Orbital Analysis for matched events on 20210813_232448.669_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 64.30° Bg 38.04° Vg 57.52km/s
mass 0.02246g, abs. mag -0.6
Path Details
------------
start 1.44° 51.69° 108.07km
end   1.33° 51.62° 99.08km

Orbit Details
-------------
Semimajor axis 4.97A.U., eccentricity 0.81, inclination 112.53°, Period 11.07Y, LA Sun 141.13°, last Perihelion 2021-07-21

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: 2459440.475563305896
Time: 2021-08-13 23:24:48.669629 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK000C and UK002F
 Convergence angle = 7.07031 deg
 R.A. =  51.16143  Dec = +59.13176 deg

Best intersection: Stations UK000C and UK002F with Qconv = 7.07 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   2861751.30 +/- 496.75 m
 Y =  -2836570.11 +/- 286.84 m
 Z =   5066230.82 +/- 421.37 m
 Vx =    19937.67 +/- 4076.25 m/s
 Vy =    23424.66 +/- 2049.75 m/s
 Vz =    49854.64 +/- 4470.30 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+1.714087e+05, +9.982844e+04, +1.524645e+05, +5.855599e+05, +2.960730e+05, +4.416881e+05
+9.982844e+04, +5.960715e+04, +9.017499e+04, +3.471694e+05, +1.836911e+05, +2.612550e+05
+1.524645e+05, +9.017499e+04, +1.386840e+05, +5.201056e+05, +2.649694e+05, +3.950498e+05
+5.855599e+05, +3.471694e+05, +5.201056e+05, +5.275820e+06, +2.716804e+06, +3.555465e+06
+2.960730e+05, +1.836911e+05, +2.649694e+05, +2.716804e+06, +1.474852e+06, +1.829043e+06
+4.416881e+05, +2.612550e+05, +3.950498e+05, +3.555465e+06, +1.829043e+06, +2.459363e+06

Timing offsets (from input data):
    UK000C: 0.000000 s
    UK000F: 0.000000 s
    UK002F: -0.000786 s
    UK002N: 0.000000 s

Reference point on the trajectory:
  Time: 2021-08-13 23:24:48.669629 UTC
  Lon     = ++1.438794 +/- 0.0079 deg
  Lat     = +51.687688 +/- 0.0013 deg
  Lat geo = +51.503470 +/- 0.0013 deg
  Ht      =  108152.05 +/- 423.33 m

  JD dynamic   = 2459440.476364046801 
  LST apparent = 315.2531914463 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  49.59756 +/- 4.0471 deg
  Dec       = +58.32503 +/- 2.1304 deg
  Azimuth   =  43.13633 +/- 3.7335 deg
  Elevation = +40.02364 +/- 0.3307 deg
  Vavg      =  58.20272 +/- 3.5038 km/s
  Vinit     =  58.58080 +/- 4.0272 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  49.55649 +/- 4.0471 deg
  Dec       = +58.08179 +/- 2.1304 deg
  Azimuth   =  43.40896 +/- 3.7335 deg
  Elevation = +39.89729 +/- 0.3307 deg
  Vavg      =  58.35710 +/- 3.5038 km/s
  Vinit     =  58.73518 +/- 4.0272 km/s
Radiant (geocentric, J2000):
  R.A.   =  49.92063 +/- 4.2334 deg
  Dec    = +57.95795 +/- 2.0688 deg
  Vg     =  57.52008 +/- 4.1179 km/s
  Vinf   =  58.58080 +/- 4.0272 km/s
  Zc     =  50.11090 +/- 0.3365 deg
  Zg     =  50.60033 +/- 0.4198 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  64.29502 +/- 3.3614 deg
  Bg     = +38.04323 +/- 1.3677 deg
  Vh     =  39.65889 +/- 2.3080 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  85.34791 +/- 16.5000 deg
  Bh     = +63.35548 +/- 1.5838 deg
  Vh_x   =  -1.44247 +/- 3.6211 km/s
  Vh_y   = -17.72658 +/- 2.7962 km/s
  Vh_z   = -35.44735 +/- 1.7227 km/s
Orbit:
  La Sun = 141.125345 +/- -0.0000 deg
  a      =   4.968182 +/- 2.0479 AU
  e      =   0.810585 +/- 0.1410
  i      = 112.531564 +/- 6.4143 deg
  peri   = 147.266876 +/- 16.3265 deg
  node   = 141.124332 +/- 0.0004 deg
  Pi     = 288.391208 +/- 16.3260 deg
  q      =   0.941051 +/- 0.0638 AU
  f      =  32.729173 +/- 16.3266 deg
  M      =   2.107844 +/- 10.3040 deg
  Q      =   8.995313 +/- 4.0485 AU
  n      =   0.089004 +/- 0.1834 deg/day
  T      =  11.073804 +/- 6.9734 years
  Last perihelion JD = 2459416.793699 (2021-07-21 07:02:55.599235) +/- 11.0069 days
  Tj     =   0.609006 +/- 1.1323
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +9.994518e-03, +3.393679e-03, +6.472605e-01, -4.513218e-07, +1.585057e-02, +6.464343e-03
q   , +3.393679e-03, +1.294683e-03, +2.383071e-01, -1.640244e-07, +5.940449e-03, +2.371699e-03
Tp  , +6.472605e-01, +2.383071e-01, +4.437318e+01, -3.059099e-05, +1.099636e+00, +4.410901e-01
node, -4.513218e-07, -1.640244e-07, -3.059099e-05, +2.175230e-11, -7.576604e-07, -3.129486e-07
peri, +1.585057e-02, +5.940449e-03, +1.099636e+00, -7.576604e-07, +2.733296e-02, +1.094018e-02
i   , +6.464343e-03, +2.371699e-03, +4.410901e-01, -3.129486e-07, +1.094018e-02, +4.506500e-03

