Orbital Analysis for matched events on 20210813_003411.647_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 62.86° Bg 39.45° Vg 58.43km/s
mass 0.00680g, abs. mag 0.8
Path Details
------------
start 0.85° 52.99° 108.02km
end   0.78° 52.95° 100.69km

Orbit Details
-------------
Semimajor axis 13.15A.U., eccentricity 0.93, inclination 111.49°, Period 47.71Y, LA Sun 140.21°, 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: 2459439.523745924700
Time: 2021-08-13 00:34:11.647894 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK002K and UK0032
 Convergence angle = 15.77414 deg
 R.A. =  49.31314  Dec = +59.22198 deg

Best intersection: Stations UK002K and UK0032 with Qconv = 15.77 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   3424658.10 +/- 137.47 m
 Y =  -1892376.02 +/- 22.06 m
 Z =   5156139.52 +/- 56.96 m
 Vx =    20890.13 +/- 1354.22 m/s
 Vy =    22217.12 +/- 842.92 m/s
 Vz =    51056.87 +/- 1197.65 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+8.609443e+03, +4.031772e+02, +3.934764e+03, +5.975871e+04, +6.346214e+03, +4.078941e+04
+4.031772e+02, +6.662279e+02, -6.613550e+01, -3.032766e+03, +3.993784e+03, -4.266884e+03
+3.934764e+03, -6.613550e+01, +2.479951e+03, +3.793182e+04, +1.116742e+03, +2.794979e+04
+5.975871e+04, -3.032766e+03, +3.793182e+04, +1.037342e+06, +6.895051e+04, +6.795769e+05
+6.346214e+03, +3.993784e+03, +1.116742e+03, +6.895051e+04, +4.075984e+04, +2.324580e+04
+4.078941e+04, -4.266884e+03, +2.794979e+04, +6.795769e+05, +2.324580e+04, +4.675862e+05

Timing offsets (from input data):
    UK002K: 0.000000 s
    UK0032: 0.000405 s

Reference point on the trajectory:
  Time: 2021-08-13 00:34:11.647894 UTC
  Lon     = ++0.854113 +/- 0.0010 deg
  Lat     = +52.989146 +/- 0.0006 deg
  Lat geo = +52.807078 +/- 0.0006 deg
  Ht      =  108058.30 +/- 116.64 m

