Orbital Analysis for matched events on 20210810_013645.746_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 61.53° Bg 38.64° Vg 58.92km/s
mass 0.00544g, abs. mag 1.4
Path Details
------------
start -1.86° 51.54° 107.52km
end   -1.94° 51.50° 98.21km

Orbit Details
-------------
Semimajor axis 20.11A.U., eccentricity 0.95, inclination 112.49°, Period 90.19Y, LA Sun 137.37°, last Perihelion 2021-07-19

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: 2459436.567196141928
Time: 2021-08-10 01:36:45.774263 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK0001 and UK0006
 Convergence angle = 68.19011 deg
 R.A. =  45.83212  Dec = +57.60958 deg
Intersection 2 - Stations: UK0001 and UK000S
 Convergence angle = 0.65692 deg
 R.A. =  86.14986  Dec = -82.95108 deg
Intersection 3 - Stations: UK0006 and UK000S
 Convergence angle = 68.70827 deg
 R.A. =  45.04483  Dec = +57.71512 deg

Best intersection: Stations UK0006 and UK000S with Qconv = 68.71 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   3824371.88 +/- 45.18 m
 Y =  -1309517.85 +/- 50.27 m
 Z =   5056643.87 +/- 108.71 m
 Vx =    22279.99 +/- 273.25 m/s
 Vy =    22693.51 +/- 334.84 m/s
 Vz =    50827.99 +/- 294.41 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+2.209452e+03, +9.031693e+02, +4.227395e+03, +4.388500e+03, -3.931190e+03, +4.734577e+03
+9.031693e+02, +2.677249e+03, +3.833207e+03, -6.551529e+03, +5.320362e+03, -2.971688e+03
+4.227395e+03, +3.833207e+03, +1.289861e+04, -1.691012e+02, -1.663268e+03, +1.840068e+04
+4.388500e+03, -6.551529e+03, -1.691012e+02, +4.587283e+04, -3.831342e+04, +2.622857e+04
-3.931190e+03, +5.320362e+03, -1.663268e+03, -3.831342e+04, +3.273927e+04, -2.900777e+04
+4.734577e+03, -2.971688e+03, +1.840068e+04, +2.622857e+04, -2.900777e+04, +9.236495e+04

Timing offsets (from input data):
    UK0001: -0.000054 s
    UK0006: 0.000336 s
    UK000S: 0.000000 s
    UK001Z: 0.000000 s

Reference point on the trajectory:
  Time: 2021-08-10 01:36:45.774263 UTC
  Lon     = +-1.852068 +/- 0.0008 deg
  Lat     = +51.545044 +/- 0.0005 deg
  Lat geo = +51.360629 +/- 0.0005 deg
  Ht      =  108703.55 +/- 101.63 m

