Orbital Analysis for matched events on 20210813_224839.941_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 63.19° Bg 38.13° Vg 60.30km/s
mass 0.06880g, abs. mag -1.0
Path Details
------------
start 1.35° 52.97° 108.75km
end   1.18° 52.86° 95.26km

Orbit Details
-------------
Semimajor axis -57.07A.U., eccentricity 1.02, inclination 114.52°, Period 1000000000.00Y, LA Sun 141.10°, 

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: 2459440.450462281704
Time: 2021-08-13 22:48:39.941139 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK000Z and UK002K
 Convergence angle = 24.28017 deg
 R.A. =  48.58970  Dec = +57.98804 deg

Best intersection: Stations UK000Z and UK002K with Qconv = 24.28 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   2306666.78 +/- 83.61 m
 Y =  -3162791.98 +/- 18.33 m
 Z =   5155581.55 +/- 28.63 m
 Vx =    21616.84 +/- 460.62 m/s
 Vy =    24084.12 +/- 236.43 m/s
 Vz =    52077.62 +/- 349.55 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+2.815510e+03, -1.336428e+02, +5.868575e+02, +1.427956e+04, -5.011365e+01, +6.567646e+03
-1.336428e+02, +3.072962e+02, +1.887202e+02, +1.767273e+01, +2.753988e+02, -2.827129e+02
+5.868575e+02, +1.887202e+02, +6.139069e+02, +1.705124e+03, -6.721414e+02, +1.169300e+03
+1.427956e+04, +1.767273e+01, +1.705124e+03, +1.142693e+05, +9.420452e+03, +4.653458e+04
-5.011365e+01, +2.753988e+02, -6.721414e+02, +9.420452e+03, +3.400463e+03, +2.030606e+03
+6.567646e+03, -2.827129e+02, +1.169300e+03, +4.653458e+04, +2.030606e+03, +2.038792e+04

Timing offsets (from input data):
    UK000Z: 0.000177 s
    UK002K: 0.000000 s

Reference point on the trajectory:
  Time: 2021-08-13 22:48:39.941139 UTC
  Lon     = ++1.350486 +/- 0.0009 deg
  Lat     = +52.973024 +/- 0.0004 deg
  Lat geo = +52.790946 +/- 0.0004 deg
  Ht      =  108735.95 +/- 51.50 m

  JD dynamic   = 2459440.451263022609 
  LST apparent = 306.1037749651 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  48.09026 +/- 0.6089 deg
  Dec       = +58.14201 +/- 0.1678 deg
  Azimuth   =  40.76017 +/- 0.4217 deg
  Elevation = +37.73983 +/- 0.1333 deg
  Vavg      =  58.99512 +/- 0.2506 km/s
  Vinit     =  61.31404 +/- 0.3009 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  47.98620 +/- 0.6089 deg
  Dec       = +57.92087 +/- 0.1678 deg
  Azimuth   =  41.01469 +/- 0.4217 deg
  Elevation = +37.63321 +/- 0.1333 deg
  Vavg      =  59.14299 +/- 0.2506 km/s
  Vinit     =  61.46191 +/- 0.3009 km/s
Radiant (geocentric, J2000):
  R.A.   =  48.32844 +/- 0.6154 deg
  Dec    = +57.74831 +/- 0.1632 deg
  Vg     =  60.30144 +/- 0.3061 km/s
  Vinf   =  61.31404 +/- 0.3009 km/s
  Zc     =  52.39818 +/- 0.1341 deg
  Zg     =  52.86765 +/- 0.1401 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  63.19118 +/- 0.4563 deg
  Bg     = +38.12555 +/- 0.0638 deg
  Vh     =  42.03484 +/- 0.1990 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  80.62495 +/- 1.3086 deg
  Bh     = +62.33578 +/- 0.0885 deg
  Vh_x   =  -3.17914 +/- 0.4526 km/s
  Vh_y   = -19.25564 +/- 0.0867 km/s
  Vh_z   = -37.22957 +/- 0.1599 km/s
Orbit:
  La Sun = 141.101237 +/- -0.0000 deg
  a      = -57.074316 +/- 179.0716 AU
  e      =   1.016829 +/- 0.0176
  i      = 114.519657 +/- 0.3637 deg
  peri   = 153.773469 +/- 1.2785 deg
  node   = 141.099829 +/- 0.0000 deg
  Pi     = 294.873298 +/- 1.2784 deg
  q      =   0.960495 +/- 0.0048 AU
  f      =  26.222432 +/- 1.2785 deg
  M      =        nan +/- nan deg
  Q      = -115.109127 +/- 358.1439 AU
  n      =   0.002286 +/- 0.0038 deg/day
  T      = 1000000000.000000 +/- 442215582.5863 years
  Last perihelion JD = NaN 
  Tj     =  -0.597575 +/- 0.1073
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +2.053811e-04, +5.275766e-05, +9.780121e-03, -5.300629e-09, +2.412332e-04, +6.843298e-05
q   , +5.275766e-05, +1.365040e-05, +2.527194e-03, -1.403075e-09, +6.238238e-05, +1.810985e-05
Tp  , +9.780121e-03, +2.527194e-03, +4.680065e-01, -2.588097e-07, +1.155097e-02, +3.340607e-03
node, -5.300629e-09, -1.403075e-09, -2.588097e-07, +1.625989e-13, -6.404131e-09, -2.096502e-09
peri, +2.412332e-04, +6.238238e-05, +1.155097e-02, -6.404131e-09, +2.851152e-04, +8.265960e-05
i   , +6.843298e-05, +1.810985e-05, +3.340607e-03, -2.096502e-09, +8.265960e-05, +2.703204e-05

