Orbital Analysis for matched events on 20210813_002121.146_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 62.76° Bg 38.71° Vg 59.26km/s
mass 0.04501g, abs. mag -0.9
Path Details
------------
start 2.87° 52.98° 108.06km
end   2.76° 52.93° 97.18km

Orbit Details
-------------
Semimajor axis 25.18A.U., eccentricity 0.96, inclination 113.01°, Period 126.36Y, LA Sun 140.20°, 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: 2459439.514828081243
Time: 2021-08-13 00:21:21.146219 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK002K and UK0032
 Convergence angle = 10.54365 deg
 R.A. =  47.22797  Dec = +58.35365 deg

Best intersection: Stations UK002K and UK0032 with Qconv = 10.54 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   3384825.21 +/- 181.46 m
 Y =  -1964132.73 +/- 131.89 m
 Z =   5155621.07 +/- 96.49 m
 Vx =    21468.38 +/- 1239.04 m/s
 Vy =    23130.63 +/- 920.29 m/s
 Vz =    51369.25 +/- 1697.41 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+1.557916e+04, +1.204676e+04, +6.263686e+03, +2.419009e+04, +2.263580e+04, +1.615355e+04
+1.204676e+04, +9.321114e+03, +4.851772e+03, +1.858603e+04, +1.730890e+04, +1.241936e+04
+6.263686e+03, +4.851772e+03, +2.559042e+03, +9.980175e+03, +8.892431e+03, +6.551634e+03
+2.419009e+04, +1.858603e+04, +9.980175e+03, +4.625584e+04, +4.015107e+04, +2.889143e+04
+2.263580e+04, +1.730890e+04, +8.892431e+03, +4.015107e+04, +3.955497e+04, +2.624365e+04
+1.615355e+04, +1.241936e+04, +6.551634e+03, +2.889143e+04, +2.624365e+04, +1.850721e+04

Timing offsets (from input data):
    UK002K: -0.000155 s
    UK0032: 0.000000 s

Reference point on the trajectory:
  Time: 2021-08-13 00:21:21.146219 UTC
  Lon     = ++2.871649 +/- 0.0030 deg
  Lat     = +52.981440 +/- 0.0002 deg
  Lat geo = +52.799358 +/- 0.0002 deg
  Ht      =  108068.64 +/- 131.23 m

  JD dynamic   = 2459439.515628822148 
  LST apparent = 329.8744365464 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  47.13448 +/- 0.5017 deg
  Dec       = +58.43594 +/- 0.8914 deg
  Azimuth   =  50.50299 +/- 1.3646 deg
  Elevation = +48.57444 +/- 0.2081 deg
  Vavg      =  59.04182 +/- 1.1148 km/s
  Vinit     =  60.28861 +/- 1.3926 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  47.24774 +/- 0.5017 deg
  Dec       = +58.21105 +/- 0.8914 deg
  Azimuth   =  50.76226 +/- 1.3646 deg
  Elevation = +48.41760 +/- 0.2081 deg
  Vavg      =  59.18802 +/- 1.1148 km/s
  Vinit     =  60.43481 +/- 1.3926 km/s
Radiant (geocentric, J2000):
  R.A.   =  47.34739 +/- 0.5344 deg
  Dec    = +58.18185 +/- 0.8886 deg
  Vg     =  59.25838 +/- 1.4152 km/s
  Vinf   =  60.28861 +/- 1.3926 km/s
  Zc     =  41.54157 +/- 0.2049 deg
  Zg     =  41.91612 +/- 0.1920 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  62.75532 +/- 0.7249 deg
  Bg     = +38.71046 +/- 0.7381 deg
  Vh     =  41.42294 +/- 0.8731 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  81.95714 +/- 2.8524 deg
  Bh     = +63.46571 +/- 1.4678 deg
  Vh_x   =  -2.58911 +/- 1.3014 km/s
  Vh_y   = -18.32299 +/- 1.1225 km/s
  Vh_z   = -37.05974 +/- 0.2368 km/s
Orbit:
  La Sun = 140.202738 +/- 0.0000 deg
  a      =  25.181494 +/- 21.3226 AU
  e      =   0.962030 +/- 0.0820
  i      = 113.005229 +/- 1.9461 deg
  peri   = 152.260087 +/- 2.1550 deg
  node   = 140.202112 +/- 0.0002 deg
  Pi     = 292.462199 +/- 2.1548 deg
  q      =   0.956147 +/- 0.0065 AU
  f      =  27.736044 +/- 2.1550 deg
  M      =   0.152350 +/- nan deg
  Q      =  49.406841 +/- 42.6467 AU
  n      =   0.007800 +/- 0.0349 deg/day
  T      = 126.363855 +/- 344827515.7867 years
  Last perihelion JD = 2459419.982953 (2021-07-24 11:35:27.134322) +/- 0.2943 days
  Tj     =  -0.262615 +/- 0.4890
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +2.134606e-04, +1.597452e-05, +4.679305e-03, -7.171344e-09, +9.644641e-05, +9.765089e-05
q   , +1.597452e-05, +1.507652e-06, +3.995575e-04, -5.205037e-10, +8.566386e-06, +7.090509e-06
Tp  , +4.679305e-03, +3.995575e-04, +1.103881e-01, -1.545828e-07, +2.327572e-03, +2.105413e-03
node, -7.171344e-09, -5.205037e-10, -1.545828e-07, +2.434523e-13, -3.169560e-09, -3.314163e-09
peri, +9.644641e-05, +8.566386e-06, +2.327572e-03, -3.169560e-09, +4.940398e-05, +4.317220e-05
i   , +9.765089e-05, +7.090509e-06, +2.105413e-03, -3.314163e-09, +4.317220e-05, +4.511669e-05

