Orbital Analysis for matched events on 20210813_224431.458_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 62.67° Bg 36.93° Vg 54.49km/s
mass 0.01958g, abs. mag 0.2
Path Details
------------
start -0.41° 52.49° 108.35km
end   -0.56° 52.38° 96.51km

Orbit Details
-------------
Semimajor axis 2.05A.U., eccentricity 0.54, inclination 112.07°, Period 2.94Y, LA Sun 141.10°, last Perihelion 2021-07-14

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: 2459440.447586321738
Time: 2021-08-13 22:44:31.491551 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK000C and UK000S
 Convergence angle = 46.67395 deg
 R.A. =  48.05102  Dec = +57.00707 deg

Best intersection: Stations UK000C and UK000S with Qconv = 46.67 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   2173501.31 +/- 283.99 m
 Y =  -3307786.78 +/- 376.65 m
 Z =   5121919.09 +/- 823.84 m
 Vx =    20292.74 +/- 1205.60 m/s
 Vy =    22509.01 +/- 917.18 m/s
 Vz =    46623.79 +/- 1827.78 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+8.686956e+04, +1.160385e+05, +2.554853e+05, +2.874722e+03, +4.445296e+04, +1.052986e+05
+1.160385e+05, +1.624245e+05, +3.611792e+05, +7.810640e+03, +9.574662e+04, +2.422046e+05
+2.554853e+05, +3.611792e+05, +8.112771e+05, +1.595436e+04, +2.283672e+05, +6.217192e+05
+2.874722e+03, +7.810640e+03, +1.595436e+04, +1.590734e+04, +3.888824e+04, +7.747945e+04
+4.445296e+04, +9.574662e+04, +2.283672e+05, +3.888824e+04, +2.759289e+05, +7.660692e+05
+1.052986e+05, +2.422046e+05, +6.217192e+05, +7.747945e+04, +7.660692e+05, +2.400913e+06

Timing offsets (from input data):
    UK000C: 0.000937 s
    UK000S: 0.000000 s

Reference point on the trajectory:
  Time: 2021-08-13 22:44:31.491551 UTC
  Lon     = +-0.406881 +/- 0.0063 deg
  Lat     = +52.487802 +/- 0.0056 deg
  Lat geo = +52.304864 +/- 0.0057 deg
  Ht      =  108221.17 +/- 550.05 m