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 0.021959
 a2 = 26.484644

Mean time residuals from time vs. length:
  Station with reference time: UK002K
  Avg. res. = 5.019e-06 s
  Stddev    = 2.24e-03 s

Begin point on the trajectory:
  Lon =     1.350695 +/- 0.0009 deg
  Lat =    52.973171 +/- 0.0003 deg
  Ht  = 108752.89 +/- 53.01 m
End point on the trajectory:
  Lon =     1.182417 +/- 0.0011 deg
  Lat =    52.855986 +/- 0.0002 deg
  Ht  = 95263.97 +/- 55.52 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
    UK000Z,   False,    -1.740490,    53.069201,  230.00,   0.001778,  33.406375,   108181.08,    95263.97,          0.009151,     32.82,     16.30,              45.46, 1.0000,    True,    True, {"ff_name": "FF_UK000Z_20210813_224838_252_0227840.fits"}
    UK002K,   False,    -0.382860,    53.537770,   34.00,   0.000643,  36.201414,   108752.89,    95580.65,          0.006771,     19.67,      0.69,              59.47, 1.0000,    True,    True, {"ff_name": "FF_UK002K_20210813_224836_597_0232704.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,     UK000Z,       0,  0.013420, 2459440.450462433975,  15.05494,  19.72489,               91.86810,  26.37029,        91.87525,       26.38315,     15.05494,     +19.72489,      15.04104,      +19.73071,  2306347.16, -3163148.08,  5154811.54,      52.968226,       +1.343580,  108181.08,  235228.27,       0.00,              906.58,   521.01,      0.00,           57665.39,    -26.27,    -52.82,          51.73,  +3.34,  +1.48
  1,     UK000Z,       0,  0.053516, 2459440.450462897774,  14.90485,  19.42517,               92.20273,  26.22944,        92.20650,       26.23620,     14.90485,     +19.42517,      14.89774,      +19.42823,  2305675.75, -3163896.12,  5153194.05,      52.958142,       +1.329023,  107015.77,  233883.00,    1904.37,             2810.95,   -33.06,  47495.26,           57665.39,    -13.74,    -27.64,          27.22,  +1.90,  +0.06
  2,     UK000Z,       0,  0.093660, 2459440.450463362504,  14.70606,  19.00428,               92.66214,  26.02388,        92.66565,       26.03012,     14.70606,     +19.00428,      14.69969,      +19.00709,  2304754.71, -3164922.29,  5150975.13,      52.944301,       +1.309118,  105417.73,  232054.13,    4516.83,             5423.41,   118.01,  65077.23,           57665.39,    -12.59,    -25.33,          25.14,  +1.47,  -0.36
  3,     UK000Z,       0,  0.133780, 2459440.450463826768,  14.51531,  18.62908,               93.08192,  25.84819,        93.07893,       25.84290,     14.51531,     +18.62908,      14.52160,      +18.62669,  2303935.19, -3165835.35,  5149000.80,      52.931976,       +1.291391,  103996.37,  230438.56,    6841.33,             7747.91,   -17.42,  57938.56,           57665.39,     10.61,     21.38,          21.36,  +1.22,  -0.59
  4,     UK000Z,       0,  0.173916, 2459440.450464291498,  14.31574,  18.21688,               93.53413,  25.64855,        93.52781,       25.63746,     14.31574,     +18.21688,      14.32849,      +18.21188,  2303054.91, -3166816.10,  5146880.10,      52.918729,       +1.272364,  102470.20,  228717.68,    9338.15,            10244.73,    18.50,  62209.10,           58848.82,     22.13,     44.60,          44.90,  +1.05,  -0.75
