Orbital Analysis for matched events on 20210813_004032.329_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 63.72° Bg 37.85° Vg 59.99km/s
mass 0.10322g, abs. mag -2.1
Path Details
------------
start -0.27° 53.35° 110.16km
end   -0.46° 53.26° 91.75km

Orbit Details
-------------
Semimajor axis 278.30A.U., eccentricity 1.00, inclination 114.35°, Period 4642.69Y, LA Sun 140.22°, last Perihelion 2021-07-23

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: 2459439.528151961975
Time: 2021-08-13 00:40:32.546009 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK000C and UK003B
 Convergence angle = 4.61827 deg
 R.A. =  48.01433  Dec = +56.86491 deg

Best intersection: Stations UK000C and UK003B with Qconv = 4.62 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   3412340.21 +/- 58.63 m
 Y =  -1849242.73 +/- 653.36 m
 Z =   5182265.86 +/- 1689.46 m
 Vx =    21260.13 +/- 5160.52 m/s
 Vy =    24500.57 +/- 3244.70 m/s
 Vz =    51667.49 +/- 7589.07 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+1.978259e+03, -8.391709e+03, -2.239342e+04, +9.141969e+03, -2.374706e+04, -6.496658e+04
-8.391709e+03, +1.286538e+05, +3.390758e+05, -3.352301e+04, +1.202915e+05, +3.532020e+05
-2.239342e+04, +3.390758e+05, +8.938759e+05, -9.013135e+04, +3.194838e+05, +9.377687e+05
+9.141969e+03, -3.352301e+04, -9.013135e+04, +1.003153e+05, -1.875582e+05, -5.317767e+05
-2.374706e+04, +1.202915e+05, +3.194838e+05, -1.875582e+05, +4.224620e+05, +1.174531e+06
-6.496658e+04, +3.532020e+05, +9.377687e+05, -5.317767e+05, +1.174531e+06, +3.287198e+06

Timing offsets (from input data):
    UK000C: -0.006432 s
    UK003B: 0.000000 s

Reference point on the trajectory:
  Time: 2021-08-13 00:40:32.546009 UTC
  Lon     = +-0.267926 +/- 0.0082 deg
  Lat     = +53.350336 +/- 0.0113 deg
  Lat geo = +53.168989 +/- 0.0113 deg
  Ht      =  110078.90 +/- 1156.70 m

  JD dynamic   = 2459439.528955208603 
  LST apparent = 331.5454956002 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  49.05051 +/- 3.2878 deg
  Dec       = +57.87791 +/- 1.8323 deg
  Azimuth   =  51.47911 +/- 3.6288 deg
  Elevation = +48.43056 +/- 0.6096 deg
  Vavg      =  60.62470 +/- 5.2581 km/s
  Vinit     =  61.00656 +/- 7.7496 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  49.15775 +/- 3.2878 deg
  Dec       = +57.65861 +/- 1.8323 deg
  Azimuth   =  51.72724 +/- 3.6288 deg
  Elevation = +48.27508 +/- 0.6096 deg
  Vavg      =  60.77211 +/- 5.2581 km/s
  Vinit     =  61.15397 +/- 7.7496 km/s
Radiant (geocentric, J2000):
  R.A.   =  49.23346 +/- 3.1886 deg
  Dec    = +57.62402 +/- 1.8689 deg
  Vg     =  59.98896 +/- 7.8547 km/s
  Vinf   =  61.00656 +/- 7.7496 km/s
  Zc     =  41.68258 +/- 0.6182 deg
  Zg     =  42.04947 +/- 0.5532 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  63.71763 +/- 2.7781 deg
  Bg     = +37.84745 +/- 1.2342 deg
  Vh     =  41.80797 +/- 8.0659 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  83.04436 +/- 2.6364 deg
  Bh     = +61.68950 +/- 2.3104 deg
  Vh_x   =  -2.40112 +/- 0.6040 km/s
  Vh_y   = -19.68149 +/- 5.8198 km/s
  Vh_z   = -36.80734 +/- 5.9522 km/s
Orbit:
  La Sun = 140.215534 +/- 0.0000 deg
  a      = 278.299807 +/- 77.1526 AU
  e      =   0.996600 +/- 0.8662
  i      = 114.353740 +/- 1.6771 deg
  peri   = 150.154587 +/- 4.2801 deg
  node   = 140.214852 +/- 0.0001 deg
  Pi     = 290.369439 +/- 4.2800 deg
  q      =   0.946167 +/- 0.0026 AU
  f      =  29.841513 +/- 4.2802 deg
  M      =   0.004385 +/- nan deg
  Q      = 555.653447 +/- 154.3049 AU
  n      =   0.000212 +/- 1.3487 deg/day
  T      = 4642.693294 +/- 462634182.8958 years
  Last perihelion JD = 2459418.874089 (2021-07-23 08:58:41.299683) +/- 5.6625 days
  Tj     =  -0.478196 +/- 4.9027
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +2.355456e-02, -7.946282e-05, +4.114209e-01, -5.963301e-08, +5.582960e-03, +8.249639e-04
q   , -7.946282e-05, +1.881056e-06, -8.251109e-04, +4.294195e-11, -6.896285e-06, -4.954736e-07
Tp  , +4.114209e-01, -8.251109e-04, +7.980512e+00, -1.075220e-06, +1.112863e-01, +1.487386e-02
node, -5.963301e-08, +4.294195e-11, -1.075220e-06, +1.799888e-13, -1.495674e-08, -2.498551e-09
peri, +5.582960e-03, -6.896285e-06, +1.112863e-01, -1.495674e-08, +1.565937e-03, +2.070716e-04
i   , +8.249639e-04, -4.954736e-07, +1.487386e-02, -2.498551e-09, +2.070716e-04, +3.469996e-05

