL HORIZONS prediction from orbit: AU km @date: 2/28/2006 No. obs.: 687 Days after discov.: na R= 0.312783853 46,791,798 km
932-J95 vs. JPL 0.81 % +/- 19 3 sigma
MPEC 2004-X06 : 2004 XJ The following Minor Planet Electronic Circular may be linked-to from your own Web pages, but must not otherwise be redistributed electronically M.P.E.C. 2004-X06 Issued 2004 Dec. 3, 10:02 UT The Minor Planet Electronic Circulars contain information on unusual minor planets and routine data on comets. They are published on behalf of Commission 20 of the International Astronomical Union by the Minor Planet Center, Smithsonian Astrophysical Observatory, Cambridge, MA 02138, U.S.A. Supported in part by the Brinson Foundation Prepared using the Tamkin Foundation Computer Network [email protected] URL http://cfa-www.harvard.edu/iau/mpc.html ISSN 1523-6714 2004 XJ Observations: K04X00J* C2004 12 02.20809 02 29 13.92 +35 54 37.1 18.0 EX006704 K04X00J C2004 12 02.22021 02 29 12.64 +35 50 52.8 18.4 EX006704 K04X00J C2004 12 02.23232 02 29 11.38 +35 47 08.8 18.7 EX006704 K04X00J C2004 12 02.24583 02 29 09.99 +35 42 58.0 18.6 EX006704 K04X00J C2004 12 02.25792 02 29 08.81 +35 39 12.3 19.0 EX006704 K04X00J C2004 12 02.98280 02 28 55.41 +31 59 47.4 18.6 R EX006J95 K04X00J C2004 12 02.98643 02 28 55.23 +31 58 41.7 19.0 R EX006J95 K04X00J C2004 12 02.98982 02 28 54.99 +31 57 41.2 18.6 R EX006J95 K04X00J C2004 12 03.01840 02 28 53.24 +31 49 07.8 18.6 R EX006J95 K04X00J C2004 12 03.03611 02 29 03.58 +31 44 33.5 18.5 R EX006932 K04X00J C2004 12 03.03611 02 28 52.19 +31 43 50.5 18.4 R EX006J95 K04X00J C2004 12 03.03993 02 29 03.27 +31 43 26.4 18.5 R EX006932 K04X00J C2004 12 03.03993 02 28 52.01 +31 42 42.0 18.7 R EX006J95 K04X00J C2004 12 03.05035 02 28 51.49 +31 39 34.9 18.4 R EX006J95 K04X00J C2004 12 03.05590 02 29 01.99 +31 38 47.0 18.7 R EX006932 K04X00J C2004 12 03.05590 02 28 51.27 +31 37 54.6 18.5 R EX006J95 RReepprroodduucceedd wwiitthh ppeerrmmiissssiioonn ffrroomm tthhee MMiinnoorr PPllaanneett CCeenntteerr
SSmmiitthhssoonniiaann AAssttrroopphhyyssiiccaall OObbsseerrvvaattoorryy CCaammbbrriiddggee,, MMAA 0022113388,, UU..SS..AA..
6' X 4' Image Series
932
J95
2004 VB2004 11 26.957 (22:58)
Range = 0.059 AU (8.8e+6 km) Parallax = 116.9"
2004 VD17
2004 12 03.06875 (01:39)
Range = 0.313 AU (4.6e+7 km) Parallax = 23.2"
932 J95
2004 VD17
2004 12 03.07361 (01:46)
Range = 0.313 AU (4.6e+7 km) Parallax = 23.2"
932 J95
2004 YR2005 Jan 02.04063 (00:58:30 UT)
Range = 0.191 AU (2.9e+7 km) Parallax = 33.5"
932 J95
2005 CR37
2005 Feb 20.04306 (01:00-01:04 UT)
Range = 0.090 AU (1.3e+7km) Parallax = 68.5"
932 J95
5260030
=
2005 CC37
2005 CC37
2005 02 07.02639 (00:38)
Range = 0.085 AU (1.3e+7 km) Parallax = 81.6"