  5,     UK000Z,       0,  0.214064, 2459440.450464756228,  14.15942,  17.82446,               93.93624,  25.43769,        93.94129,       25.44649,     14.15942,     +17.82446,      14.15076,      +17.82843,  2302252.97, -3167709.57,  5144948.14,      52.906653,       +1.255018,  101080.37,  227161.69,   11612.76,            12519.34,  -168.52,  56655.64,           58873.38,    -17.50,    -35.21,          35.71,  +1.06,  -0.72
  6,     UK000Z,       0,  0.254200, 2459440.450465220492,  13.93252,  17.38348,               94.42906,  25.23072,        94.42361,       25.22127,     13.93252,     +17.38348,      13.94382,      +17.37922,  2301327.87, -3168740.26,  5142719.46,      52.892713,       +1.235037,   99477.69,  225383.62,   14236.72,            15143.30,    -5.47,  65376.59,           59579.06,     18.63,     37.54,          38.35,  +0.84,  -0.92
  7,     UK000Z,       0,  0.294344, 2459440.450465685222,  13.74007,  16.95487,               94.88402,  25.01201,        94.88043,       25.00583,     13.74007,     +16.95487,      13.74799,      +16.95209,  2300461.81, -3169705.17,  5140633.01,      52.879653,       +1.216323,   97977.88,  223733.56,   16693.21,            17599.80,   -10.36,  61192.14,           60007.51,     12.12,     24.41,          25.13,  +0.84,  -0.91
  8,     UK000Z,       0,  0.334484, 2459440.450466149952,  13.55093,  16.54146,               95.32477,  24.80248,        95.32102,       24.79607,     13.55093,     +16.54146,      13.55927,      +16.53858,  2299635.59, -3170625.69,  5138642.54,      52.867186,       +1.198464,   96547.59,  222172.94,   19036.71,            19943.29,  -128.01,  58383.06,           60099.11,     12.51,     25.20,          26.12,  +0.86,  -0.87
  9,     UK000Z,       0,  0.374612, 2459440.450466614217,  13.38223,  16.16415,               95.72297,  24.60831,        95.72059,       24.60426,     13.38223,     +16.16415,      13.38819,      +16.16232,  2298893.85, -3171452.09,  5136855.60,      52.855986,       +1.182417,   95263.97,  220782.76,   21140.58,            22047.16,  -484.55,  52428.91,           59727.43,      7.87,     15.85,          16.53,  +1.47,  -0.25
  0,     UK002K,       0,  0.000000, 2459440.450462281704, 350.44684,  16.66633,              117.81478,  38.72610,       117.81058,       38.71919,    350.44684,     +16.66633,     350.45365,      +16.66235,  2306676.54, -3162781.10,  5155605.07,      52.973171,       +1.350695,  108752.89,  171601.52,       0.00,               27.68,   464.93,      0.00,           58565.67,      0.81,     22.89,          27.53,  +3.27,  +2.10
  1,     UK002K,       0,  0.040240, 2459440.450462747365, 350.13565,  16.15302,              118.49343,  38.45918,       118.49702,       38.46499,    350.13565,     +16.15302,     350.13007,      +16.15636,  2305951.08, -3163589.37,  5153857.33,      52.962278,       +1.334978,  107493.59,  170544.89,    2057.71,             2030.03,    -0.00,  51136.02,           58565.67,     -0.68,    -19.19,          23.23,  +2.32,  +1.16
  2,     UK002K,       0,  0.080524, 2459440.450463213492, 349.71786,  15.51026,              119.36706,  38.13576,       119.36597,       38.13402,    349.71786,     +15.51026,     349.71992,      +15.50926,  2305037.33, -3164607.41,  5151655.99,      52.948549,       +1.315228,  105908.01,  169242.40,    4649.48,             4621.80,   121.79,  64337.35,           58565.67,      0.20,      5.73,           6.99,  +1.48,  +0.34
