Orbital Analysis for matched events on 20210813_003107.103_UK

Summary for Event
-----------------
shower ID 12 KCG
Lg 299.20° Bg 69.83° Vg 22.24km/s
mass 0.04604g, abs. mag 0.5
Path Details
------------
start -2.78° 52.74° 93.61km
end   -2.70° 52.74° 81.33km

Orbit Details
-------------
Semimajor axis 3.92A.U., eccentricity 0.75, inclination 32.99°, Period 7.77Y, LA Sun 140.21°, last Perihelion 2013-11-24

Full details below
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Input measurement type: Azimuth +east of due north for meas1, Elevation angle above the horizon for meas2

Uncertainties type:
 Purely geometric uncertainties

Reference JD: 2459439.521609988529
Time: 2021-08-13 00:31:07.103009 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK001L and UK002Z
 Convergence angle = 78.16612 deg
 R.A. = 288.52636  Dec = +48.27736 deg

Best intersection: Stations UK001L and UK002Z with Qconv = 78.17 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   3280280.71 +/- 60.61 m
 Y =  -2157196.43 +/- 150.43 m
 Z =   5127973.76 +/- 87.85 m
 Vx =     4712.03 +/- 193.58 m/s
 Vy =   -15781.81 +/- 38.64 m/s
 Vz =    18616.24 +/- 324.28 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+2.944573e+03, -3.829249e+03, +1.072884e+03, +6.889323e+03, -4.412792e+03, -4.472695e+03
-3.829249e+03, +1.484238e+04, -6.277242e+03, -4.131501e+03, +2.100128e+04, +2.937475e+03
+1.072884e+03, -6.277242e+03, +6.785402e+03, -1.708203e+03, -8.578803e+02, +2.109210e+03
+6.889323e+03, -4.131501e+03, -1.708203e+03, +2.379930e+04, -9.076029e+03, -1.358269e+04
-4.412792e+03, +2.100128e+04, -8.578803e+02, -9.076029e+03, +5.518124e+04, +4.172780e+03
-4.472695e+03, +2.937475e+03, +2.109210e+03, -1.358269e+04, +4.172780e+03, +1.327783e+04

Timing offsets (from input data):
    UK001L: -0.001940 s
    UK002Z: 0.000000 s

Reference point on the trajectory:
  Time: 2021-08-13 00:31:07.103009 UTC
  Lon     = +-2.780901 +/- 0.0015 deg
  Lat     = +52.744841 +/- 0.0007 deg
  Lat geo = +52.561932 +/- 0.0007 deg
  Ht      =   93634.04 +/- 131.00 m

  JD dynamic   = 2459439.522410729434 
  LST apparent = 326.6700579240 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      = 286.62424 +/- 0.4863 deg
  Dec       = +48.50003 +/- 0.5696 deg
  Azimuth   = 276.64186 +/- 1.2946 deg
  Elevation = +64.58256 +/- 0.3519 deg
  Vavg      =  24.46628 +/- 0.0963 km/s
  Vinit     =  24.85625 +/- 0.2115 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      = 287.39524 +/- 0.4863 deg
  Dec       = +48.81703 +/- 0.5696 deg
  Azimuth   = 276.82457 +/- 1.2946 deg
  Elevation = +65.17740 +/- 0.3519 deg
  Vavg      =  24.34559 +/- 0.0963 km/s
  Vinit     =  24.73555 +/- 0.2115 km/s
Radiant (geocentric, J2000):
  R.A.   = 284.52109 +/- 0.5032 deg
  Dec    = +47.85783 +/- 0.5892 deg
  Vg     =  22.23507 +/- 0.2361 km/s
  Vinf   =  24.85625 +/- 0.2115 km/s
  Zc     =  25.43920 +/- 0.3506 deg
  Zg     =  26.87884 +/- 0.3511 deg
Radiant (ecliptic geocentric, J2000):
  Lg     = 299.20028 +/- 0.9209 deg
  Bg     = +69.82770 +/- 0.5964 deg
  Vh     =  39.05077 +/- 0.2569 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     = 243.28818 +/- 0.3916 deg
  Bh     = +32.30822 +/- 0.1380 deg
  Vh_x   =  14.83591 +/- 0.1547 km/s
  Vh_y   =  29.48278 +/- 0.2684 km/s
  Vh_z   = -20.87161 +/- 0.1734 km/s
Orbit:
  La Sun = 140.209250 +/- 0.0000 deg
  a      =   3.923114 +/- 0.3822 AU
  e      =   0.752742 +/- 0.0221
  i      =  32.991598 +/- 0.1378 deg
  peri   = 205.742032 +/- 0.6166 deg
  node   = 140.215570 +/- 0.0000 deg
  Pi     = 345.957603 +/- 0.6166 deg
  q      =   0.970023 +/- 0.0023 AU
  f      = 334.251393 +/- 0.6166 deg
  M      = 357.537587 +/- 0.3598 deg
  Q      =   6.876206 +/- 0.7653 AU
  n      =   0.126841 +/- 0.0167 deg/day
  T      =   7.770467 +/- 1.1704 years
  Last perihelion JD = 2456620.723534 (2013-11-24 05:21:53.322924) +/- 427.5880 days
  Tj     =   2.285376 +/- 0.1130
Shower association:
  IAU No.  =   12
  IAU code =  KCG