  JD dynamic   = 2459436.567997202277 
  LST apparent = 341.0980865867 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  45.52680 +/- 0.4836 deg
  Dec       = +57.96632 +/- 0.1562 deg
  Azimuth   =  53.97681 +/- 0.2411 deg
  Elevation = +53.73033 +/- 0.2655 deg
  Vavg      =  54.44874 +/- 0.1825 km/s
  Vinit     =  59.95730 +/- 0.2444 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  45.75413 +/- 0.4836 deg
  Dec       = +57.75122 +/- 0.1562 deg
  Azimuth   =  54.25497 +/- 0.2411 deg
  Elevation = +53.54676 +/- 0.2655 deg
  Vavg      =  54.59034 +/- 0.1825 km/s
  Vinit     =  60.09890 +/- 0.2444 km/s
Radiant (geocentric, J2000):
  R.A.   =  45.69836 +/- 0.4877 deg
  Dec    = +57.77848 +/- 0.1588 deg
  Vg     =  58.92147 +/- 0.2488 km/s
  Vinf   =  59.95730 +/- 0.2444 km/s
  Zc     =  36.37839 +/- 0.2655 deg
  Zg     =  36.70646 +/- 0.2700 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  61.52536 +/- 0.2943 deg
  Bg     = +38.63918 +/- 0.2017 deg
  Vh     =  41.30499 +/- 0.2951 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  83.12037 +/- 0.6771 deg
  Bh     = +62.96786 +/- 0.2213 deg
  Vh_x   =  -2.24867 +/- 0.2063 km/s
  Vh_y   = -18.63755 +/- 0.1379 km/s
  Vh_z   = -36.79249 +/- 0.3138 km/s
Orbit:
  La Sun = 137.373606 +/- 0.0000 deg
  a      =  20.110915 +/- 5.7049 AU
  e      =   0.953232 +/- 0.0254
  i      = 112.494778 +/- 0.0593 deg
  peri   = 148.433039 +/- 1.0814 deg
  node   = 137.373354 +/- 0.0000 deg
  Pi     = 285.806393 +/- 1.0814 deg
  q      =   0.940548 +/- 0.0040 AU
  f      =  31.563172 +/- 1.0814 deg
  M      =   0.240301 +/- 0.2758 deg
  Q      =  39.281282 +/- 11.4072 AU
  n      =   0.010928 +/- 0.0116 deg/day
  T      =  90.187921 +/- 35.9932 years
  Last perihelion JD = 2459414.579283 (2021-07-19 01:54:10.069383) +/- 0.8058 days
  Tj     =  -0.195855 +/- 0.1443
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +7.000994e-04, +7.199417e-05, +1.864442e-02, +2.000283e-09, +3.961783e-04, -2.792213e-05
q   , +7.199417e-05, +1.731646e-05, +3.308740e-03, +1.888801e-10, +7.997422e-05, -2.639858e-06
Tp  , +1.864442e-02, +3.308740e-03, +6.919761e-01, +5.093356e-08, +1.606002e-02, -7.114559e-04
node, +2.000283e-09, +1.888801e-10, +5.093356e-08, +5.937996e-15, +1.065572e-09, -8.286726e-11
peri, +3.961783e-04, +7.997422e-05, +1.606002e-02, +1.065572e-09, +3.795095e-04, -1.488749e-05
i   , -2.792213e-05, -2.639858e-06, -7.114559e-04, -8.286726e-11, -1.488749e-05, +1.156471e-06

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 0.013823
 a2 = 45.830118

Mean time residuals from time vs. length:
  Station with reference time: UK000S
  Avg. res. = 5.297e-06 s
  Stddev    = 2.30e-03 s