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: UK000C
  Avg. res. = 1.662e-06 s
  Stddev    = 1.29e-03 s

Begin point on the trajectory:
  Lon =     1.437828 +/- 0.0077 deg
  Lat =    51.687047 +/- 0.0012 deg
  Ht  = 108068.61 +/- 410.02 m
End point on the trajectory:
  Lon =     1.332635 +/- 0.0085 deg
  Lat =    51.617780 +/- 0.0013 deg
  Ht  = 99076.41 +/- 447.80 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,   108068.61,    99076.41,          0.012054,     28.86,     26.22,              27.46, 1.0000,    True,    True, {"ff_name": "FF_UK000C_20210813_232445_118_0295168.fits"}
    UK000F,    True,    -1.306160,    51.883100,   80.00, 26206.407362,   0.285998,   108570.37,   103992.53,          0.150175,       nan,       nan,              48.00, 0.0000,    True,    True, {"ff_name": "FF_UK000F_20210813_232444_473_0279296.fits"}
    UK002F,   False,    -1.306160,    51.883100,   80.00,   0.000000,   0.000000,   107657.38,   101670.84,          0.010272,     31.93,     22.20,              48.00, 1.0000,    True,    True, {"ff_name": "FF_UK002F_20210813_232446_656_0246016.fits"}
    UK002N,    True,    -0.727590,    51.263100,   57.00,   0.000000,   0.000000,   108299.92,    99797.32,          0.035283,       nan,       nan,              27.46, 0.0000,    True,    True, {"ff_name": "FF_UK002N_20210813_232440_398_0299008.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,  0.000000, 2459440.475563305896,  32.98031,  36.42004,               71.74133,  33.46730,        71.74756,       33.48072,     32.98031,     +36.42004,      32.96365,      +36.42525,  2861707.14, -2836621.99,  5066120.41,      51.687047,       +1.437828,  108068.61,  192206.99,       0.00,              129.74,   -43.34,      0.00,           58491.67,    -32.48,    -35.71,          51.80,  +2.27,  +0.85
  1,     UK000C,       0,  0.040016, 2459440.475563769229,  32.80841,  36.14463,               72.09689,  33.38369,        72.09099,       33.37103,     32.80841,     +36.14463,      32.82425,      +36.13972,  2860866.76, -2837609.35,  5064019.02,      51.674847,       +1.419277,  106480.94,  189953.10,    2469.20,             2598.94,    81.69,  61705.32,           58491.67,     30.26,     33.35,          48.90,  +1.63,  +0.24
  2,     UK000C,       0,  0.080064, 2459440.475564232562,  32.69670,  35.87426,               72.40841,  33.26744,        72.40893,       33.26854,     32.69670,     +35.87426,      32.69568,      +35.87468,  2860104.02, -2838505.49,  5062111.76,      51.663767,       +1.402426,  105040.41,  187911.38,    4710.29,             4840.03,   -23.26,  55960.18,           58491.67,     -2.59,     -2.85,           4.23,  +1.46,  +0.09
  3,     UK000C,       0,  0.120088, 2459440.475564695895,  32.54193,  35.59573,               72.75504,  33.17115,        72.74870,       33.15777,     32.54193,     +35.59573,      32.55895,      +35.59056,  2859305.00, -2839444.25,  5060113.80,      51.652152,       +1.384781,  103531.84,  185778.09,    7057.96,             7187.70,   -20.23,  58656.51,           58491.67,     31.38,     34.59,          51.85,  +1.17,  -0.17
  4,     UK000C,       0,  0.160140, 2459440.475565159228,  32.41646,  35.29787,               73.09897,  33.04399,        73.09827,       33.04252,     32.41646,     +35.29787,      32.41894,      +35.29731,  2858499.60, -2840390.52,  5058099.86,      51.640436,       +1.366998,  102011.70,  183633.27,    9424.40,             9554.14,    -0.07,  59084.07,           58542.30,      3.41,      3.76,           5.70,  +1.31,  -0.01
  5,     UK000C,       0,  0.200184, 2459440.475565623026,  32.26675,  34.98124,               73.47490,  32.91830,        73.47430,       32.91704,     32.26675,     +34.98124,      32.26912,      +34.98076,  2857651.55, -2841386.89,  5055979.30,      51.628091,       +1.348283,  100411.61,  181381.50,   11916.13,            12045.87,   145.85,  62224.86,           59082.97,      2.87,      3.16,           4.86,  +1.58,  +0.29
