Orbital Analysis for matched events on 20210816_230409.369_UK

Summary for Event
-----------------
shower ID 547 KAP
Lg 61.83° Bg 18.64° Vg 64.00km/s
mass 0.03647g, abs. mag -1.1
Path Details
------------
start 0.23° 52.60° 111.57km
end   0.05° 52.52° 105.10km

Orbit Details
-------------
Semimajor axis 2.69A.U., eccentricity 0.64, inclination 146.29°, Period 4.40Y, LA Sun 143.99°, last Perihelion 2021-07-24

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: 2459443.461219551507
Time: 2021-08-16 23:04:09.423404 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK000C and UK002K
 Convergence angle = 76.65686 deg
 R.A. =  54.92384  Dec = +39.12082 deg

Best intersection: Stations UK000C and UK002K with Qconv = 76.66 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   2635713.15 +/- 34.84 m
 Y =  -2941169.41 +/- 22.77 m
 Z =   5134506.63 +/- 23.22 m
 Vx =    28932.04 +/- 200.64 m/s
 Vy =    41179.01 +/- 193.29 m/s
 Vz =    41070.61 +/- 171.18 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+1.225276e+03, -5.691475e+01, +9.786864e+00, +3.059855e+03, -3.569193e+03, -3.518221e+03
-5.691475e+01, +5.314406e+02, -2.980062e+02, -1.627842e+03, +1.492885e+03, -1.698047e+03
+9.786864e+00, -2.980062e+02, +5.527617e+02, +1.200584e+03, -9.754949e+02, +2.117166e+03
+3.059855e+03, -1.627842e+03, +1.200584e+03, +1.481842e+04, -1.578856e+04, -3.055939e+03
-3.569193e+03, +1.492885e+03, -9.754949e+02, -1.578856e+04, +1.714461e+04, +6.213115e+03
-3.518221e+03, -1.698047e+03, +2.117166e+03, -3.055939e+03, +6.213115e+03, +2.963396e+04

Timing offsets (from input data):
    UK000C: -0.000944 s
    UK002K: 0.000000 s

Reference point on the trajectory:
  Time: 2021-08-16 23:04:09.423404 UTC
  Lon     = ++0.271247 +/- 0.0004 deg
  Lat     = +52.615805 +/- 0.0002 deg
  Lat geo = +52.433219 +/- 0.0002 deg
  Ht      =  112978.74 +/- 29.59 m

  JD dynamic   = 2459443.462020919193 
  LST apparent = 311.8649357447 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  54.90843 +/- 0.1926 deg
  Dec       = +39.21721 +/- 0.1059 deg
  Azimuth   =  55.29002 +/- 0.1450 deg
  Elevation = +23.34207 +/- 0.1252 deg
  Vavg      =  65.48218 +/- 0.1084 km/s
  Vinit     =  64.95821 +/- 0.1239 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  54.83485 +/- 0.1926 deg
  Dec       = +39.06125 +/- 0.1059 deg
  Azimuth   =  55.44693 +/- 0.1450 deg
  Elevation = +23.25953 +/- 0.1252 deg
  Vavg      =  65.69982 +/- 0.1084 km/s
  Vinit     =  65.17585 +/- 0.1239 km/s
Radiant (geocentric, J2000):
  R.A.   =  55.01533 +/- 0.1919 deg
  Dec    = +38.72128 +/- 0.1082 deg
  Vg     =  64.00393 +/- 0.1258 km/s
  Vinf   =  64.95821 +/- 0.1239 km/s
  Zc     =  66.76198 +/- 0.1253 deg
  Zg     =  67.32068 +/- 0.1273 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  61.82903 +/- 0.1554 deg
  Bg     = +18.64302 +/- 0.1113 deg
  Vh     =  37.71098 +/- 0.1534 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  68.49016 +/- 0.2797 deg
  Bh     = +32.85771 +/- 0.1572 deg
  Vh_x   = -11.61509 +/- 0.1166 km/s
  Vh_y   = -29.47177 +/- 0.1491 km/s
  Vh_z   = -20.46026 +/- 0.1508 km/s
Orbit:
  La Sun = 143.994031 +/- -0.0000 deg
  a      =   2.686213 +/- 0.1059 AU
  e      =   0.644411 +/- 0.0126
  i      = 146.291321 +/- 0.1460 deg
  peri   = 148.817201 +/- 0.5673 deg
  node   = 143.988898 +/- 0.0000 deg
  Pi     = 292.806100 +/- 0.5673 deg
  q      =   0.955187 +/- 0.0021 AU
  f      =  31.176170 +/- 0.5672 deg
  M      =   5.362196 +/- 0.3251 deg
  Q      =   4.417238 +/- 0.2120 AU
  n      =   0.223869 +/- 0.0115 deg/day
  T      =   4.402620 +/- 0.2679 years
  Last perihelion JD = 2459419.509612 (2021-07-24 00:13:50.437660) +/- 0.4212 days
  Tj     =   1.023381 +/- 0.0705
Shower association:
  IAU No.  =  547
  IAU code =  KAP