  JD dynamic   = 2459440.448387448676 
  LST apparent = 303.3083668068 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  47.96412 +/- 0.6399 deg
  Dec       = +56.97571 +/- 0.5527 deg
  Azimuth   =  40.38186 +/- 0.7636 deg
  Elevation = +35.52831 +/- 0.1890 deg
  Vavg      =  55.89330 +/- 1.6486 km/s
  Vinit     =  55.60781 +/- 1.8403 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  47.82732 +/- 0.6399 deg
  Dec       = +56.73507 +/- 0.5527 deg
  Azimuth   =  40.65906 +/- 0.7636 deg
  Elevation = +35.41634 +/- 0.1890 deg
  Vavg      =  56.04602 +/- 1.6486 km/s
  Vinit     =  55.76053 +/- 1.8403 km/s
Radiant (geocentric, J2000):
  R.A.   =  48.34223 +/- 0.6008 deg
  Dec    = +56.47995 +/- 0.5760 deg
  Vg     =  54.48921 +/- 1.8742 km/s
  Vinf   =  55.60781 +/- 1.8403 km/s
  Zc     =  54.61113 +/- 0.1878 deg
  Zg     =  55.21219 +/- 0.2133 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  62.66681 +/- 0.6101 deg
  Bg     = +36.92726 +/- 0.4505 deg
  Vh     =  36.31410 +/- 1.9018 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  83.48213 +/- 0.6349 deg
  Bh     = +64.35692 +/- 0.7832 deg
  Vh_x   =  -1.78391 +/- 0.2593 km/s
  Vh_y   = -15.61385 +/- 1.3128 km/s
  Vh_z   = -32.73743 +/- 1.4696 km/s
Orbit:
  La Sun = 141.098475 +/- 0.0000 deg
  a      =   2.050357 +/- 150.6760 AU
  e      =   0.543965 +/- 0.1592
  i      = 112.066774 +/- 0.7402 deg
  peri   = 141.384336 +/- 3.0279 deg
  node   = 141.097178 +/- 0.0001 deg
  Pi     = 282.481515 +/- 3.0279 deg
  q      =   0.935035 +/- 0.0047 AU
  f      =  38.611629 +/- 3.0280 deg
  M      =  10.106181 +/- nan deg
  Q      =   3.165678 +/- 301.3528 AU
  n      =   0.335707 +/- 0.1056 deg/day
  T      =   2.935924 +/- 399999868.5114 years
  Last perihelion JD = 2459410.344185 (2021-07-14 20:15:37.607078) +/- 2.8974 days
  Tj     =   2.142486 +/- 0.9154
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +1.688281e-02, +5.473533e-04, +3.957919e-01, -8.981411e-08, +6.624868e-03, +1.170841e-03
q   , +5.473533e-04, +1.954183e-05, +1.339376e-02, -2.746998e-09, +2.267874e-04, +3.581919e-05
Tp  , +3.957919e-01, +1.339376e-02, +9.529219e+00, -2.059045e-06, +1.602267e-01, +2.685939e-02
node, -8.981411e-08, -2.746998e-09, -2.059045e-06, +6.223989e-13, -3.422921e-08, -8.112980e-09
peri, +6.624868e-03, +2.267874e-04, +1.602267e-01, -3.422921e-08, +2.697906e-03, +4.465031e-04
i   , +1.170841e-03, +3.581919e-05, +2.685939e-02, -8.112980e-09, +4.465031e-04, +1.057576e-04

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 55.261390
 a2 = 1.429080

Mean time residuals from time vs. length:
  Station with reference time: UK000S
  Avg. res. = 9.236e-06 s
  Stddev    = 3.04e-03 s

