Orbital Analysis for matched events on 20210813_231231.645_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 65.06° Bg 39.27° Vg 60.30km/s
mass 0.04491g, abs. mag -1.3
Path Details
------------
start -4.55° 52.08° 107.37km
end   -4.73° 51.94° 91.94km

Orbit Details
-------------
Semimajor axis -11.45A.U., eccentricity 1.08, inclination 112.62°, Period 1000000000.00Y, LA Sun 141.12°, 

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: 2459440.467032933608
Time: 2021-08-13 23:12:31.685737 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK0006 and UK0020
 Convergence angle = 27.05555 deg
 R.A. =  44.55658  Dec = +52.36679 deg

Best intersection: Stations UK0006 and UK0020 with Qconv = 27.06 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   2358702.50 +/- 1943.71 m
 Y =  -3222290.49 +/- 37.04 m
 Z =   5095388.14 +/- 3952.68 m
 Vx =    19894.71 +/- 8929.69 m/s
 Vy =    23686.95 +/- 6224.32 m/s
 Vz =    52933.78 +/- 10191.16 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+1.339719e+04, -3.107570e+02, -2.754265e+04, +3.426461e+04, -2.024853e+03, -7.663259e+04
-3.107570e+02, +4.603192e+02, +2.379798e+02, -9.925670e+02, +1.989073e+03, -3.614730e+02
-2.754265e+04, +2.379798e+02, +5.958872e+04, -7.463588e+04, +6.822392e+02, +1.702442e+05
+3.426461e+04, -9.925670e+02, -7.463588e+04, +1.093607e+05, -1.347170e+03, -2.409783e+05
-2.024853e+03, +1.989073e+03, +6.822392e+02, -1.347170e+03, +1.069008e+04, -9.008842e+03
-7.663259e+04, -3.614730e+02, +1.702442e+05, -2.409783e+05, -9.008842e+03, +5.481279e+05

Timing offsets (from input data):
    UK0006: -0.001499 s
    UK0020: 0.000000 s

Reference point on the trajectory:
  Time: 2021-08-13 23:12:31.685737 UTC
  Lon     = +-4.531260 +/- 0.0223 deg
  Lat     = +52.097289 +/- 0.0296 deg
  Lat geo = +51.913728 +/- 0.0297 deg
  Ht      =  108845.01 +/- 2404.56 m

  JD dynamic   = 2459440.467834140640 
  LST apparent = 306.2039640684 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  49.97305 +/- 11.9049 deg
  Dec       = +59.69893 +/- 4.5897 deg
  Azimuth   =  38.09221 +/- 7.8536 deg
  Elevation = +37.40805 +/- 0.8356 deg
  Vavg      =  59.45588 +/- 4.9573 km/s
  Vinit     =  61.30951 +/- 9.5723 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  49.84584 +/- 11.9049 deg
  Dec       = +59.47119 +/- 4.5897 deg
  Azimuth   =  38.36085 +/- 7.8536 deg
  Elevation = +37.30599 +/- 0.8356 deg
  Vavg      =  59.59910 +/- 4.9573 km/s
  Vinit     =  61.45273 +/- 9.5723 km/s
Radiant (geocentric, J2000):
  R.A.   =  50.23870 +/- 11.7240 deg
  Dec    = +59.30907 +/- 4.6580 deg
  Vg     =  60.29690 +/- 9.6747 km/s
  Vinf   =  61.30951 +/- 9.5723 km/s
  Zc     =  52.73650 +/- 0.8257 deg
  Zg     =  53.20951 +/- 0.9070 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  65.06093 +/- 7.2216 deg
  Bg     = +39.26602 +/- 3.7627 deg
  Vh     =  42.76560 +/- 11.8642 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  85.61676 +/- 9.3510 deg
  Bh     = +63.17483 +/- 0.3592 deg
  Vh_x   =  -1.47496 +/- 5.8690 km/s
  Vh_y   = -19.24237 +/- 4.3384 km/s
  Vh_z   = -38.16350 +/- 10.3904 km/s
Orbit:
  La Sun = 141.117152 +/- 0.0000 deg
  a      = -11.445638 +/- 215.8182 AU
  e      =   1.082951 +/- 1.5410
  i      = 112.623747 +/- 3.3152 deg
  peri   = 151.541846 +/- 0.6970 deg
  node   = 141.115886 +/- 0.0002 deg
  Pi     = 292.657732 +/- 0.6971 deg
  q      =   0.949431 +/- 0.0137 AU
  f      =  28.454127 +/- 0.6970 deg
  M      =        nan +/- nan deg
  Q      = -23.840706 +/- 431.6369 AU
  n      =   0.025453 +/- 4.3363 deg/day
  T      = 1000000000.000000 +/- 442216623.4878 years
  Last perihelion JD = NaN 
  Tj     =  -0.928957 +/- 8.9435
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +3.901666e-03, -4.930832e-05, +4.301846e-02, +3.196506e-08, +4.614192e-04, -4.102371e-04
q   , -4.930832e-05, +2.234826e-06, -2.871785e-04, -2.739709e-10, +1.088885e-06, +3.514849e-06
Tp  , +4.301846e-02, -2.871785e-04, +5.182985e-01, +3.765115e-07, +6.237186e-03, -4.830544e-03
node, +3.196506e-08, -2.739709e-10, +3.765115e-07, +2.775609e-13, +4.390091e-09, -3.560394e-09
peri, +4.614192e-04, +1.088885e-06, +6.237186e-03, +4.390091e-09, +8.502198e-05, -5.632040e-05
i   , -4.102371e-04, +3.514849e-06, -4.830544e-03, -3.560394e-09, -5.632040e-05, +4.567173e-05