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +3.232616e-04, -5.632351e-06, -5.796379e+00, -1.903360e-09, -3.042619e-05, +9.018875e-06
q   , -5.632351e-06, +4.555401e-06, +1.314530e-01, -4.168419e-10, -2.246018e-05, +1.960299e-06
Tp  , -5.796379e+00, +1.314530e-01, +1.060940e+05, +3.807644e-05, +3.884101e-01, -1.808667e-01
node, -1.903360e-09, -4.168419e-10, +3.807644e-05, +1.963592e-13, +2.524883e-09, -9.270406e-10
peri, -3.042619e-05, -2.246018e-05, +3.884101e-01, +2.524883e-09, +1.214645e-04, -1.188693e-05
i   , +9.018875e-06, +1.960299e-06, -1.808667e-01, -9.270406e-10, -1.188693e-05, +4.376901e-06

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = -0.000082
 a2 = 26.706260

Mean time residuals from time vs. length:
  Station with reference time: UK002Z
  Avg. res. = 7.136e-06 s
  Stddev    = 2.67e-03 s

Begin point on the trajectory:
  Lon =    -2.780761 +/- 0.0012 deg
  Lat =    52.744831 +/- 0.0007 deg
  Ht  = 93613.72 +/- 63.40 m
End point on the trajectory:
  Lon =    -2.698302 +/- 0.0008 deg
  Lat =    52.738807 +/- 0.0005 deg
  Ht  = 81325.56 +/- 41.62 m

Stations
--------
        ID, Ignored, Lon +E (deg), Lat +N (deg),  Ht (m), Jacchia a1, Jacchia a2,  Beg Ht (m),  End Ht (m), +/- Obs ang (deg), +/- V (m), +/- H (m), Persp. angle (deg), Weight, FOV Beg, FOV End, Comment
    UK001L,   False,    -1.306160,    51.883100,   80.00,  17.396165,   0.000000,    89846.11,    82671.28,          0.022846,     61.77,     18.78,              38.59, 1.0000,    True,    True, {"ff_name": "FF_UK001L_20210813_003106_984_0367872.fits"}
    UK002Z,   False,    -0.382830,    53.537790,   34.00,   0.000436,  23.732974,    93613.72,    81325.56,          0.027797,     93.79,     31.56,              43.60, 1.0000,    True,    True, {"ff_name": "FF_UK002Z_20210813_003101_759_0382720.fits"}