Begin point on the trajectory:
  Lon =    -1.862002 +/- 0.0002 deg
  Lat =    51.540539 +/- 0.0003 deg
  Ht  = 107522.63 +/- 46.95 m
End point on the trajectory:
  Lon =    -1.941347 +/- 0.0002 deg
  Lat =    51.504907 +/- 0.0001 deg
  Ht  = 98208.79 +/- 26.05 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
    UK0001,   False,    -1.778230,    50.857470,   24.00,   0.000000,   0.000000,   107522.63,    98860.72,          0.022060,      6.89,     48.25,              33.16, 0.2991,    True,    True, {"ff_name": "FF_UK0001_20210810_013639_234_0479744.fits"}
    UK0006,   False,    -1.306160,    51.883100,   80.00,   0.000000,   0.000000,   105580.92,    98208.79,          0.013130,     23.62,     13.22,              61.95, 0.7789,   False,    True, {"ff_name": "FF_UK0006_20210810_013645_796_0460032.fits"}
    UK000S,   False,    -1.778230,    50.857470,   24.00,   0.000000,   0.000000,   106992.92,    98389.21,          0.019511,      6.16,     43.65,              33.16, 0.2991,    True,    True, {"ff_name": "FF_UK000S_20210810_013645_930_0476672.fits"}
    UK001Z,    True,    -2.949729,    50.877448,   82.00,  40.292714,   0.000000,   108220.13,    96345.90,          0.093564,       nan,       nan,               9.78, 0.0000,    True,    True, {"ff_name": "FF_UK001Z_20210810_013639_120_0472832.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,     UK0001,       0,  0.027550, 2459436.567196461372, 303.42676,  85.80980,              355.62592,  54.09370,       355.62676,       54.09253,    303.42676,     +85.80980,     303.42141,      +85.81100,  3823827.57, -1310072.25,  5055402.13,      51.540539,       -1.862002,  107522.63,  132148.98,       0.00,             1464.77,   528.38,      0.00,           56581.54,      2.89,      0.41,           4.55,  +3.05,  +2.44
  1,     UK0001,       0,  0.067266, 2459436.567196920980, 297.72183,  85.66439,              354.93748,  53.90131,       354.92477,       53.91863,    297.72183,     +85.66439,     297.82360,      +85.64716,  3823141.36, -1310771.20,  5053836.66,      51.534856,       -1.874695,  106033.99,  130607.20,    1846.65,             3311.42,    -6.24,  46496.27,           56581.54,    -42.58,     -6.07,          67.93,  +1.22,  +0.64
  2,     UK0001,       0,  0.106802, 2459436.567197378725, 289.59688,  85.33663,              353.83825,  53.60122,       353.81536,       53.63132,    289.59688,     +85.33663,     289.81232,      +85.30865,  3822072.75, -1311859.64,  5051398.81,      51.525998,       -1.894372,  103716.14,  128222.17,    4722.36,             6187.13,   499.01,  72736.66,           56581.54,    -73.16,    -10.46,         118.88,  +0.49,  -0.05
  3,     UK0001,       0,  0.146490, 2459436.567197837867, 285.14578,  85.06200,              353.11988,  53.42366,       353.10646,       53.44094,    285.14578,     +85.06200,     285.27797,      +85.04671,  3821405.69, -1312539.09,  5049877.01,      51.520464,       -1.906722,  102269.45,  126744.09,    6517.49,             7982.26,   -85.45,  45231.08,           56581.54,    -41.70,     -5.94,          68.54,  +0.34,  -0.17
  4,     UK0001,       0,  0.186078, 2459436.567198296078, 279.85650,  84.66441,              352.17891,  53.16762,       352.16938,       53.17954,    279.85650,     +84.66441,     279.95206,      +84.65457,  3820535.58, -1313425.35,  5047892.01,      51.513240,       -1.922783,  100382.68,  124828.56,    8859.03,            10323.80,  -117.50,  59147.53,           56495.47,    -28.51,     -4.06,          47.59,  +0.53,  +0.05
  5,     UK0001,       0,  0.225750, 2459436.567198755220, 275.88940,  84.31941,              351.42165,  52.92968,       351.39925,       52.95711,    275.88940,     +84.31941,     276.11106,      +84.29807,  3819833.62, -1314140.33,  5046290.61,      51.507407,       -1.935776,   98860.72,  123294.27,   10748.06,            12212.83,  -607.10,  47616.18,           55200.94,    -65.12,     -9.29,         110.05,  +1.51,  +1.06