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 48.096902
 a2 = 6.180998

Mean time residuals from time vs. length:
  Station with reference time: UK0020
  Avg. res. = 1.200e-05 s
  Stddev    = 3.46e-03 s

Begin point on the trajectory:
  Lon =    -4.548343 +/- 0.0197 deg
  Lat =    52.083863 +/- 0.0255 deg
  Ht  = 107369.26 +/- 2064.17 m
End point on the trajectory:
  Lon =    -4.728943 +/- 0.0126 deg
  Lat =    51.942690 +/- 0.0022 deg
  Ht  = 91942.65 +/- 57.83 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
    UK0006,   False,    -1.306160,    51.883100,   80.00,  42.852713,   6.341489,   105069.58,    91942.65,          0.030083,     12.25,    132.04,             100.17, 1.0000,    True,    True, {"ff_name": "FF_UK0006_20210813_231234_711_0204544.fits"}
    UK0020,   False,    -3.515726,    50.691998,   17.00,  11.251086,  12.253468,   107369.26,    97213.08,          0.010089,     18.24,     29.76,              54.28, 1.0000,    True,   False, {"ff_name": "FF_UK0020_20210813_231225_448_0266752.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,     UK0006,       0,  0.103571, 2459440.467034148984, 229.95823,  22.32648,              276.36798,  23.77948,       276.37587,       23.77308,    229.95823,     +22.32648,     229.94825,      +22.32648,  2356684.83, -3224692.75,  5090019.74,      52.062913,       -4.575241,  105069.58,  250429.69,       0.00,             6217.84,   -92.10,      0.00,           58650.99,     41.97,      3.86,          34.71,  +4.36,  +2.37
  1,     UK0006,       0,  0.184547, 2459440.467035085894, 229.96313,  21.20009,              275.55317,  22.93731,       275.56568,       22.92722,    229.96313,     +21.20009,     229.94747,      +21.20009,  2355069.71, -3226615.75,  5085722.38,      52.035355,       -4.610557,  102050.01,  251189.89,    4977.33,            11195.17,   -79.36,  61466.76,           58650.99,     66.88,      6.14,          55.15,  +3.96,  +1.96
  2,     UK0006,       0,  0.225111, 2459440.467035555746, 229.91343,  20.55901,              275.13403,  22.42390,       275.10904,       22.44404,    229.91343,     +20.55901,     229.94711,      +20.55902,  2354145.72, -3227715.87,  5083263.93,      52.019573,       -4.630732,  100323.63,  251666.72,    7824.79,            14042.64,   281.14,  70196.76,           58650.99,   -134.04,    -12.42,         110.33,  +1.02,  -0.98
  3,     UK0006,       0,  0.265387, 2459440.467036021873, 229.88922,  20.24457,              274.92959,  22.17170,       274.88650,       22.20637,    229.88922,     +20.24457,     229.94668,      +20.24460,  2353691.87, -3228256.22,  5082056.38,      52.011817,       -4.640725,   99475.90,  251917.80,    9223.41,            15441.25,  -789.55,  34725.69,           58650.99,   -231.42,    -21.53,         190.30,  +2.43,  +0.42
  4,     UK0006,       0,  0.386919, 2459440.467037428170, 229.91453,  18.46111,              273.65948,  20.83567,       273.63675,       20.85382,    229.91453,     +18.46111,     229.94560,      +18.46112,  2351096.02, -3231346.89,  5075149.60,      51.967400,       -4.697413,   94630.98,  253469.58,   17223.05,            23440.89,  -240.97,  65823.38,           60193.03,   -123.06,    -11.40,         100.57,  +0.22,  -1.80
  5,     UK0006,       0,  0.427267, 2459440.467037895229, 229.91505,  18.05561,              273.37788,  20.52741,       273.35595,       20.54490,    229.91505,     +18.05561,     229.94520,      +18.05562,  2350501.54, -3232054.69,  5073567.86,      51.957215,       -4.710444,   93522.25,  253862.60,   19055.07,            25272.91,  -882.67,  45405.35,           59158.16,   -118.97,    -11.02,          97.08,  +0.07,  -1.95
  6,     UK0006,       0,  0.467759, 2459440.467038364150, 229.91387,  17.48021,              272.98171,  20.08804,       272.95923,       20.10594,    229.91387,     +17.48021,     229.94485,      +17.48022,  2349654.25, -3233063.47,  5071313.50,      51.942690,       -4.728943,   91942.65,  254440.08,   21666.14,            27883.98,  -754.15,  64483.65,           59129.32,   -122.42,    -11.34,          99.66,  +1.64,  -0.39