Points
------
 No, Station ID,  Ignore,  Time (s),                   JD,     meas1,     meas2, Azim +E of due N (deg), Alt (deg), Azim line (deg), Alt line (deg), RA obs (deg), Dec obs (deg), RA line (deg), Dec line (deg),       X (m),       Y (m),       Z (m), Latitude (deg), Longitude (deg), Height (m),  Range (m), Length (m), State vect dist (m),  Lag (m), Vel (m/s), Vel prev avg (m/s), H res (m), V res (m), Ang res (asec), AppMag, AbsMag
  0,     UK001L,       0,  0.170964, 2459439.521612236276, 225.30256,  51.92304,              314.63871,  32.32359,       314.64036,       32.32423,    225.30256,     +51.92304,     225.30171,      +51.92448,  3279485.63, -2154533.51,  5124832.58,      52.742993,       -2.755604,   89846.11,  165075.18,       0.00,             4194.08,    16.11,      0.00,           24127.57,     -1.29,     -4.24,           5.54,  +3.16,  +2.07
  1,     UK001L,       0,  0.211140, 2459439.521612701472, 224.99425,  51.84558,              314.73180,  32.13382,       314.73785,       32.13616,    224.99425,     +51.84558,     224.99126,      +51.85086,  3279305.43, -2153929.98,  5124120.65,      52.742573,       -2.749850,   88987.63,  164336.32,     950.56,             5144.64,   -31.96,  23659.87,           24127.57,     -4.69,    -15.46,          20.28,  +2.84,  +1.76
  2,     UK001L,       0,  0.251324, 2459439.521613166202, 224.68659,  51.75262,              314.81247,  31.93341,       314.83755,       31.94309,    224.68659,     +51.75262,     224.67368,      +51.77452,  3279122.16, -2153316.17,  5123396.60,      52.742145,       -2.743994,   88114.54,  163586.92,    1917.31,             6111.39,   -64.03,  24058.04,           24127.57,    -19.41,    -63.86,          84.16,  +2.99,  +1.92
  3,     UK001L,       0,  0.291500, 2459439.521613631397, 224.33743,  51.70771,              314.95539,  31.74890,       314.94042,       31.74312,    224.33743,     +51.70771,     224.34592,      +51.69464,  3278934.13, -2152686.41,  5122653.73,      52.741706,       -2.737981,   87218.79,  162820.20,    2909.17,             7103.25,   -70.79,  24687.99,           24127.57,     11.54,     38.01,          50.32,  +1.78,  +0.72
  4,     UK001L,       0,  0.331704, 2459439.521614096593, 224.03435,  51.56477,              314.99427,  31.51497,       315.04696,       31.53526,    224.03435,     +51.56477,     224.00649,      +51.61075,  3278740.58, -2152038.17,  5121889.07,      52.741254,       -2.731784,   86296.75,  162033.25,    3930.15,             8124.23,   -49.13,  25394.92,           24434.91,    -40.58,   -133.34,         177.43,  +1.89,  +0.84
  5,     UK001L,       0,  0.371896, 2459439.521614561789, 223.61830,  51.54966,              315.19808,  31.32291,       315.16257,       31.30920,    223.61830,     +51.54966,     223.63857,      +51.51864,  3278532.16, -2151340.11,  5121065.64,      52.740766,       -2.725096,   85303.90,  161188.15,    5029.58,             9223.66,    51.28,  27354.54,           24939.88,     27.18,     89.63,         119.85,  +2.29,  +1.25
  6,     UK001L,       0,  0.412088, 2459439.521615026984, 223.32773,  51.42274,              315.24591,  31.10572,       315.26232,       31.11204,    223.32773,     +51.42274,     223.31965,      +51.43707,  3278352.43, -2150738.14,  5120355.55,      52.740345,       -2.719350,   84447.69,  160462.74,    5977.68,            10171.76,     0.36,  23589.32,           24975.46,    -12.55,    -41.28,          55.46,  +1.64,  +0.61
  7,     UK001L,       0,  0.452284, 2459439.521615492180, 222.98022,  51.33644,              315.35767,  30.89284,       315.37054,       30.89779,    222.98022,     +51.33644,     222.97418,      +51.34767,  3278158.91, -2150089.99,  5119590.99,      52.739892,       -2.713149,   83525.84,  159683.69,    6998.52,            11192.59,    22.07,  25396.32,           25025.37,     -9.80,    -32.26,          43.55,  +2.52,  +1.50