  0,     UK0006,       0,  0.080553, 2459436.567197070457, 318.84258,  29.30830,              225.65623,  61.80161,       225.68189,       61.80283,    318.84258,     +29.30830,     318.83163,      +29.31550,  3822932.50, -1310983.94,  5053360.17,      51.533126,       -1.878562,  105580.92,  119428.95,       0.00,             3873.48,  -240.83,      0.00,           61829.70,     12.40,    -22.17,          43.87,  +0.24,  -0.15
  1,     UK0006,       0,  0.121557, 2459436.567197544966, 318.03737,  28.32378,              225.88862,  60.59560,       225.93632,       60.59787,    318.03737,     +28.32378,     318.01619,      +28.33753,  3821900.84, -1312034.74,  5051006.62,      51.524573,       -1.897572,  103343.29,  118232.95,    2776.27,             6649.76,    76.95,  67707.40,           61829.70,     23.70,    -42.37,          84.70,  -0.32,  -0.68
  2,     UK0006,       0,  0.162445, 2459436.567198018078, 317.32252,  27.47757,              226.13106,  59.54653,       226.14414,       59.54715,    317.32252,     +27.47757,     317.31708,      +27.48143,  3821018.37, -1312933.60,  5048993.40,      51.517249,       -1.913862,  101429.54,  117253.20,    5151.10,             9024.58,     0.24,  58081.15,           61829.70,      6.66,    -11.90,          23.98,  -0.03,  -0.38
  3,     UK0006,       0,  0.203405, 2459436.567198492121, 316.57158,  26.56889,              226.37223,  58.42504,       226.35199,       58.42408,    316.57158,     +26.56889,     316.58215,      +26.56276,  3820090.94, -1313878.23,  5046877.65,      51.509546,       -1.930979,   99418.63,  116266.95,    7646.86,            11520.35,    40.16,  60931.85,           61829.70,    -10.55,     18.83,          38.30,  +0.78,  +0.45
  4,     UK0006,       0,  0.243997, 2459436.567198961973, 316.13788,  25.99946,              226.47255,  57.73754,       226.47537,       57.73768,    316.13788,     +25.99946,     316.13752,      +26.00032,  3819532.91, -1314446.62,  5045604.60,      51.504907,       -1.941347,   98208.79,  115697.27,    9148.57,            13022.05,  -891.92,  36995.07,           56690.80,      1.49,     -2.66,           5.44,  +3.36,  +3.04
  0,     UK000S,       1,  0.000000, 2459436.567196141928, 308.28136,  85.86355,              356.15381,  54.27145,       356.18492,       54.22707,    308.28136,     +85.86355,     308.12259,      +85.91013,  3824381.69, -1309507.85,  5056666.25,      51.545125,       -1.851773,  108724.84,  133399.79,       0.00,               26.40,   741.82,      0.00,           54685.71,    110.56,     15.55,         172.63,  +5.58,  +4.95
  1,     UK000S,       0,  0.040184, 2459436.567196607124, 301.49690,  85.73821,              355.36454,  54.05098,       355.37852,       54.03160,    301.49690,     +85.73821,     301.39798,      +85.75793,  3823583.40, -1310320.95,  5054845.10,      51.538517,       -1.866512,  106992.92,  131599.44,    2148.25,             2121.85,   427.94,  53460.41,           54685.71,     47.85,      6.77,          75.75,  +1.87,  +1.27
  2,     UK000S,       0,  0.080332, 2459436.567197071854, 295.40295,  85.52104,              354.55539,  53.86175,       354.57852,       53.83051,    295.40295,     +85.52104,     295.20727,      +85.55153,  3822805.31, -1311113.49,  5053070.01,      51.532072,       -1.880885,  105305.03,  129855.00,    4242.17,             4215.77,   114.69,  52154.94,           54685.71,     76.51,     10.79,         122.74,  +1.07,  +0.50
  3,     UK000S,       0,  0.120528, 2459436.567197537050, 288.89177,  85.23122,              353.63607,  53.61026,       353.65275,       53.58839,    288.89177,     +85.23122,     288.73448,      +85.25134,  3821919.86, -1312015.38,  5051050.00,      51.524730,       -1.897222,  103384.53,  127882.74,    6624.99,             6598.59,    87.47,  59280.11,           54685.71,     53.06,      7.50,          86.43,  +0.88,  +0.35
  4,     UK000S,       0,  0.160724, 2459436.567198002245, 283.29218,  84.90541,              352.76159,  53.35210,       352.76555,       53.34705,    283.29218,     +84.90541,     283.25375,      +84.90977,  3821087.24, -1312863.45,  5049150.53,      51.517821,       -1.912598,  101578.89,  126041.34,    8865.63,             8839.23,   -81.93,  55742.82,           55272.60,     12.13,      1.72,          20.06,  +0.86,  +0.36