  JD dynamic   = 2459439.524546665605 
  LST apparent = 331.0761143650 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  46.76321 +/- 1.8573 deg
  Dec       = +59.15046 +/- 0.3922 deg
  Azimuth   =  50.09162 +/- 1.1311 deg
  Elevation = +49.62801 +/- 0.6832 deg
  Vavg      =  54.36884 +/- 1.2124 km/s
  Vinit     =  59.47102 +/- 1.1550 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  46.89455 +/- 1.8573 deg
  Dec       = +58.92227 +/- 0.3922 deg
  Azimuth   =  50.36234 +/- 1.1311 deg
  Elevation = +49.46743 +/- 0.6832 deg
  Vavg      =  54.51112 +/- 1.2124 km/s
  Vinit     =  59.61330 +/- 1.1550 km/s
Radiant (geocentric, J2000):
  R.A.   =  46.99529 +/- 1.8952 deg
  Dec    = +58.90546 +/- 0.3811 deg
  Vg     =  58.42637 +/- 1.1772 km/s
  Vinf   =  59.47102 +/- 1.1550 km/s
  Zc     =  40.48900 +/- 0.6857 deg
  Zg     =  40.86347 +/- 0.7096 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  62.85817 +/- 1.3186 deg
  Bg     = +39.45274 +/- 0.1850 deg
  Vh     =  41.03233 +/- 0.8385 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  83.41065 +/- 4.4243 deg
  Bh     = +64.79940 +/- 0.3087 deg
  Vh_x   =  -2.00485 +/- 1.2904 km/s
  Vh_y   = -17.35570 +/- 0.4447 km/s
  Vh_z   = -37.12698 +/- 0.7470 km/s
Orbit:
  La Sun = 140.211301 +/- 0.0000 deg
  a      =  13.154385 +/- 2.7291 AU
  e      =   0.927323 +/- 0.0649
  i      = 111.492682 +/- 1.2792 deg
  peri   = 151.960409 +/- 5.0473 deg
  node   = 140.210817 +/- 0.0001 deg
  Pi     = 292.171226 +/- 5.0472 deg
  q      =   0.956021 +/- 0.0198 AU
  f      =  28.035776 +/- 5.0473 deg
  M      =   0.411490 +/- 1.7452 deg
  Q      =  25.352748 +/- 5.4424 AU
  n      =   0.020658 +/- 0.0505 deg/day
  T      =  47.709673 +/- 11.3054 years
  Last perihelion JD = 2459419.605859 (2021-07-24 02:32:26.195975) +/- 3.6081 days
  Tj     =  -0.040379 +/- 0.4223
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +3.439993e-03, +7.996060e-04, +1.621864e-01, -6.450262e-08, +3.827522e-03, +9.160067e-04
q   , +7.996060e-04, +1.941002e-04, +3.879275e-02, -1.573883e-08, +9.200702e-04, +2.236958e-04
Tp  , +1.621864e-01, +3.879275e-02, +7.793329e+00, -3.146197e-06, +1.845131e-01, +4.470330e-02
node, -6.450262e-08, -1.573883e-08, -3.146197e-06, +1.472477e-12, -7.461569e-08, -2.090896e-08
peri, +3.827522e-03, +9.200702e-04, +1.845131e-01, -7.461569e-08, +4.371146e-03, +1.060287e-03
i   , +9.160067e-04, +2.236958e-04, +4.470330e-02, -2.090896e-08, +1.060287e-03, +2.969190e-04

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: UK002K
  Avg. res. = 2.701e-07 s
  Stddev    = 5.20e-04 s