Begin point on the trajectory:
  Lon =    -0.405168 +/- 0.0019 deg
  Lat =    52.489031 +/- 0.0033 deg
  Ht  = 108351.59 +/- 282.53 m
End point on the trajectory:
  Lon =    -0.562334 +/- 0.0011 deg
  Lat =    52.376934 +/- 0.0025 deg
  Ht  = 96512.45 +/- 234.61 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
    UK000C,   False,    -0.727590,    51.263100,   57.00,  43.956589,   2.819953,   107684.96,    97456.94,          0.007958,     16.54,     16.77,              23.76, 1.0000,    True,    True, {"ff_name": "FF_UK000C_20210813_224431_403_0235520.fits"}
    UK000S,   False,    -1.778230,    50.857470,   24.00,  63.106113,   0.562324,   108351.59,    96512.45,          0.048787,    189.14,      3.66,              11.72, 1.0000,    True,    True, {"ff_name": "FF_UK000S_20210813_224428_339_0232960.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,     UK000C,       0,  0.013505, 2459440.447586612310,  95.26583,  74.60630,                8.92172,  37.22925,         8.92249,       37.21744,     95.26583,     +74.60630,      95.27989,      +74.59508,  2173164.56, -3308160.31,  5121145.38,      52.482746,       -0.413890,  107684.96,  175456.08,       0.00,              922.80,   -13.41,      0.00,           55092.19,     25.80,     25.42,          42.58,  +3.14,  +1.92
  1,     UK000C,       0,  0.053425, 2459440.447587074246,  96.42581,  74.68328,                8.52703,  37.19101,         8.52633,       37.20081,     96.42581,     +74.68328,      96.41489,      +74.69264,  2172347.85, -3309066.21,  5119268.94,      52.470479,       -0.431136,  106384.88,  173428.60,    2238.01,             3160.80,     4.73,  56062.31,           55092.19,    -21.13,    -20.85,          35.31,  +1.90,  +0.70
  2,     UK000C,       0,  0.093325, 2459440.447587536182,  97.60084,  74.78433,                8.11876,  37.17947,         8.11854,       37.18229,     97.60084,     +74.78433,      97.59813,      +74.78705,  2171526.21, -3309977.59,  5117381.16,      52.458131,       -0.448483,  105077.43,  171394.30,    4489.55,             5412.34,    37.52,  56429.51,           55092.19,     -6.03,     -5.95,          10.19,  +1.43,  +0.26
  3,     UK000C,       0,  0.133229, 2459440.447587998118,  98.73646,  74.86907,                7.73154,  37.16149,         7.73138,       37.16346,     98.73646,     +74.86907,      98.73496,      +74.87096,  2170764.05, -3310822.99,  5115630.07,      52.446670,       -0.464583,  103865.10,  169512.25,    6578.06,             7500.86,   -92.94,  52338.60,           55092.19,     -4.14,     -4.08,           7.08,  +1.20,  +0.05
  4,     UK000C,       0,  0.173149, 2459440.447588460054,  99.89909,  74.93455,                7.34510,  37.12820,         7.34378,       37.14334,     99.89909,     +74.93455,      99.88565,      +74.94927,  2170017.40, -3311651.18,  5113914.59,      52.435436,       -0.480358,  102677.84,  167673.35,    8624.10,             9546.89,  -266.77,  51253.27,           54093.38,    -31.59,    -31.18,          54.60,  +0.94,  -0.18
  5,     UK000C,       0,  0.213029, 2459440.447588921525, 101.24115,  75.03118,                6.89271,  37.11633,         6.89254,       37.11822,    101.24115,     +75.03118,     101.24034,      +75.03303,  2169166.49, -3312595.02,  5111959.58,      52.422626,       -0.498308,  101325.32,  165583.93,   10955.83,            11878.62,  -152.68,  58468.70,           54432.63,     -3.90,     -3.84,           6.82,  +1.03,  -0.07
  6,     UK000C,       0,  0.252921, 2459440.447589383461, 102.64159,  75.10890,                6.43121,  37.08924,         6.43106,       37.09075,    102.64159,     +75.10890,     102.64140,      +75.11038,  2168317.34, -3313536.92,  5110008.60,      52.409834,       -0.516219,   99976.13,  163505.52,   13282.74,            14205.54,   -44.07,  58330.35,           54971.27,     -3.07,     -3.03,           5.45,  +0.83,  -0.24
  7,     UK000C,       0,  0.292813, 2459440.447589844931, 104.05485,  75.17391,                5.97159,  37.05642,         5.97105,       37.06158,    104.05485,     +75.17391,     104.05248,      +75.17900,  2167491.44, -3314453.01,  5108111.05,      52.397385,       -0.533642,   98664.40,  161490.67,   15545.93,            16468.73,     0.81,  56732.94,           55342.51,    -10.39,    -10.24,          18.63,  +1.19,  +0.15
  8,     UK000C,       0,  0.332701, 2459440.447590306401, 105.38973,  75.24349,                5.53627,  37.04013,         5.53712,       37.03245,    105.38973,     +75.24349,     105.39559,      +75.23588,  2166730.92, -3315296.60,  5106363.70,      52.385914,       -0.549695,   97456.94,  159641.27,   17629.98,            18552.78,  -133.23,  52247.49,           55309.52,     15.29,     15.06,          27.73,  +1.35,  +0.33