932 J95
MPEC 2005-C30 : 2005 CC37 The following Minor Planet Electronic Circular may be linked-to from your own Web pages, but must not otherwise be redistributed electronically M.P.E.C. 2005-C30 Issued 2005 Feb. 7, 21:54 UT The Minor Planet Electronic Circulars contain information on unusual minor planets and routine data on comets. They are published on behalf of Commission 20 of the International Astronomical Union by the Minor Planet Center, Smithsonian Astrophysical Observatory, Cambridge, MA 02138, U.S.A. Supported in part by the Brinson Foundation Prepared using the Tamkin Foundation Computer Network [email protected] URL http://cfa-www.harvard.edu/iau/mpc.html ISSN 1523-6714 2005 CC37 Observations: K05C37C* C2005 02 06.86339 08 52 10.62 +51 38 54.1 18.6 R EC030106 K05C37C C2005 02 06.86911 08 52 15.76 +51 38 33.0 18.8 R EC030106 K05C37C C2005 02 06.87492 08 52 21.10 +51 38 11.8 18.9 R EC030106 K05C37C C2005 02 06.91749 08 52 58.70 +51 35 33.3 18.7 R EC030106 K05C37C C2005 02 06.92654 08 53 06.76 +51 34 59.2 18.6 R EC030106 K05C37C C2005 02 06.96330 08 53 40.93 +51 32 27.0 EC030J95 K05C37C C2005 02 06.96911 08 53 46.06 +51 32 04.9 EC030J95 K05C37C C2005 02 06.97838 08 53 54.19 +51 31 29.7 18.1 R EC030J95 K05C37C C2005 02 07.01736 08 54 28.36 +51 28 58.9 EC030J95 K05C37C C2005 02 07.01737 08 54 36.78 +51 28 43.6 18.1 R EC030932 K05C37C C2005 02 07.02125 08 54 31.70 +51 28 43.9 EC030J95 K05C37C C2005 02 07.02126 08 54 40.26 +51 28 29.6 18.0 R EC030932 K05C37C C2005 02 07.02500 08 54 34.96 +51 28 29.1 18.1 R EC030J95 K05C37C C2005 02 07.02501 08 54 43.59 +51 28 16.6 18.0 R EC030932
RReepprroodduucceedd wwiitthh ppeerrmmiissssiioonn ffrroomm tthhee MMiinnoorr PPllaanneett CCeenntteerr SSmmiitthhssoonniiaann AAssttrroopphhyyssiiccaall OObbsseerrvvaattoorryy
CCaammbbrriiddggee,, MMAA 0022113388,, UU..SS..AA..
Event Date - Time Time from DiscoveryDiscovery by 106 2005 02 06.86339 0h 0.0m
106 sends MPC Report 2005 02 06.94236 1h 53.7mMPC adds to NEOCP 2005 02 06.94931 2h 03.7m
J95 sees NEOCP change 2005 02 06.95000 2h 04.7mJ95 Confirms 2005 02 06.96330 2h 23.9m
J95-932 first observation 2005 02 07.01736 3h 41.7mJ95 FindOrb Range (0.0848 AU) 2005 02 07.05102 4h 30.2m
MPEC 2005-C30 issued 2005 02 07.91250 1d 01h 10.7mJPL adds to Risk Page 2005 02 08.03333 1d 04h 04.7m
J95-932 Range falls outside JPL uncert. 2005 02 28.03512 21d 04h 07.3mJPL removes from Risk Page 2005 03 09.53611 30d 16h 08.8m
2005 CC37 Chronology
JJMO Asteroid Range Calulator.xls Computes the distance to an asteroid observed simultaneously at two locations.Enter observation DATA in yellow blocks. Do NOT modify this spreadsheet; duplicate the worksheet for each observation.The RANGE is in the blue cells.