  5,     UK000S,       0,  0.200940, 2459436.567198467441, 277.95020,  84.48163,              351.78576,  53.06649,       351.78386,       53.06885,    277.95020,     +84.48163,     277.96993,      +84.47973,  3820181.86, -1313785.63,  5047085.05,      51.510301,       -1.929308,   99615.74,  124054.06,   11302.09,            11275.69,   -56.72,  60584.33,           56199.78,     -5.63,     -0.80,           9.45,  +1.06,  +0.59
  6,     UK000S,       0,  0.241076, 2459436.567198932171, 274.94005,  84.18610,              351.16363,  52.87879,       351.15772,       52.88599,    274.94005,     +84.18610,     274.99885,      +84.18060,  3819616.14, -1314361.85,  5045794.46,      51.505599,       -1.939815,   98389.21,  122821.03,   12824.49,            12798.09,  -940.76,  37931.05,           54575.88,    -17.06,     -2.42,          28.93,  +2.36,  +1.91
  0,     UK001Z,       1,  0.029849, 2459436.567196487449,  63.49758,  59.49331,               45.30490,  44.80367,        45.46940,       44.73758,     63.49758,     +59.49331,      63.50470,      +59.35916,  3824149.07, -1309744.79,  5056135.57,      51.543200,       -1.856143,  108220.13,  152350.80,       0.00,              599.60,  -474.67,      0.00,           66566.75,     10.30,    356.66,         483.08,  +3.11,  +2.20
  1,     UK001Z,       1,  0.069993, 2459436.567196952179,  63.82149,  59.45190,               45.24747,  44.63899,        45.35450,       44.59645,     63.82149,     +59.45190,      63.82470,      +59.36466,  3823178.56, -1310733.31,  5053921.52,      51.535164,       -1.874027,  106114.68,  149768.94,    2611.72,             3211.32,  -269.88,  65058.75,           66566.75,      5.50,    228.01,         314.11,  +2.18,  +1.30
  2,     UK001Z,       1,  0.110149, 2459436.567197416909,  64.18144,  59.47632,               45.09573,  44.48947,        45.22631,       44.43738,     64.18144,     +59.47632,      64.18479,      +59.36957,  3822125.59, -1311805.82,  5051519.35,      51.526437,       -1.893421,  103830.73,  146969.63,    5445.35,             6044.95,   156.10,  70565.58,           66566.75,      7.22,    273.77,         384.36,  +2.00,  +1.16
  3,     UK001Z,       1,  0.150297, 2459436.567197881639,  64.51458,  59.46629,               44.99513,  44.33593,        45.10830,       44.29094,     64.51458,     +59.46629,      64.51660,      +59.37365,  3821189.55, -1312759.23,  5049383.94,      51.518670,       -1.910686,  101800.77,  144481.82,    7964.30,             8563.90,   267.89,  62741.59,           66566.75,      5.87,    233.54,         333.51,  +1.95,  +1.15
  4,     UK001Z,       1,  0.190425, 2459436.567198345903,  64.81133,  59.47893,               44.87865,  44.20974,        45.00274,       44.16032,     64.81133,     +59.47893,      64.81299,      +59.37714,  3820379.66, -1313584.16,  5047536.31,      51.511945,       -1.925650,  100044.62,  142329.50,   10143.79,            10743.39,    41.41,  54313.44,           63868.24,      6.66,    252.78,         366.45,  +1.93,  +1.16
  5,     UK001Z,       1,  0.230585, 2459436.567198810633,  65.17051,  59.44215,               44.80071,  44.03217,        44.87676,       44.00214,     65.17051,     +59.44215,      65.17090,      +59.37976,  3819433.79, -1314547.58,  5045378.47,      51.504083,       -1.943104,   97993.94,  139818.12,   12689.20,            13288.80,   178.94,  63381.74,           63027.46,      3.46,    152.21,         224.60,  +2.46,  +1.73
  6,     UK001Z,       1,  0.270725, 2459436.567199275363,  65.46543,  59.34429,               44.81785,  43.85336,        44.77173,       43.87120,     65.46543,     +59.34429,      65.46792,      +59.38202,  3818673.54, -1315321.95,  5043644.07,      51.497758,       -1.957168,   96345.90,  137799.42,   14735.12,            15334.71,  -181.83,  50969.49,           61435.49,     -1.21,    -90.75,         135.85,  +5.86,  +5.16

Notes
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- 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.