  3,     UK002K,       0,  0.120792, 2459440.450463679619, 349.33980,  14.91682,              120.16074,  37.82929,       120.15768,       37.82451,    349.33980,     +14.91682,     349.34505,      +14.91405,  2304209.79, -3165529.40,  5149662.37,      52.936107,       +1.297328,  104472.59,  168088.01,    6996.69,             6969.01,     0.00,  58289.73,           58565.67,      0.55,     15.70,          19.28,  +1.10,  -0.03
  4,     UK002K,       0,  0.161072, 2459440.450464145746, 348.96906,  14.30037,              120.95719,  37.49582,       120.96132,       37.50215,    348.96906,     +14.30037,     348.96342,      +14.30403,  2303374.03, -3166460.55,  5147648.91,      52.923533,       +1.279253,  103023.41,  166947.77,    9367.25,             9339.56,   -99.17,  58851.94,           58787.73,     -0.73,    -20.78,          25.69,  +0.83,  -0.28
  5,     UK002K,       0,  0.201396, 2459440.450464612804, 348.52555,  13.58488,              121.88859,  37.11070,       121.89311,       37.11751,    348.52555,     +13.58488,     348.51958,      +13.58883,  2302409.47, -3167535.20,  5145325.17,      52.909011,       +1.258422,  101351.57,  165665.57,   12103.12,            12075.44,   164.28,  67847.39,           60147.25,     -0.79,    -22.29,          27.77,  +0.88,  -0.22
  6,     UK002K,       0,  0.241664, 2459440.450465078931, 348.16365,  12.98983,              122.65045,  36.78295,       122.65788,       36.79396,    348.16365,     +12.98983,     348.15362,      +12.99622,  2301621.90, -3168412.67,  5143427.81,      52.897145,       +1.241385,   99987.01,  164643.70,   14337.00,            14309.32,   -70.83,  55475.31,           60132.00,     -1.27,    -35.93,          45.04,  +0.81,  -0.27
  7,     UK002K,       0,  0.281956, 2459440.450465545058, 347.74686,  12.32164,              123.51082,  36.41588,       123.51491,       36.42184,    347.74686,     +12.32164,     347.74204,      +12.32512,  2300742.39, -3169392.56,  5141308.97,      52.883885,       +1.222382,   98463.72,  163532.14,   16831.63,            16803.95,   -46.67,  61913.69,           60274.17,     -0.68,    -19.44,          24.53,  +0.76,  -0.31
  8,     UK002K,       0,  0.322232, 2459440.450466011185, 347.35280,  11.69096,              124.31781,  36.06558,       124.31728,       36.06482,    347.35280,     +11.69096,     347.35491,      +11.69052,  2299922.12, -3170306.45,  5139332.83,      52.871510,       +1.204649,   97043.55,  162522.75,   19158.25,            19130.57,  -189.53,  57767.00,           60173.38,      0.09,      2.49,           3.16,  +0.77,  -0.28
  9,     UK002K,       0,  0.362524, 2459440.450466477778, 346.94845,  11.02957,              125.14865,  35.68958,       125.14656,       35.68660,    346.94845,     +11.02957,     346.95298,      +11.02783,  2299076.86, -3171248.19,  5137296.50,      52.858750,       +1.186384,   95580.65,  161511.46,   21555.75,            21528.07,  -262.50,  59503.11,           60085.50,      0.34,      9.65,          12.33,  +0.90,  -0.14
 10,     UK002K,       1,  0.402680, 2459440.450466942508, 346.71065,  10.66166,              125.62166,  35.48477,       125.61227,       35.47158,    346.71065,     +10.66166,     346.72570,      +10.65393,  2298604.54, -3171774.42,  5136158.62,      52.851616,       +1.176105,   94763.37,  160955.94,   22895.44,            22867.76, -1384.94,  33362.10,           58827.05,      1.48,     42.80,          54.88,  +6.07,  +5.04

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.