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 0.000000
 a2 = 0.000000

Mean time residuals from time vs. length:
  Station with reference time: UK003B
  Avg. res. = 7.403e-06 s
  Stddev    = 2.72e-03 s

Begin point on the trajectory:
  Lon =    -0.267076 +/- 0.0084 deg
  Lat =    53.350741 +/- 0.0114 deg
  Ht  = 110161.95 +/- 1182.91 m
End point on the trajectory:
  Lon =    -0.457642 +/- 0.0071 deg
  Lat =    53.260438 +/- 0.0110 deg
  Ht  = 91754.43 +/- 1048.83 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
    UK000C,   False,    -0.727590,    51.263100,   57.00,   0.000000,   0.000000,   109218.15,    93041.09,          0.013916,     54.01,     29.44,              38.85, 1.0000,    True,    True, {"ff_name": "FF_UK000C_20210813_004031_691_0406016.fits"}
    UK003B,   False,    -1.072290,    52.276980,  129.00,   0.000000,   0.000000,   110161.95,    91754.43,          0.013299,     31.69,     20.55,              18.96, 1.0000,    True,    True, {"ff_name": "FF_UK003B_20210813_004023_823_0401152.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,     UK000C,       0,  0.015555, 2459439.528152470477, 136.60697,  61.94547,                7.38353,  23.79255,         7.39107,       23.78572,    136.60697,     +61.94547,     136.59428,      +61.93757,  3411939.26, -1849704.79,  5181291.46,      53.346135,       -0.276023,  109218.15,  259847.30,       0.00,             1150.52,   188.82,      0.00,           59637.58,     21.08,     38.65,          34.95,  +3.04,  +0.97
  1,     UK000C,       0,  0.055655, 2459439.528152934741, 137.18582,  61.76274,                7.12300,  23.56666,         7.13768,       23.55339,    137.18582,     +61.76274,     137.16183,      +61.74744,  3411152.69, -1850611.26,  5179379.88,      53.337890,       -0.293490,  107529.79,  258139.12,    2257.11,             3407.63,    -0.44,  56286.93,           59637.58,     40.79,     74.73,          68.03,  +1.77,  -0.29
  2,     UK000C,       0,  0.095799, 2459439.528153399006, 137.81866,  61.51803,                6.84235,  23.27697,         6.84036,       23.27877,    137.81866,     +61.51803,     137.82148,      +61.52010,  3410237.95, -1851665.41,  5177156.84,      53.328292,       -0.313779,  105566.75,  256163.64,    4881.96,             6032.49,   175.37,  65386.05,           59637.58,     -5.49,    -10.07,           9.24,  +1.08,  -0.96
  3,     UK000C,       0,  0.135919, 2459439.528153863735, 138.35502,  61.30648,                6.60173,  23.02862,         6.58593,       23.04284,    138.35502,     +61.30648,     138.38031,      +61.32271,  3409464.55, -1852556.69,  5175277.28,      53.320171,       -0.330962,  103907.37,  254502.45,    7101.26,             8251.78,   -52.92,  55316.35,           59637.58,    -43.21,    -79.33,          73.21,  +1.10,  -0.93
  4,     UK000C,       0,  0.176035, 2459439.528154328000, 138.96595,  61.08812,                6.32028,  22.76959,         6.30646,       22.78201,    138.96595,     +61.08812,     138.98834,      +61.10223,  3408622.65, -1853526.92,  5173231.23,      53.311322,       -0.349654,  102101.37,  252704.08,    9517.14,            10667.66,   -84.38,  60222.35,           59514.09,    -37.55,    -68.91,          64.05,  +0.79,  -1.22