Target: 2005 CC37Date and Time of the observations:
mm/dd/yyyy Excel # Time of day (d) Julian Date time Tu Greenwich Mean Sidereal TimeDate: 7-Feb-05 38390 0.025005 2453408.525 0.051020534 9.750917882 hours = 2.552784332 radians
hours minutes seconds decimal time, hours hours minutes secondsUTC: 0 36 0 0.6 9 45 3.304376175
Observatory data: Geographic Coordinates (use decimal degrees) Cylindrical CoordinatesNumber Observer(s) IAU Code Elevation (m) Longitude East (°) Latitude (°) u(radians) Z ( Dz) km ρ (Dxy) km Long. East
1 PB J95 128.854 358.55321 51.4749 0.896769267 4966.593459 3980.811016 358.553212 MR 932 79.0495 286.5739 41.5259 0.723097038 4206.300597 4782.044187 286.5739
Cartesian Coordinates (km) Unit vector to each observatoryx y z r (km) x y z
1 J95 3979.54195 -100.5097685 4966.593459 6365.053568 0.625217354 -0.015790876 0.780290912 932 1364.086675 -4583.362756 4206.300597 6368.744878 0.214184537 -0.719664996 0.6604599
Separation vector, d -2615.455275 -4482.852987 -760.292861 Baseline dist., d (km) 5245.43825Separation unit vector -0.498615206 -0.854619342 -0.14494363
Asteroid position data:Equatorial Coordinates
------------------- Right Ascension --------------------- ------------------------------------ Declination -------------------------------------hours minutes seconds radians ° ' " decimal deg. radians
J95 8 54 34.96 2.332556914 51 28 29.1 51.47475 0.89840387932 8 54 43.59 2.333184506 51 28 16.6 51.47127778 0.89834327
Geocentric unit vector to asteroid Transform to Geographical Coordinates at GMST: x y z
J95 -0.220227418 0.898403869 0.607816038 -0.136064619 0.78233374932 -0.219599826 0.898343267 0.607947583 -0.135693459 0.78229599
Calculate distances from each observatory to the asteroid, R1 & R2: Parallax = 0.000395586 radians = 0.022665383 degrees(Law of Sines)
J95 arccos(d·R2/dxR2) = 1.265522371 radians R1 = 12,646,900 km932 arccos(d·R1/dxR1) = 1.875674697 radians R2 = 12,648,400 km
Calculate distance from Center of Earth to asteroid, R:(Law of Cosines)
r2·R2/r2xR2 = 0.74454194 Theta = 138.12 degrees R= 12,653,000 km
JPL HORIZONS prediction AU km @date: 3/9/2005 No. obs.: 92 Days after discov.: 30 R= 0.084798162 12,685,625 km
932-J95 vs JPL 0.26 % 32,625 +/- 12,989 3 sigma
2005 CC37
Who date range uncert. # obs932-J95 2/7/2005 12653000 1 12.653JPL 27 2/9/2005 12701195 207375 27 12493820 12908570 12.7012 0.207375JPL 68 2/14/2005 12672437 97904 68 12574533 12770341 12.67244 0.097904JPL 71 2/16/2005 12677376 91076 71 12586300 12768452 12.67738 0.091076JPL 76 2/17/2005 12684245 79094 76 12605151 12763339 12.68425 0.079094JLP78 2/18/2005 12683744 68800 78 12614944 12752544 12.68374 0.0688JPL 81 2/19/2005 12684263 55565 81 12628698 12739828 12.68426 0.055565JPL 83 2/28/2005 12680355 30771 83 12649584 12711126 12.68036 0.030771JPL 85 3/1/2005 12683055 24185 85 12658870 12707240 12.68306 0.024185JPL 92 3/11/2005 12685625 18151 92 12667474 12703776 12.68563 0.018151
2005 CC37 Range Uncertainty
12.4
12.5
12.6
12.7
12.8
12.9
13
0 50 100
Number of observations
Ran
ge
e+6
km
JPL932-J95
Reduction in uncertainty area
2004 XJ
Date RA residual Dec. Residual Observatory
2004 12 02.98280 -0.46 0.29 J95
2004 12 02.98643 0.33 -0.28 J95
2004 12 02.98982 0.12 0.04 J95
2004 12 03.01840 0.41 -0.40 J952004 12 03.03611
-20.14 -5.98 932
2004 12 03.03611 -0.43 0.23 J952004 12 03.03993
-20.17 -6.56 932
2004 12 03.03993 -0.17 0.31 J95
2004 12 03.05035 -0.17 0.25 J952004 12 03.05590
-19.77 -7.69 932
2004 12 03.05590 0.37 -0.43 J95
2004 XJ
Date RA residual Dec. Residual Observatory
2004 12 02.98280 -0.40 0.30 J95
2004 12 02.98643 0.35 -0.29 J95
2004 12 02.98982 0.10 0.03 J95
2004 12 03.01840 0.23 -0.42 J952004 12 03.03611
0.20 0.14 932
2004 12 03.03611 -0.53 0.25 J952004 12 03.03993
0.03 -0.18 932
2004 12 03.03993 -0.24 0.34 J95
2004 12 03.05035 -0.10 0.34 J952004 12 03.05590
-0.18 -0.19 932
2004 12 03.05590 0.54 -0.31 J95
2004 XJ
Source
#Positions
Timespan Distance from Earth
(A.U.)
% error(c.f. JPL orbit)
Orbit 1(Only J95 positions)
8 1h 45m 0.0410 -13.0%
Orbit 2(J95 & 932 positions)
11 1h 45m 0.0472 +0.2%
JPL(All reported positions from all observatories)
75 13 days 0.0471 0%
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