  0,     UK000S,       0,  0.000000, 2459440.447586707771,  71.21838,  58.30320,               27.09027,  26.73728,        27.08281,       26.74612,     71.21838,     +58.30320,      71.21980,      +58.31425,  2173583.20, -3307695.94,  5122107.24,      52.489031,       -0.405168,  108351.59,  233272.22,       0.00,              224.41,    39.17,      0.00,           59768.16,      0.84,    -45.05,          39.84,  +3.80,  +1.96
  1,     UK000S,       0,  0.040044, 2459440.447587171104,  71.48304,  58.39458,               26.90413,  26.73799,        26.96262,       26.66775,     71.48304,     +58.39458,      71.47265,      +58.30721,  2172688.09, -3308688.82,  5120050.66,      52.475590,       -0.424056,  106926.43,  230872.90,    2452.87,             2228.45,  -183.55,  61254.28,           59768.16,     -3.71,    352.76,         315.18,  +2.14,  +0.32
  2,     UK000S,       0,  0.080180, 2459440.447587635834,  71.72697,  58.30659,               26.83746,  26.59455,        26.84213,       26.58902,     71.72697,     +58.30659,      71.72634,      +58.29968,  2171808.22, -3309664.79,  5118029.10,      52.462370,       -0.442623,  105526.12,  228515.57,    4863.97,             4639.56,    -4.32,  60073.35,           59768.16,     -0.46,     27.65,          24.97,  +2.25,  +0.46
  3,     UK000S,       0,  0.120288, 2459440.447588100098,  71.97166,  58.26901,               26.73930,  26.49333,        26.72381,       26.51159,     71.97166,     +58.26901,      71.97560,      +58.29186,  2170961.09, -3310604.43,  5116082.77,      52.449634,       -0.460501,  104178.48,  226246.99,    7185.34,             6960.93,    86.73,  57878.02,           59768.16,      1.72,    -90.52,          82.54,  +2.01,  +0.24
  4,     UK000S,       0,  0.160356, 2459440.447588563897,  72.21121,  58.29533,               26.60495,  26.44763,        26.61245,       26.43874,     72.21121,     +58.29533,      72.21019,      +58.28422,  2170179.65, -3311471.22,  5114287.37,      52.437878,       -0.477004,  102935.80,  224155.03,    9326.70,             9102.29,    -0.01,  53443.10,           58325.33,     -0.70,     43.58,          40.11,  +1.78,  +0.03
  5,     UK000S,       0,  0.200448, 2459440.447589027695,  72.41248,  58.26253,               26.52493,  26.36313,        26.51480,       26.37507,     72.41248,     +58.26253,      72.41573,      +58.27747,  2169508.20, -3312216.00,  5112744.67,      52.427771,       -0.491205,  101868.39,  222357.68,   11166.66,            10942.25,  -389.47,  45893.49,           56137.17,      1.05,    -58.18,          53.98,  +1.52,  -0.22
  6,     UK000S,       0,  0.240556, 2459440.447589491960,  72.67482,  58.23060,               26.41381,  26.26234,        26.38864,       26.29188,     72.67482,     +58.23060,      72.68217,      +58.26763,  2168649.89, -3313168.05,  5110772.65,      52.414844,       -0.509310,  100504.43,  220062.62,   13518.68,            13294.27,  -267.78,  58642.06,           55624.04,      2.79,   -142.77,         133.84,  +1.30,  -0.41
  7,     UK000S,       0,  0.280696, 2459440.447589956690,  72.94705,  58.15396,               26.32385,  26.12111,        26.25373,       26.20254,     72.94705,     +58.15396,      72.96747,      +58.25637,  2167749.17, -3314167.14,  5108703.19,      52.401270,       -0.528297,   99073.67,  217655.85,   15986.90,            15762.49,   -31.65,  61490.44,           55899.70,      9.49,   -390.84,         370.49,  +1.39,  -0.30
  8,     UK000S,       0,  0.320776, 2459440.447590420488,  73.23773,  58.19407,               26.15538,  26.07402,        26.12085,       26.11438,     73.23773,     +58.19407,      73.24861,      +58.24472,  2166880.46, -3315130.73,  5106707.28,      52.388170,       -0.546613,   97694.34,  215335.89,   18367.41,            18143.00,   120.10,  59393.86,           56261.13,      3.85,   -191.24,         183.22,  +1.40,  -0.27
  9,     UK000S,       0,  0.360856, 2459440.447590884287,  73.48900,  58.21147,               26.01992,  26.01906,        26.00438,       26.03728,     73.48900,     +58.21147,      73.49488,      +58.23431,  2166135.83, -3315956.68,  5104996.45,      52.376934,       -0.562334,   96512.45,  213347.80,   20407.90,            20183.49,   -68.17,  50910.52,           56153.41,      1.53,    -85.48,          82.65,  +3.71,  +2.06

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.