  8,     UK001L,       0,  0.492468, 2459439.521615957376, 222.65132,  51.26227,              315.47042,  30.69685,       315.47111,       30.69712,    222.65132,     +51.26227,     222.65228,      +51.26287,  3277979.52, -2149489.16,  5118882.26,      52.739471,       -2.707412,   82671.28,  158964.40,    7944.81,            12138.89,   -30.46,  23549.13,           24950.25,     -0.52,     -1.72,           2.33,  +2.55,  +1.54
  0,     UK002Z,       0,  0.000000, 2459439.521609988529, 276.08912,   5.97979,              242.14255,  26.08213,       242.15361,       26.07816,    276.08912,      +5.97979,     276.07772,       +5.98167,  3280276.44, -2157182.14,  5127956.90,      52.744831,       -2.780761,   93613.72,  206831.76,       0.00,               22.51,    94.05,      0.00,           22851.09,    -12.32,    -36.59,          38.51,  +4.51,  +2.93
  1,     UK002Z,       0,  0.040108, 2459439.521610452794, 276.11351,   5.74874,              241.98396,  25.89869,       242.06373,       25.87004,    276.11351,      +5.74874,     276.03639,       +5.76226,  3280055.80, -2156443.18,  5127085.22,      52.744319,       -2.773686,   92562.54,  205997.27,    1163.86,             1186.37,   260.98,  29018.19,           22851.09,    -88.50,   -263.37,         278.21,  +4.14,  +2.57
  2,     UK002Z,       0,  0.080200, 2459439.521610916592, 276.03347,   5.67197,              242.01416,  25.79146,       242.02900,       25.78615,    276.03347,      +5.67197,     276.01877,       +5.67450,  3279968.20, -2156149.77,  5126739.12,      52.744115,       -2.770977,   92145.17,  205672.12,    1625.97,             1648.48,  -273.45,  11526.24,           22851.09,    -16.47,    -48.90,          51.75,  +3.63,  +2.06
  3,     UK002Z,       0,  0.120344, 2459439.521611381322, 276.01659,   5.42364,              241.88480,  25.57155,       241.92970,       25.55546,    276.01659,      +5.42364,     275.97318,       +5.43129,  3279726.45, -2155340.08,  5125784.00,      52.743553,       -2.763206,   90993.41,  204761.90,    2901.24,             2923.74,     3.99,  31767.23,           22851.09,    -49.67,   -147.64,         156.91,  +3.38,  +1.82
  4,     UK002Z,       0,  0.160500, 2459439.521611846052, 275.94573,   5.21419,              241.82915,  25.35632,       241.84256,       25.35153,    275.94573,      +5.21419,     275.93272,       +5.21648,  3279514.73, -2154630.99,  5124947.56,      52.743061,       -2.756419,   89984.78,  203969.04,    4018.04,             4040.55,   122.67,  27811.72,           24359.18,    -14.80,    -43.95,          46.89,  +2.34,  +0.79
  5,     UK002Z,       0,  0.200620, 2459439.521612310316, 275.88734,   5.06546,              241.79735,  25.19925,       241.78086,       25.20514,    275.88734,      +5.06546,     275.90322,       +5.06263,  3279364.17, -2154126.71,  5124352.71,      52.742710,       -2.751639,   89267.47,  203409.54,    4812.28,             4834.79,   -80.33,  19796.53,           24137.95,     18.19,     53.96,          57.74,  +2.55,  +1.01
  6,     UK002Z,       0,  0.240740, 2459439.521612774581, 275.87630,   4.85014,              241.68275,  25.01026,       241.69614,       25.00547,    275.87630,      +4.85014,     275.86361,       +4.85244,  3279159.71, -2153441.93,  5123544.94,      52.742233,       -2.745087,   88293.43,  202649.05,    5890.81,             5913.32,     0.97,  26882.63,           24352.98,    -14.72,    -43.71,          46.95,  +1.92,  +0.39
  7,     UK002Z,       0,  0.280864, 2459439.521613239311, 275.83508,   4.66905,              241.61651,  24.83456,       241.62317,       24.83218,    275.83508,      +4.66905,     275.82902,       +4.67020,  3278983.71, -2152852.45,  5122849.60,      52.741822,       -2.739469,   87454.96,  201997.92,    6819.23,             6841.73,   -67.95,  23138.67,           24341.39,     -7.31,    -21.70,          23.39,  +1.99,  +0.46
  8,     UK002Z,       0,  0.320992, 2459439.521613703575, 275.78776,   4.48576,              241.55490,  24.65375,       241.54911,       24.65582,    275.78776,      +4.48576,     275.79387,       +4.48476,  3278805.77, -2152256.49,  5122146.60,      52.741406,       -2.733786,   86607.28,  201341.67,    7757.86,             7780.37,  -126.74,  23391.05,           24272.62,      6.35,     18.83,          20.35,  +1.49,  -0.03