  0,     UK0020,       1,  0.000000, 2459440.467032933608, 178.95436,  63.83428,              336.06097,  31.43017,       336.07819,       31.39690,    178.95436,     +63.83428,     178.88336,      +63.81580,  2358709.36, -3222282.32,  5095406.40,      52.097406,       -4.530943,  108857.85,  204420.49,       0.00,               21.14,    61.08,      0.00,           61755.46,    110.68,     67.72,         130.92,  +5.49,  +3.94
  1,     UK0020,       0,  0.040292, 2459440.467033399735, 179.46700,  63.34466,              335.50967,  31.16596,       335.50305,       31.17859,    179.46700,     +63.34466,     179.49389,      +63.35158,  2357914.06, -3223229.22,  5093290.35,      52.083863,       -4.548343,  107369.26,  202877.37,    2450.87,             2429.73,    -0.61,  60827.78,           61755.46,    -41.77,    -25.62,          49.82,  +4.33,  +2.79
  2,     UK0020,       0,  0.080560, 2459440.467033865862, 180.09894,  62.85995,              334.90733,  30.94146,       334.90416,       30.94744,    180.09894,     +62.85995,     180.11182,      +62.86318,  2357094.52, -3224204.98,  5091109.79,      52.069898,       -4.566265,  105835.88,  201306.05,    4976.46,             4955.32,    56.16,  62719.44,           61755.46,    -19.67,    -12.06,          23.65,  +2.29,  +0.77
  3,     UK0020,       0,  0.120828, 2459440.467034331989, 180.68657,  62.37016,              334.31653,  30.70578,       334.31162,       30.71492,    180.68657,     +62.37016,     180.70609,      +62.37503,  2356292.24, -3225160.19,  5088975.16,      52.056218,       -4.583810,  104335.38,  199787.01,    7448.85,             7427.71,    59.75,  61398.51,           61755.46,    -29.94,    -18.36,          36.26,  +1.87,  +0.37
  4,     UK0020,       0,  0.161076, 2459440.467034798115, 181.29590,  61.89538,              333.72279,  30.49281,       333.72847,       30.48236,    181.29590,     +61.89538,     181.27502,      +61.88989,  2355510.70, -3226090.69,  5086895.74,      52.042883,       -4.600904,  102874.24,  198325.96,    9857.30,             9836.16,     0.61,  59840.18,           61369.11,     34.08,     20.88,          41.56,  +1.33,  -0.16
  5,     UK0020,       0,  0.201336, 2459440.467035263777, 181.82276,  61.41651,              333.15897,  30.25773,       333.16169,       30.25277,    181.82276,     +61.41651,     181.81347,      +61.41394,  2354758.55, -3226986.21,  5084894.49,      52.030042,       -4.617358,  101468.56,  196937.72,   12175.20,            12154.06,  -149.81,  57573.33,           60716.55,     16.07,      9.85,          19.74,  +0.90,  -0.57
  6,     UK0020,       0,  0.241584, 2459440.467035729904, 182.34600,  60.94344,              332.59771,  30.03006,       332.60187,       30.02255,    182.34600,     +60.94344,     182.33180,      +60.93960,  2354022.53, -3227862.53,  5082936.16,      52.017468,       -4.633462,  100093.50,  195596.53,   14443.40,            14422.26,  -349.19,  56355.59,           60016.43,     24.23,     14.85,          29.97,  +0.74,  -0.72
  7,     UK0020,       0,  0.281852, 2459440.467036195565, 182.90260,  60.43050,              331.99061,  29.78424,       331.99834,       29.77044,    182.90260,     +60.43050,     182.87608,      +60.42352,  2353236.01, -3228798.98,  5080843.47,      52.004024,       -4.650656,   98624.64,  194182.17,   16867.23,            16846.09,  -394.18,  60192.31,           59739.30,     44.36,     27.16,          55.25,  +0.65,  -0.79
  8,     UK0020,       0,  0.322124, 2459440.467036661692, 183.39483,  59.91955,              331.41104,  29.52479,       331.41264,       29.52195,    183.39483,     +59.91955,     183.39053,      +59.91814,  2352479.89, -3229699.23,  5078831.66,      51.991091,       -4.667190,   97213.08,  192841.76,   19197.37,            19176.22,  -533.10,  57859.98,           59484.64,      9.07,      5.56,          11.38,  +0.71,  -0.72

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.