Orbital Analysis for matched events on 20210810_012907.098_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 61.70° Bg 41.06° Vg 58.42km/s
mass 0.01546g, abs. mag -0.3
Path Details
------------
start 2.09° 52.19° 109.25km
end   2.01° 52.16° 98.59km

Orbit Details
-------------
Semimajor axis -78.15A.U., eccentricity 1.01, inclination 109.10°, Period 1000000000.00Y, LA Sun 137.37°, 

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: 2459436.561887711287
Time: 2021-08-10 01:29:07.098255 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK002K and UK0032
 Convergence angle = 3.18054 deg
 R.A. =  44.26361  Dec = +59.69611 deg

Best intersection: Stations UK002K and UK0032 with Qconv = 3.18 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   3813193.48 +/- 924.98 m
 Y =  -1157020.19 +/- 497.85 m
 Z =   5102439.95 +/- 171.18 m
 Vx =    21216.59 +/- 5690.12 m/s
 Vy =    20518.34 +/- 2875.88 m/s
 Vz =    51617.62 +/- 4803.46 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+1.275306e+06, +6.888747e+05, +2.367237e+05, +6.771060e+06, +3.184200e+06, -1.385008e+06
+6.888747e+05, +3.723463e+05, +1.277707e+05, +3.648646e+06, +1.718525e+06, -7.454921e+05
+2.367237e+05, +1.277707e+05, +4.431486e+04, +1.274667e+06, +5.973982e+05, -2.599831e+05
+6.771060e+06, +3.648646e+06, +1.274667e+06, +3.828820e+07, +1.789111e+07, -7.425382e+06
+3.184200e+06, +1.718525e+06, +5.973982e+05, +1.789111e+07, +8.411718e+06, -3.375570e+06
-1.385008e+06, -7.454921e+05, -2.599831e+05, -7.425382e+06, -3.375570e+06, +1.907045e+06

Timing offsets (from input data):
    UK002K: -0.001538 s
    UK0032: 0.000000 s

Reference point on the trajectory:
  Time: 2021-08-10 01:29:07.098255 UTC
  Lon     = ++2.087092 +/- 0.0107 deg
  Lat     = +52.194546 +/- 0.0042 deg
  Lat geo = +52.011152 +/- 0.0042 deg
  Ht      =  109231.23 +/- 588.84 m

  JD dynamic   = 2459436.562688452192 
  LST apparent = 343.1208640040 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  44.04150 +/- 5.1904 deg
  Dec       = +60.23889 +/- 4.9523 deg
  Azimuth   =  51.78859 +/- 9.3088 deg
  Elevation = +56.48787 +/- 1.0815 deg
  Vavg      =  55.22880 +/- 2.9631 km/s
  Vinit     =  59.46028 +/- 2.7988 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  44.31332 +/- 5.1904 deg
  Dec       = +60.02663 +/- 4.9523 deg
  Azimuth   =  52.10013 +/- 9.3088 deg
  Elevation = +56.30443 +/- 1.0815 deg
  Vavg      =  55.35543 +/- 2.9631 km/s
  Vinit     =  59.58691 +/- 2.7988 km/s
Radiant (geocentric, J2000):
  R.A.   =  44.21722 +/- 5.4001 deg
  Dec    = +60.07876 +/- 4.9674 deg
  Vg     =  58.41568 +/- 2.8525 km/s
  Vinf   =  59.46028 +/- 2.7988 km/s
  Zc     =  33.62585 +/- 1.0985 deg
  Zg     =  33.93269 +/- 1.1427 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  61.69823 +/- 5.3690 deg
  Bg     = +41.05935 +/- 3.8386 deg
  Vh     =  41.97101 +/- 0.9808 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  85.99553 +/- 19.2502 deg
  Bh     = +66.09572 +/- 2.9653 deg
  Vh_x   =  -1.18768 +/- 5.3152 km/s
  Vh_y   = -16.96554 +/- 2.5833 km/s
  Vh_z   = -38.37089 +/- 1.3750 km/s
Orbit:
  La Sun = 137.368513 +/- -0.0000 deg
  a      = -78.150306 +/- 300.3786 AU
  e      =   1.012147 +/- 0.0883
  i      = 109.099009 +/- 7.9449 deg
  peri   = 150.878912 +/- 6.0681 deg
  node   = 137.368541 +/- 0.0005 deg
  Pi     = 288.247453 +/- 6.0675 deg
  q      =   0.949294 +/- 0.0282 AU
  f      =  29.117391 +/- 6.0682 deg
  M      =        nan +/- nan deg
  Q      = -157.249907 +/- 600.7570 AU
  n      =   0.001427 +/- 0.0333 deg/day
  T      = 1000000000.000000 +/- 462634560.1274 years
  Last perihelion JD = NaN 
  Tj     =  -0.463050 +/- 0.4896
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +1.000131e-02, -2.799055e-03, -2.990827e-01, +9.191368e-07, -1.003140e-02, -1.337827e-02
q   , -2.799055e-03, +1.076653e-03, +1.318799e-01, -3.570159e-07, +4.114155e-03, +5.159256e-03
Tp  , -2.990827e-01, +1.318799e-01, +1.742996e+01, -4.434734e-05, +5.258526e-01, +6.343140e-01
node, +9.191368e-07, -3.570159e-07, -4.434734e-05, +1.193473e-10, -1.375675e-06, -1.721146e-06
peri, -1.003140e-02, +4.114155e-03, +5.258526e-01, -1.375675e-06, +1.610357e-02, +1.975822e-02
i   , -1.337827e-02, +5.159256e-03, +6.343140e-01, -1.721146e-06, +1.975822e-02, +2.486985e-02

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: UK0032
  Avg. res. = 2.404e-05 s
  Stddev    = 4.90e-03 s