  9,     UK002Z,       0,  0.361144, 2459439.521614168305, 275.75337,   4.24178,              241.44653,  24.42796,       241.45221,       24.42593,    275.75337,      +4.24178,     275.74858,       +4.24276,  3278575.24, -2151484.39,  5121235.83,      52.740867,       -2.726371,   85509.11,  200492.13,    8973.92,             8996.43,    91.29,  30286.46,           24565.87,     -6.22,    -18.45,          20.03,  +1.43,  -0.08
 10,     UK002Z,       0,  0.401292, 2459439.521614633035, 275.67816,   4.05683,              241.41046,  24.23109,       241.37604,       24.24337,    275.67816,      +4.05683,     275.71229,       +4.05087,  3278393.85, -2150876.88,  5120519.21,      52.740442,       -2.720571,   84645.03,  199828.19,    9930.74,             9953.25,    50.18,  23832.30,           24692.44,     37.59,    111.38,         121.34,  +1.75,  +0.25
 11,     UK002Z,       0,  0.441404, 2459439.521615097299, 275.68552,   3.83714,              241.27776,  24.04765,       241.29225,       24.04247,    275.68552,      +3.83714,     275.67253,       +3.83964,  3278195.56, -2150212.73,  5119735.78,      52.739978,       -2.714213,   83700.42,  199104.18,   10976.78,            10999.28,    99.18,  26077.85,           24818.71,    -15.77,    -46.81,          51.18,  +1.91,  +0.41
 12,     UK002Z,       0,  0.481524, 2459439.521615561564, 275.62264,   3.68391,              241.24874,  23.88421,       241.22984,       23.89095,    275.62264,      +3.68391,     275.64214,       +3.68064,  3278047.27, -2149716.08,  5119149.93,      52.739630,       -2.709499,   82994.01,  198566.84,   11758.99,            11781.50,  -115.84,  19496.88,           24719.63,     20.55,     60.92,          66.79,  +1.59,  +0.10
 13,     UK002Z,       0,  0.521664, 2459439.521616026293, 275.57177,   3.48120,              241.18047,  23.68480,       241.14910,       23.69598,    275.57177,      +3.48120,     275.60353,       +3.47576,  3277857.34, -2149079.95,  5118399.55,      52.739184,       -2.703414,   82089.26,  197878.44,   12760.89,            12783.40,  -111.66,  24960.17,           24664.22,     34.04,    100.87,         110.97,  +2.24,  +0.76
 14,     UK002Z,       0,  0.561764, 2459439.521616490558, 275.56114,   3.30308,              241.08900,  23.52727,       241.08099,       23.53013,    275.56114,      +3.30308,     275.57045,       +3.30169,  3277697.02, -2148543.00,  5117766.17,      52.738807,       -2.698302,   81325.56,  197300.79,   13606.58,            13629.09,  -262.71,  21089.47,           24538.91,      8.67,     25.72,          28.38,  +3.09,  +1.61

Notes
-----
- Points that have not been taken into consideration when computing the trajectory have '1' in the 'Ignore' column.
- The time already has time offsets applied to it.
- 'meas1' and 'meas2' are given input points.
- X, Y, Z are ECI (Earth-Centered Inertial) positions of projected lines of sight on the radiant line.
- Zc is the observed zenith distance of the entry angle, while the Zg is the entry zenith distance corrected for Earth's gravity.
- Latitude (deg) and Longitude (deg) are in WGS84 coordinates, while Height (m) is in the EGM96 datum. There values are coordinates of each point on the radiant line.
- Jacchia (1955) deceleration equation fit was done on the lag.
- Right ascension and declination in the table are given in the epoch of date for the corresponding JD, per every point.
- 'RA and Dec obs' are the right ascension and declination calculated from the observed values, while the 'RA and Dec line' are coordinates of the lines of sight projected on the fitted radiant line. The coordinates are in the epoch of date, and NOT J2000!. 'Azim and alt line' are thus corresponding azimuthal coordinates.
- 'Vel prev avg' is the average velocity including all previous points up to the given point. For the first 4 points this velocity is computed as the average velocity of those 4 points.