Begin point on the trajectory:
  Lon =     0.853789 +/- 0.0010 deg
  Lat =    52.988983 +/- 0.0006 deg
  Ht  = 108024.34 +/- 118.66 m
End point on the trajectory:
  Lon =     0.782920 +/- 0.0016 deg
  Lat =    52.953548 +/- 0.0001 deg
  Ht  = 100688.02 +/- 176.70 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
    UK002K,   False,    -0.382860,    53.537770,   34.00,   0.000000,   0.000000,   108024.34,   101409.36,          0.013989,     34.24,     12.51,              50.88, 1.0000,    True,    True, {"ff_name": "FF_UK002K_20210813_003404_270_0387328.fits"}
    UK0032,   False,    -0.023645,    52.984073,    6.00,   0.000000,   0.000000,   107357.51,   100688.02,          0.013450,     27.70,      2.18,              26.74, 1.0000,    True,    True, {"ff_name": "FF_UK0032_20210813_003410_760_0393472.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,     UK002K,       0,  0.000000, 2459439.523745924700,   6.62631,  19.39176,              125.98884,  45.72351,       126.01083,       45.74677,      6.62631,     +19.39176,       6.59975,      +19.40394,  3424642.44, -1892392.67,  5156101.25,      52.988983,       +0.853789,  108024.34,  149595.96,       0.00,               44.58,   865.64,      0.00,           53262.12,    -24.98,    -68.32,         100.30,  +4.93,  +4.06
  1,     UK002K,       0,  0.040184, 2459439.523746389896,   6.39133,  18.97852,              126.56183,  45.47997,       126.57176,       45.49037,      6.39133,     +18.97852,       6.37959,      +18.98398,  3424078.68, -1892992.24,  5154723.38,      52.983087,       +0.841943,  106801.67,  148543.67,    1604.94,             1649.52,    80.80,  39939.77,           53262.12,    -11.13,    -30.48,          45.06,  +2.58,  +1.72
  2,     UK002K,       0,  0.080448, 2459439.523746856023,   6.06436,  18.39019,              127.36218,  45.12616,       127.35718,       45.12100,      6.06436,     +18.39019,       6.07063,      +18.38747,  3423292.34, -1893828.53,  5152801.52,      52.974859,       +0.825484,  105096.54,  147095.23,    3843.53,             3888.11,   -75.15,  55597.80,           53262.12,      5.50,     15.09,          22.51,  +1.61,  +0.77
  3,     UK002K,       0,  0.120776, 2459439.523747322615,   5.71116,  17.69166,              128.26150,  44.68456,       128.26001,       44.68304,      5.71116,     +17.69166,       5.71342,      +17.69086,  3422394.03, -1894783.90,  5150605.99,      52.965451,       +0.806702,  103149.00,  145466.15,    6400.87,             6445.45,    83.84,  63413.55,           53262.12,      1.61,      4.43,           6.68,  +2.80,  +1.99
  4,     UK002K,       0,  0.161076, 2459439.523747789208,   5.38721,  17.05553,              129.07367,  44.27899,       129.07228,       44.27759,      5.38721,     +17.05553,       5.38950,      +17.05479,  3421591.46, -1895637.45,  5148644.46,      52.957039,       +0.789902,  101409.36,  144033.00,    8685.67,             8730.25,   -28.04,  56694.80,           55043.39,      1.48,      4.06,           6.18,  +3.98,  +3.19
  0,     UK0032,       0,  0.022392, 2459439.523746171966,  13.10367,  44.47627,               89.47246,  60.93568,        89.46751,       60.94971,     13.10367,     +44.47627,      13.08898,      +44.48583,  3424334.98, -1892719.66,  5155349.79,      52.985768,       +0.847331,  107357.51,  122487.87,       0.00,              919.88,   409.23,      0.00,           56557.43,     -2.39,    -30.34,          51.25,  +2.44,  +2.00
  1,     UK0032,       0,  0.062324, 2459439.523746634368,  12.70383,  44.20145,               90.26761,  61.02804,        90.27060,       61.01899,     12.70383,     +44.20145,      12.71358,      +44.19533,  3423644.62, -1893453.87,  5153662.53,      52.978546,       +0.832863,  105860.41,  120704.63,    1965.33,             2885.20,    -0.24,  49216.82,           56557.43,      1.49,     19.24,          32.98,  +1.76,  +1.35
  2,     UK0032,       0,  0.102280, 2459439.523747096770,  12.24739,  43.81446,               91.30825,  61.09101,        91.30568,       61.09968,     12.24739,     +43.81446,      12.23875,      +43.82027,  3422787.84, -1894365.07,  5151568.50,      52.969577,       +0.814944,  104002.74,  118501.04,    4404.45,             5324.33,    62.67,  61045.34,           56557.43,     -1.41,    -18.05,          31.51,  +1.63,  +1.26
  3,     UK0032,       0,  0.142236, 2459439.523747559171,  11.80060,  43.43435,               92.33470,  61.14856,        92.32866,       61.17153,     11.80060,     +43.43435,      11.77724,      +43.44963,  3421975.09, -1895229.46,  5149582.07,      52.961061,       +0.797935,  102240.86,  116419.30,    6718.25,             7638.13,     0.24,  57908.56,           56557.43,     -3.69,    -46.90,          83.34,  +2.06,  +1.73
  4,     UK0032,       0,  0.182164, 2459439.523748021573,  11.36240,  43.10893,               93.26567,  61.22856,        93.26513,       61.23086,     11.36240,     +43.10893,      11.36076,      +43.11046,  3421258.63, -1895991.42,  5147831.01,      52.953548,       +0.782920,  100688.02,  114591.14,    8757.88,             9677.76,  -334.69,  51082.72,           55747.76,     -0.36,     -4.63,           8.35,  +3.40,  +3.10

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.