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 0.015353
 a2 = 37.617802

Mean time residuals from time vs. length:
  Station with reference time: UK0032
  Avg. res. = 7.593e-06 s
  Stddev    = 2.76e-03 s

Begin point on the trajectory:
  Lon =     2.871534 +/- 0.0030 deg
  Lat =    52.981383 +/- 0.0002 deg
  Ht  = 108057.15 +/- 131.33 m
End point on the trajectory:
  Lon =     2.761966 +/- 0.0030 deg
  Lat =    52.927266 +/- 0.0002 deg
  Ht  = 97179.80 +/- 117.57 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,   107699.20,    97179.80,          0.006609,     18.74,     21.27,              47.20, 1.0000,    True,    True, {"ff_name": "FF_UK002K_20210813_002115_701_0368128.fits"}
    UK0032,   False,    -0.023645,    52.984073,    6.00,   0.000515,  49.050857,   108057.15,    97206.50,          0.007205,     14.29,     23.93,              34.57, 1.0000,    True,    True, {"ff_name": "FF_UK0032_20210813_002111_911_0374016.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,  0.001527, 2459439.514828098938,  30.60784,  11.17842,              104.67026,  24.30566,       104.67203,       24.30741,     30.60784,     +11.17842,      30.60546,      +11.17889,  3384649.77, -1964321.77,  5155201.26,      52.979608,       +2.867959,  107699.20,  251709.65,       0.00,              492.70,   356.41,      0.00,           58152.86,     -7.87,     -6.93,           8.59,  +3.01,  +1.01
  1,     UK002K,       0,  0.041767, 2459439.514828564599,  30.52162,  10.82081,              104.97493,  24.06523,       104.96852,       24.05892,     30.52162,     +10.82081,      30.53038,      +10.81911,  3383891.09, -1965139.19,  5153385.90,      52.971681,       +2.851863,  106101.85,  250304.14,    2130.57,             2623.27,    60.97,  52946.54,           58152.86,     28.22,     24.85,          30.99,  +1.78,  -0.21
  2,     UK002K,       0,  0.082039, 2459439.514829030726,  30.45006,  10.42519,              105.29003,  23.78505,       105.29141,       23.78640,     30.45006,     +10.42519,      30.44856,      +10.42555,  3383070.89, -1966022.89,  5151423.35,      52.963104,       +2.834474,  104375.33,  248797.15,    4433.88,             4926.58,   -63.66,  57193.90,           58152.86,     -6.02,     -5.30,           6.65,  +1.42,  -0.56
  3,     UK002K,       0,  0.122343, 2459439.514829497319,  30.34954,   9.97569,              105.66338,  23.47708,       105.65949,       23.47327,     30.34954,      +9.97569,      30.35524,       +9.97467,  3382143.39, -1967022.21,  5149204.03,      52.953397,       +2.814828,  102423.33,  247109.20,    7038.54,             7531.25,   111.13,  64625.42,           58152.86,     16.88,     14.87,          18.78,  +1.13,  -0.83
  4,     UK002K,       0,  0.162611, 2459439.514829963446,  30.26417,   9.57568,              105.99076,  23.20008,       105.98509,       23.19454,     30.26417,      +9.57568,      30.27242,       +9.57419,  3381329.96, -1967898.61,  5147257.68,      52.944877,       +2.797576,  100711.78,  245640.94,    9322.84,             9815.54,   -32.28,  56727.31,           58483.42,     24.48,     21.56,          27.39,  +1.19,  -0.76
  5,     UK002K,       0,  0.202895, 2459439.514830429573,  30.18911,   9.16496,              106.31466,  22.90793,       106.31607,       22.90930,     30.18911,      +9.16496,      30.18808,       +9.16533,  3380509.45, -1968782.66,  5145294.37,      52.936275,       +2.780172,   98985.66,  244172.77,   11627.05,            12119.75,  -156.73,  57199.19,           58394.35,     -6.03,     -5.31,           6.79,  +1.14,  -0.80