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +1.671533e-04, -4.694962e-06, +2.218724e-03, +4.662182e-09, +2.087106e-05, -2.250815e-05
q   , -4.694962e-06, +4.531846e-06, +7.582270e-04, +6.947635e-10, +2.027804e-05, -3.358546e-06
Tp  , +2.218724e-03, +7.582270e-04, +1.824988e-01, +2.158647e-07, +4.168428e-03, -1.042950e-03
node, +4.662182e-09, +6.947635e-10, +2.158647e-07, +2.855208e-13, +4.497460e-09, -1.379221e-09
peri, +2.087106e-05, +2.027804e-05, +4.168428e-03, +4.497460e-09, +1.015501e-04, -2.173342e-05
i   , -2.250815e-05, -3.358546e-06, -1.042950e-03, -1.379221e-09, -2.173342e-05, +6.662603e-06

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 144.553066
 a2 = -0.000001

Mean time residuals from time vs. length:
  Station with reference time: UK002K
  Avg. res. = 5.621e-06 s
  Stddev    = 2.37e-03 s

Begin point on the trajectory:
  Lon =     0.232422 +/- 0.0002 deg
  Lat =    52.599423 +/- 0.0004 deg
  Ht  = 111574.37 +/- 32.93 m
End point on the trajectory:
  Lon =     0.051929 +/- 0.0002 deg
  Lat =    52.523413 +/- 0.0002 deg
  Ht  = 105101.00 +/- 22.19 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, 125.867667,   0.000000,   111574.37,   105349.68,          0.008593,     21.04,     19.44,              28.78, 1.0000,    True,    True, {"ff_name": "FF_UK000C_20210816_230409_282_0276224.fits"}
    UK002K,   False,    -0.382860,    53.537770,   34.00,   0.024454,  30.096703,   111257.91,   105101.00,          0.015815,     39.79,     17.81,              81.42, 1.0000,    True,    True, {"ff_name": "FF_UK002K_20210816_230402_155_0266496.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,  0.073462, 2459443.461220178287,  77.87759,  65.30913,               23.56697,  33.46061,        23.56829,       33.46474,     77.87759,     +65.30913,      77.86979,      +65.31177,  2634133.64, -2943417.53,  5132264.43,      52.599423,       +0.232422,  111574.37,  198407.04,       0.00,             3546.31,  -746.03,      0.00,           70354.70,    -10.03,    -10.86,          15.37,  +4.63,  +3.14
  1,     UK000C,       0,  0.113246, 2459443.461220638826,  78.58173,  65.69039,               23.01301,  33.59238,        23.01155,       33.58774,     78.58173,     +65.69039,      78.59121,      +65.68737,  2632650.45, -2945528.56,  5130158.96,      52.584023,       +0.195809,  110257.10,  195504.77,    3330.06,             6876.37,    -0.27,  83703.56,           70354.70,     11.13,     12.03,          17.29,  +2.61,  +1.15
  2,     UK000C,       0,  0.153090, 2459443.461221099831,  79.22168,  65.97987,               22.55362,  33.67064,        22.55829,       33.68577,     79.22168,     +65.97987,      79.19259,      +65.98980,  2631479.55, -2947195.09,  5128496.81,      52.571853,       +0.166877,  109218.20,  193222.76,    5958.95,             9505.26,    40.43,  65979.55,           70354.70,    -35.75,    -38.71,          56.25,  +1.44,  +0.01
  3,     UK000C,       0,  0.192914, 2459443.461221560836,  79.79937,  66.27979,               22.11431,  33.77594,        22.11546,       33.77973,     79.79937,     +66.27979,      79.79265,      +66.28230,  2630364.58, -2948782.04,  5126914.04,      52.560254,       +0.139326,  108229.72,  191058.06,    8462.30,            12008.61,   -43.12,  62860.19,           70354.70,     -8.84,     -9.57,          14.07,  +1.30,  -0.11
  4,     UK000C,       0,  0.232734, 2459443.461222021375,  80.40857,  66.58723,               21.66025,  33.88353,        21.65770,       33.87499,     80.40857,     +66.58723,      80.42632,      +66.58151,  2629240.27, -2950382.27,  5125318.02,      52.548548,       +0.111551,  107233.78,  188883.96,   10986.60,            14532.91,  -105.45,  63392.92,           68067.12,     19.72,     21.32,          31.71,  +1.37,  -0.01
  5,     UK000C,       0,  0.272530, 2459443.461222482380,  81.15598,  66.93259,               21.12949,  33.99463,        21.12614,       33.98321,     81.15598,     +66.93259,      81.17961,      +66.92484,  2627968.14, -2952192.90,  5123512.17,      52.535290,       +0.080155,  106107.89,  186435.42,   13842.78,            17389.09,   165.65,  71770.52,           67942.31,     25.98,     28.08,          42.33,  +1.39,  +0.04