  5,     UK000C,       0,  0.216159, 2459439.528154792264, 139.61727,  60.84672,                6.01738,  22.48673,         6.00447,       22.49830,    139.61727,     +60.84672,     139.63845,      +60.85979,  3407722.00, -1854564.84,  5171042.45,      53.301847,       -0.369642,  100169.81,  250791.94,   12101.55,            13252.08,    52.22,  64410.81,           60178.36,    -34.80,    -63.86,          59.81,  +0.82,  -1.18
  6,     UK000C,       0,  0.256283, 2459439.528155256528, 140.21392,  60.61251,                5.73787,  22.21630,         5.72143,       22.23101,    140.21392,     +60.61251,     140.24116,      +60.62904,  3406887.42, -1855526.63,  5169014.20,      53.293059,       -0.388178,   98380.30,  249030.91,   14496.41,            15646.94,    -0.75,  59686.43,           60362.90,    -44.02,    -80.79,          76.21,  +0.83,  -1.15
  7,     UK000C,       0,  0.296395, 2459439.528155720793, 140.85482,  60.38335,                5.43047,  21.94987,         5.42791,       21.95216,    140.85482,     +60.38335,     140.85948,      +60.38591,  3406030.67, -1856513.96,  5166932.09,      53.284030,       -0.407205,   96543.66,  247234.35,   16954.87,            18105.40,    10.61,  61289.87,           60517.01,     -6.81,    -12.48,          11.86,  +0.90,  -1.07
  8,     UK000C,       0,  0.336511, 2459439.528156185057, 141.47026,  60.14343,                5.13390,  21.67612,         5.13653,       21.67378,    141.47026,     +60.14343,     141.46654,      +60.14083,  3405189.14, -1857483.76,  5164886.95,      53.275153,       -0.425900,   94740.03,  245480.96,   19369.67,            20520.20,   -21.93,  60195.48,           60567.50,      6.95,     12.73,          12.19,  +0.93,  -1.02
  9,     UK000C,       0,  0.376631, 2459439.528156649787, 142.03938,  59.90529,                4.85795,  21.40839,         4.85907,       21.40739,    142.03938,     +59.90529,     142.03831,      +59.90419,  3404396.30, -1858397.44,  5162960.15,      53.266783,       -0.443525,   93041.09,  243839.41,   21644.75,            22795.27,  -194.43,  56706.77,           60382.63,      2.94,      5.39,           5.20,  +1.19,  -0.75
  0,     UK003B,       0,  0.000000, 2459439.528154467698,  89.48057,  68.80261,               24.12376,  39.13029,        24.11419,       39.14212,     89.48057,     +68.80261,      89.47277,      +68.81628,  3412378.89, -1849198.15,  5182359.87,      53.350741,       -0.267076,  110161.95,  172132.40,       0.00,              111.00,    98.27,      0.00,           64191.73,    -22.81,    -35.21,          50.27,  +1.62,  +0.44
  1,     UK003B,       0,  0.040152, 2459439.528154932428,  90.28600,  68.86362,               23.79797,  38.97442,        23.78838,       38.98621,     90.28600,     +68.86362,      90.27885,      +68.87731,  3411514.31, -1850194.52,  5180258.70,      53.341681,       -0.286258,  108305.95,  169808.97,    2480.95,             2369.95,   -92.32,  61789.06,           64191.73,    -22.47,    -34.67,          50.19,  +1.83,  +0.68
  2,     UK003B,       0,  0.080308, 2459439.528155397158,  91.08250,  68.91405,               23.48398,  38.81592,        23.47033,       38.83261,     91.08250,     +68.91405,      91.07312,      +68.93353,  3410689.47, -1851145.08,  5178254.13,      53.333031,       -0.304568,  106535.65,  167596.54,    4847.86,             4736.86,  -175.19,  58942.82,           64191.73,    -31.48,    -48.59,          71.25,  +0.97,  -0.15