  6,     UK002K,       0,  0.243179, 2459439.514830896165,  30.08652,   8.73447,              106.67374,  22.61475,       106.66511,       22.60635,     30.08652,      +8.73447,      30.09901,       +8.73220,  3379650.86, -1969707.73,  5143239.95,      52.927266,       +2.761966,   97179.80,  242650.95,   14038.18,            14530.89,  -174.27,  59853.37,           58518.90,     36.78,     32.40,          41.66,  +1.48,  -0.44
  0,     UK0032,       0,  0.000000, 2459439.514828081243,  40.00559,  22.61688,               88.93890,  27.98897,        88.93227,       27.98269,     40.00559,     +22.61688,      40.01484,      +22.61593,  3384819.76, -1964138.61,  5155608.02,      52.981383,       +2.871534,  108057.15,  223869.56,       0.00,               15.32,   -28.92,      0.00,           60111.81,     28.81,     17.20,          30.92,  +3.49,  +1.74
  1,     UK0032,       0,  0.040208, 2459439.514828546438,  39.95501,  22.26725,               89.23663,  27.75411,        89.22458,       27.74272,     39.95501,     +22.26725,      39.97193,      +22.26553,  3383993.39, -1965028.96,  5153630.70,      52.972750,       +2.854018,  106317.24,  221990.72,    2320.65,             2335.96,  -132.36,  57716.10,           60111.81,     51.89,     31.00,          56.16,  +1.64,  -0.09
  2,     UK0032,       0,  0.080452, 2459439.514829012565,  39.92547,  21.87199,               89.54988,  27.47138,        89.55109,       27.47253,     39.92547,     +21.87199,      39.92413,      +21.87216,  3383082.29, -1966010.61,  5151450.62,      52.963223,       +2.834720,  104399.32,  219930.16,    4879.26,             4894.58,    -0.00,  63577.45,           60111.81,     -5.18,     -3.09,           5.66,  +1.18,  -0.53
  3,     UK0032,       0,  0.120672, 2459439.514829477761,  39.88368,  21.50744,               89.84908,  27.21886,        89.85211,       27.22171,     39.88368,     +21.50744,      39.88000,      +21.50787,  3382253.29, -1966903.80,  5149467.00,      52.954548,       +2.817143,  102654.60,  218063.67,    7207.30,             7222.61,   -96.77,  57882.60,           60111.81,    -12.81,     -7.64,          14.11,  +1.04,  -0.65
  4,     UK0032,       0,  0.160908, 2459439.514829943422,  39.83443,  21.10561,               90.18005,  26.94185,        90.18255,       26.94419,     39.83443,     +21.10561,      39.83166,      +21.10596,  3381355.03, -1967871.61,  5147317.65,      52.945139,       +2.798110,  100764.52,  216052.32,    9729.84,             9745.16,     0.00,  62693.70,           60520.97,    -10.47,     -6.25,          11.64,  +1.01,  -0.66
  5,     UK0032,       0,  0.201148, 2459439.514830409549,  39.77727,  20.69648,               90.52119,  26.66342,        90.51791,       26.66035,     39.77727,     +20.69648,      39.78262,      +20.69602,  3380455.72, -1968840.55,  5145165.81,      52.935711,       +2.779051,   98872.65,  214049.62,   12255.31,            12270.63,    99.46,  62760.26,           60957.86,     13.62,      8.14,          15.29,  +1.20,  -0.45
  6,     UK0032,       0,  0.241368, 2459439.514830874745,  39.73778,  20.32864,               90.81713,  26.40539,        90.81714,       26.40540,     39.73778,     +20.32864,      39.73877,      +20.32864,  3379663.55, -1969694.05,  5143270.32,      52.927399,       +2.762241,   97206.50,  212293.66,   14479.93,            14495.24,  -100.74,  55311.12,           60509.01,     -0.05,     -0.03,           0.06,  +1.36,  -0.27
  7,     UK0032,       1,  0.281584, 2459439.514831340406,  39.73296,  19.98714,               91.06521,  26.14625,        91.09126,       26.17046,     39.73296,     +19.98714,      39.69853,      +19.99076,  3378946.18, -1970466.97,  5141553.80,      52.919866,       +2.747000,   95697.94,  210710.27,   16494.49,            16509.80,  -510.74,  50093.45,           59454.36,   -106.34,    -63.36,         121.17,  +6.29,  +4.67

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.