  6,     UK000C,       0,  0.240240, 2459440.475566086359,  32.16406,  34.70345,               73.78520,  32.79055,        73.79435,       32.80934,     32.16406,     +34.70345,      32.14197,      +34.71066,  2856943.68, -2842218.56,  5054209.25,      51.617780,       +1.332635,   99076.41,  179505.35,   13995.99,            14125.73,  -120.80,  51923.81,           58508.59,    -42.81,    -47.08,          73.12,  +4.17,  +2.90
  0,     UK000F,       1,  0.519505, 2459440.475569318514,  19.99905,  19.05639,               95.43966,  28.70063,        95.35444,       28.55900,     19.99905,     +19.05639,      20.15873,      +18.99739,  2861973.39, -2836309.18,  5066786.17,      51.690910,       +1.441482,  108570.37,  220875.12,       0.00,              652.55, -29953.52,      0.00,           59358.14,    350.30,    508.46,         576.61,  +2.24,  +0.52
  1,     UK000F,       1,  0.559805, 2459440.475569785107,  19.82874,  18.67971,               95.85782,  28.51872,        95.76634,       28.36759,     19.82874,     +18.67971,      19.99911,      +18.61676,  2861215.71, -2837199.38,  5064891.56,      51.679914,       +1.424738,  107138.55,  219291.14,    2226.23,             1573.68, -31393.20,  55241.37,           59358.14,    371.61,    539.70,         616.34,  +1.13,  -0.58
  2,     UK000F,       1,  0.600185, 2459440.475570252631,  19.68868,  18.21321,               96.31606,  28.24900,        96.24963,       28.14026,     19.68868,     +18.21321,      19.81215,      +18.16800,  2860336.78, -2838232.02,  5062693.80,      51.667149,       +1.405344,  105478.20,  217469.56,    4808.67,             4156.12, -31176.25,  63953.60,           59358.14,    266.27,    385.75,         444.58,  +1.12,  -0.57
  3,     UK000F,       1,  0.640501, 2459440.475570719223,  19.50195,  17.81154,               96.76377,  28.05651,        96.68738,       27.93223,     19.50195,     +17.81154,      19.64285,      +17.75986,  2859550.08, -2839156.31,  5060726.62,      51.655716,       +1.387968,  103992.53,  215851.34,    7120.16,             6467.61, -31226.50,  57334.29,           59358.14,    302.43,    438.54,         509.05,  +1.74,  +0.07
  0,     UK002F,       0,  0.010175, 2459440.475563418586,  20.06015,  18.74785,               95.61776,  28.42846,        95.61069,       28.41683,     20.06015,     +18.74785,      20.07315,      +18.74303,  2861489.50, -2836877.70,  5065576.18,      51.683888,       +1.433026,  107657.38,  219997.79,       0.00,              769.23,     0.06,      0.00,           59371.20,     28.90,     41.59,          47.49,  +1.90,  +0.19
  1,     UK002F,       0,  0.050223, 2459440.475563882384,  19.89502,  18.34287,               96.05124,  28.22131,        96.04608,       28.21287,     19.89502,     +18.34287,      19.90464,      +18.33937,  2860693.55, -2837812.86,  5063585.89,      51.672332,       +1.415447,  106153.77,  218342.54,    2338.65,             3107.88,    -7.33,  58396.17,           59371.20,     20.87,     30.02,          34.54,  +1.32,  -0.38
  2,     UK002F,       0,  0.090283, 2459440.475564345717,  19.73728,  17.92048,               96.49019,  27.99554,        96.49353,       28.00096,     19.73728,     +17.92048,      19.73161,      +17.92272,  2859884.74, -2838763.12,  5061563.45,      51.660581,       +1.397588,  104626.36,  216673.75,    4715.09,             5484.31,    22.36,  59321.94,           59371.20,    -13.33,    -19.17,          22.23,  +1.22,  -0.46