  3,     UK003B,       0,  0.120488, 2459439.528155862354,  92.09889,  68.99991,               23.06400,  38.63369,        23.06421,       38.63344,     92.09889,     +68.99991,      92.09953,      +68.99962,  3409659.10, -1852332.49,  5175750.08,      53.322214,       -0.327403,  104324.76,  164839.98,    7804.53,             7693.52,   330.23,  73585.45,           64191.73,      0.46,      0.71,           1.06,  +0.93,  -0.16
  4,     UK003B,       0,  0.160640, 2459439.528156327084,  92.85715,  69.03032,               22.77892,  38.47570,        22.76879,       38.48795,     92.85715,     +69.03032,      92.85176,      +69.04475,  3408930.50, -1853172.15,  5173979.39,      53.314558,       -0.343602,  102761.71,  162894.07,    9895.28,             9784.27,   -28.56,  52070.87,           62532.94,    -22.58,    -34.80,          52.53,  +0.70,  -0.36
  5,     UK003B,       0,  0.200812, 2459439.528156791814,  93.73767,  69.07058,               22.44266,  38.29888,        22.42712,       38.31756,     93.73767,     +69.07058,      93.73013,      +69.09268,  3408103.88, -1854124.76,  5171970.50,      53.305865,       -0.361960,  100988.74,  160691.44,   12267.28,            12156.28,  -107.30,  59046.33,           61560.75,    -34.03,    -52.48,          80.28,  +0.60,  -0.43
  6,     UK003B,       0,  0.240996, 2459439.528157257009,  94.75779,  69.13684,               22.03573,  38.11306,        22.03183,       38.11772,     94.75779,     +69.13684,      94.75694,      +69.14239,  3407168.82, -1855202.34,  5169698.06,      53.296023,       -0.382707,   98983.63,  158206.41,   14950.47,            14839.47,   124.39,  66772.46,           61772.29,     -8.41,    -12.94,          20.12,  +0.68,  -0.32
  7,     UK003B,       0,  0.281176, 2459439.528157722205,  95.70400,  69.17586,               21.67570,  37.92751,        21.67072,       37.93343,     95.70400,     +69.17586,      95.70312,      +69.18292,  3406336.42, -1856161.61,  5167675.13,      53.287253,       -0.401197,   97199.06,  155999.54,   17339.05,            17228.05,    61.73,  59447.09,           61666.56,    -10.54,    -16.22,          25.57,  +0.50,  -0.47
  8,     UK003B,       0,  0.321372, 2459439.528158187401,  96.71379,  69.20885,               21.29699,  37.72681,        21.28898,       37.73627,     96.71379,     +69.20885,      96.71235,      +69.22020,  3405476.58, -1857152.51,  5165585.50,      53.278186,       -0.420294,   95356.05,  153725.91,   19806.39,            19695.38,    76.85,  61382.57,           61598.28,    -16.65,    -25.63,          41.01,  +0.78,  -0.15
  9,     UK003B,       0,  0.361548, 2459439.528158652131,  97.63182,  69.23424,               20.95493,  37.54425,        20.94432,       37.55672,     97.63182,     +69.23424,      97.63029,      +69.24924,  3404718.95, -1858025.61,  5163744.27,      53.270190,       -0.437144,   93732.44,  151727.34,   21980.42,            21869.42,  -200.11,  54112.82,           61155.15,    -21.70,    -33.41,          54.16,  -0.16,  -1.07
 10,     UK003B,       0,  0.401760, 2459439.528159117792,  98.78242,  69.27404,               20.51817,  37.32648,        20.51532,       37.32981,     98.78242,     +69.27404,      98.78349,      +69.27807,  3403795.74, -1859089.54,  5161500.64,      53.260438,       -0.457642,   91754.43,  149299.53,   24629.60,            24518.60,    -4.13,  65880.35,           61128.48,     -5.73,     -8.80,          14.51,  +1.22,  +0.35

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.