Begin point on the trajectory:
  Lon =     2.087228 +/- 0.0107 deg
  Lat =    52.194612 +/- 0.0042 deg
  Ht  = 109249.36 +/- 593.15 m
End point on the trajectory:
  Lon =     2.006419 +/- 0.0050 deg
  Lat =    52.155933 +/- 0.0029 deg
  Ht  = 98590.56 +/- 205.65 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,   107648.03,    98590.56,          0.007188,     19.84,     23.91,              63.27, 1.0000,    True,    True, {"ff_name": "FF_UK002K_20210810_012904_938_0458752.fits"}
    UK0032,   False,    -0.023645,    52.984073,    6.00,   0.000000,   0.000000,   109249.36,    99782.83,          0.007960,     16.21,     21.93,              52.31, 1.0000,    True,    True, {"ff_name": "FF_UK0032_20210810_012902_190_0464896.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,  0.031443, 2459436.561888099182,  23.85271,  -1.28817,              131.21529,  24.52047,       131.21868,       24.52284,     23.85271,      -1.28817,      23.84903,       -1.28743,  3812515.90, -1157675.47,  5100791.48,      52.188814,       +2.075106,  107648.03,  249692.92,       0.00,             1898.93,   649.29,      0.00,           54776.74,    -13.02,    -10.81,          13.98,  +3.82,  +1.83
  1,     UK002K,       0,  0.112011, 2459436.561889031436,  23.67632,  -2.22922,              131.84729,  23.75624,       131.86038,       23.76538,     23.67632,      -2.22922,      23.66200,       -2.22634,  3810867.48, -1159269.64,  5096781.05,      52.174852,       +2.045939,  103797.05,  247650.60,    4619.76,             6518.70,   478.46,  57339.94,           54776.74,    -50.13,    -41.59,          54.25,  +2.17,  +0.20
  2,     UK002K,       0,  0.152203, 2459436.561889496632,  23.59195,  -2.56775,              132.09322,  23.48989,       132.09253,       23.48941,     23.59195,      -2.56775,      23.59338,       -2.56791,  3810274.43, -1159843.18,  5095338.23,      52.169823,       +2.035395,  102411.81,  246930.82,    6281.81,             8180.74,  -249.32,  41352.60,           54776.74,      2.65,      2.20,           2.88,  +2.21,  +0.25
  3,     UK002K,       0,  0.192539, 2459436.561889963690,  23.47729,  -3.12926,              132.47420,  23.03614,       132.47114,       23.03401,     23.47729,      -3.12926,      23.48157,       -3.12993,  3809305.89, -1160779.84,  5092981.87,      52.161604,       +2.018276,  100149.78,  245779.84,    8996.19,            10895.12,    66.66,  67294.16,           54776.74,     11.65,      9.67,          12.70,  +2.13,  +0.18
  4,     UK002K,       0,  0.232771, 2459436.561890429351,  23.40397,  -3.52080,              132.73182,  22.71626,       132.73334,       22.71731,     23.40397,      -3.52080,      23.40323,       -3.52046,  3808638.20, -1161425.56,  5091357.44,      52.155933,       +2.006419,   98590.56,  244998.46,   10867.42,            12766.35,  -454.31,  46511.09,           54141.79,     -5.78,     -4.80,           6.32,  +3.07,  +1.12
  0,     UK0032,       0,  0.000000, 2459436.561887711287,  28.60929,   9.40924,              120.71115,  32.07557,       120.71294,       32.07690,     28.60929,      +9.40924,      28.60727,       +9.40958,  3813201.24, -1157012.69,  5102458.82,      52.194612,       +2.087228,  109249.36,  201480.93,       0.00,               21.74,   641.73,      0.00,           55034.13,     -5.70,     -4.21,           7.25,  +4.77,  +3.25
  1,     UK0032,       0,  0.080468, 2459436.561888642609,  28.40218,   8.28965,              121.60206,  31.22690,       121.59509,       31.22175,     28.40218,      +8.28965,      28.41037,       +8.28833,  3811419.60, -1158735.70,  5098124.29,      52.179531,       +2.055738,  105086.79,  198437.97,    4993.11,             4971.37,   806.70,  62050.87,           55034.13,     21.94,     16.21,          28.36,  +2.97,  +1.48
  2,     UK0032,       0,  0.120624, 2459436.561889107339,  28.34771,   7.92980,              121.87328,  30.94681,       121.87450,       30.94771,     28.34771,      +7.92980,      28.34684,       +7.93003,  3810861.32, -1159275.60,  5096766.06,      52.174800,       +2.045804,  103782.65,  197497.82,    6557.71,             6535.97,   -16.38,  38963.05,           55034.13,     -3.81,     -2.82,           4.95,  +2.05,  +0.57
  3,     UK0032,       0,  0.160848, 2459436.561889573000,  28.23542,   7.37361,              122.31730,  30.52719,       122.30560,       30.51860,     28.23542,      +7.37361,      28.24926,       +7.37141,  3810001.61, -1160107.02,  5094674.47,      52.167509,       +2.030593,  101774.60,  196070.23,    8967.09,             8945.35,     1.27,  59899.04,           55034.13,     36.45,     26.94,          47.68,  +1.68,  +0.22
  4,     UK0032,       0,  0.201088, 2459436.561890038662,  28.14193,   6.81061,              122.74321,  30.09086,       122.73565,       30.08532,     28.14193,      +6.81061,      28.15128,       +6.80918,  3809148.76, -1160931.80,  5092599.58,      52.160270,       +2.015498,   99782.83,  194673.20,   11357.23,            11335.49,    -1.27,  59397.19,           55554.72,     23.41,     17.30,          30.84,  +1.89,  +0.44

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.