  6,     UK000C,       0,  0.312402, 2459443.461222943850,  81.71051,  67.16044,               20.75806,  34.05725,        20.75789,       34.05667,     81.71051,     +67.16044,      81.71289,      +67.16004,  2627110.82, -2953413.12,  5122295.16,      52.526349,       +0.058946,  105349.68,  184790.89,   15767.63,            19313.94,  -499.51,  48275.77,           65787.56,      1.31,      1.41,           2.15,  +3.17,  +1.84
  7,     UK000C,       1,  0.352158, 2459443.461223403923,  82.61446,  67.56627,               20.13373,  34.19370,        20.12965,       34.17920,     82.61446,     +67.56627,      82.64459,      +67.55620,  2625679.64, -2955450.12,  5120263.52,      52.511409,       +0.023661,  104085.08,  182060.50,   18980.92,            22527.23,   131.30,  80825.21,           66141.15,     32.13,     34.72,          53.59,  +5.29,  +3.99
  0,     UK002K,       1,  0.000000, 2459443.461219551507, 327.92387,  10.13786,              156.58257,  44.57662,       156.59401,       44.59440,    327.92387,     +10.13786,     327.91150,      +10.15317,  2635716.36, -2941164.85,  5134511.18,      52.615838,       +0.271552,  112981.60,  159459.78,       0.00,                7.20,   486.80,      0.00,           62172.18,     22.23,    -49.68,          70.40,  +5.13,  +4.12
  1,     UK002K,       0,  0.080004, 2459443.461220477708, 326.68102,   9.17505,              158.55640,  43.92141,       158.56435,       43.93316,    326.68102,      +9.17505,     326.67308,       +9.18525,  2633777.47, -2943924.47,  5131758.83,      52.595727,       +0.223560,  111257.91,  158853.10,    4353.19,             4345.99,  -371.33,  54412.12,           62172.18,     14.81,    -33.08,          47.06,  +1.66,  +0.66
  2,     UK002K,       0,  0.120012, 2459443.461220940575, 325.87606,   8.54091,              159.81850,  43.47188,       159.82615,       43.48284,    325.87606,      +8.54091,     325.86878,       +8.55048,  2632517.98, -2945717.10,  5129970.91,      52.582647,       +0.192445,  110139.52,  158523.13,    7181.00,             7173.80,  -142.37,  70681.16,           62172.18,     13.90,    -31.03,          44.24,  +1.06,  +0.06
  3,     UK002K,       0,  0.160020, 2459443.461221403442, 325.07804,   7.91005,              161.05472,  43.01270,       161.06128,       43.02184,    325.07804,      +7.91005,     325.07216,       +7.91807,  2631271.21, -2947491.63,  5128201.06,      52.569686,       +0.161650,  109033.43,  158245.86,    9980.24,             9973.04,    58.02,  69967.01,           62172.18,     11.64,    -26.00,          37.13,  +0.75,  -0.25
  4,     UK002K,       0,  0.200016, 2459443.461221866310, 324.32528,   7.33243,              162.20204,  42.58648,       162.19723,       42.57996,    324.32528,      +7.33243,     324.33083,       +7.32667,  2630111.53, -2949142.20,  5126554.84,      52.557620,       +0.133001,  108005.50,  158032.11,   12583.94,            12576.74,    63.66,  65099.08,           63531.99,     -8.37,     18.68,          26.72,  +0.33,  -0.66
  5,     UK002K,       0,  0.240048, 2459443.461222329643, 323.61638,   6.73705,              163.28211,  42.12555,       163.29128,       42.13771,    323.61638,      +6.73705,     323.60854,       +6.74786,  2628981.56, -2950750.49,  5124950.78,      52.545853,       +0.105088,  107004.73,  157865.06,   15120.96,            15113.76,     0.27,  63374.71,           64008.54,     15.68,    -35.01,          50.12,  +0.35,  -0.64
  6,     UK002K,       0,  0.280064, 2459443.461222792976, 322.91886,   6.17578,              164.32616,  41.68775,       164.33559,       41.69999,    322.91886,      +6.17578,     322.91106,       +6.18671,  2627890.05, -2952304.04,  5123401.31,      52.534476,       +0.078126,  106038.80,  157742.44,   17571.63,            17564.42,  -148.43,  61242.18,           63957.73,     15.88,    -35.46,          50.81,  +0.80,  -0.19
  7,     UK002K,       0,  0.320092, 2459443.461223256309, 322.25127,   5.61702,              165.31804,  41.23974,       165.33805,       41.26520,    322.25127,      +5.61702,     322.23380,       +5.63991,  2626829.50, -2953813.52,  5121895.81,      52.523413,       +0.051929,  105101.00,  157659.89,   19952.77,            19945.57,  -367.44,  59486.93,           63609.10,     33.24,    -74.26,         106.45,  +1.74,  +0.75

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.