  3,     UK002F,       0,  0.130323, 2459440.475564809050,  19.54563,  17.49461,               96.95837,  27.78705,        96.95423,       27.78036,     19.54563,     +17.49461,      19.55363,      +17.49184,  2859061.48, -2839730.37,  5059504.86,      51.648611,       +1.379414,  103072.16,  214989.12,    7133.99,             7903.22,    95.69,  60412.22,           59371.20,     16.33,     23.50,          27.46,  +0.94,  -0.72
  4,     UK002F,       0,  0.170383, 2459440.475565272849,  19.40314,  17.09271,               97.36734,  27.56599,        97.37436,       27.57724,     19.40314,     +17.09271,      19.39131,      +17.09736,  2858318.97, -2840602.74,  5057648.20,      51.637808,       +1.363007,  101670.84,  213480.94,    9315.63,            10084.85,   -69.43,  54459.17,           58491.00,    -27.35,    -39.32,          46.27,  +1.97,  +0.32
  0,     UK002N,       1, -0.014753, 2459440.475563134998,  32.89553,  36.49373,               71.73115,  33.56735,        71.69840,       33.49598,     32.89553,     +36.49373,      32.98393,      +36.46582,  2861829.55, -2836478.17,  5066426.50,      51.688823,       +1.440567,  108299.92,  192537.81,       0.00,              229.93,   921.09,     -0.00,           57973.14,    172.05,    190.60,         275.08,  +3.83,  +2.41
  1,     UK002N,       1,  0.025423, 2459440.475563600194,  32.85610,  36.27448,               71.95102,  33.44297,        71.94012,       33.41948,     32.85610,     +36.27448,      32.88532,      +36.26534,  2861233.56, -2837178.40,  5064936.20,      51.680173,       +1.427362,  107173.84,  190935.50,    1751.15,             1521.22,  -141.16,  43587.06,           57973.14,     56.38,     62.20,          90.69,  +2.12,  +0.72
  2,     UK002N,       1,  0.065659, 2459440.475564065855,  32.69685,  35.96466,               72.32867,  33.32851,        72.31480,       33.29889,     32.69685,     +35.96466,      32.73377,      +35.95315,  2860328.48, -2838241.77,  5062673.04,      51.667029,       +1.407396,  105464.29,  188512.36,    4410.44,             4180.51,   161.07,  66092.23,           57973.14,     70.27,     77.57,         114.52,  +1.25,  -0.13
  3,     UK002N,       1,  0.105895, 2459440.475564531516,  32.57678,  35.65939,               72.67618,  33.19349,        72.67119,       33.18294,     32.57678,     +35.65939,      32.59025,      +35.65531,  2859486.21, -2839231.36,  5060566.90,      51.654787,       +1.388804,  103873.92,  186262.62,    6885.22,             6655.29,   278.79,  61506.52,           57973.14,     24.79,     27.32,          40.86,  +0.72,  -0.63
  4,     UK002N,       1,  0.146099, 2459440.475564996712,  32.46619,  35.39272,               72.98305,  33.07867,        72.98385,       33.08034,     32.46619,     +35.39272,      32.46473,      +35.39336,  2858761.46, -2840082.86,  5058754.65,      51.644246,       +1.372784,  102505.89,  184330.24,    9014.67,             8784.74,    53.06,  52966.24,           57596.07,     -3.90,     -4.29,           6.49,  +1.02,  -0.31
  5,     UK002N,       1,  0.186299, 2459440.475565461908,  32.33648,  35.12766,               73.30078,  32.97616,        73.30043,       32.97543,     32.33648,     +35.12766,      32.33816,      +35.12738,  2858041.07, -2840929.24,  5056953.31,      51.633763,       +1.356861,  101146.48,  182413.92,   11131.30,            10901.37,  -185.25,  52652.55,           56782.44,      1.69,      1.86,           2.85,  +1.83,  +0.52
  6,     UK002N,       1,  0.226491, 2459440.475565927103,  32.17205,  34.86945,               73.63539,  32.89896,        73.62058,       32.86828,     32.17205,     +34.86945,      32.21069,      +34.85763,  2857325.91, -2841769.47,  5055165.04,      51.623349,       +1.341052,   99797.32,  180516.00,   13232.58,            13002.65,  -438.46,  52280.94,           56009.81,     70.02,     77.32,         119.19,  +3.84,  +2.56

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.