Orbital Analysis for matched events on 20210813_225854.958_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 64.90° Bg 38.35° Vg 56.70km/s
mass 0.01896g, abs. mag 0.0
Path Details
------------
start -2.24° 52.15° 108.84km
end   -2.36° 52.06° 99.15km

Orbit Details
-------------
Semimajor axis 4.07A.U., eccentricity 0.77, inclination 111.40°, Period 8.20Y, LA Sun 141.11°, last Perihelion 2021-07-19

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: 2459440.457580538001
Time: 2021-08-13 22:58:54.958483 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK000S and UK0027
 Convergence angle = 26.67428 deg
 R.A. =  49.80858  Dec = +58.28131 deg

Best intersection: Stations UK000S and UK0027 with Qconv = 26.67 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   2292431.63 +/- 38.68 m
 Y =  -3263913.58 +/- 39.55 m
 Z =   5099207.45 +/- 189.07 m
 Vx =    19116.33 +/- 692.42 m/s
 Vy =    22979.69 +/- 730.86 m/s
 Vz =    49443.31 +/- 1035.73 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+1.553024e+03, +4.293018e+01, -2.403775e+03, +5.199198e+03, -1.110978e+03, -1.527266e+04
+4.293018e+01, +1.986678e+03, +1.672119e+03, -1.744254e+03, +6.097632e+03, -6.618980e+03
-2.403775e+03, +1.672119e+03, +2.835449e+04, -1.216205e+04, -1.489886e+03, +1.233882e+05
+5.199198e+03, -1.744254e+03, -1.216205e+04, +3.574603e+04, -7.314247e+03, -9.412917e+04
-1.110978e+03, +6.097632e+03, -1.489886e+03, -7.314247e+03, +2.784389e+04, -3.954687e+04
-1.527266e+04, -6.618980e+03, +1.233882e+05, -9.412917e+04, -3.954687e+04, +7.927159e+05

Timing offsets (from input data):
    UK000S: 0.000000 s
    UK0027: -0.000876 s

Reference point on the trajectory:
  Time: 2021-08-13 22:58:54.958483 UTC
  Lon     = +-2.240333 +/- 0.0006 deg
  Lat     = +52.151441 +/- 0.0011 deg
  Lat geo = +51.967968 +/- 0.0012 deg
  Ht      =  108921.30 +/- 142.69 m

  JD dynamic   = 2459440.458381278906 
  LST apparent = 305.0825441080 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  50.24362 +/- 0.3736 deg
  Dec       = +58.84450 +/- 0.6297 deg
  Azimuth   =  38.31639 +/- 0.6449 deg
  Elevation = +36.35038 +/- 0.4065 deg
  Vavg      =  57.16297 +/- 0.9165 km/s
  Vinit     =  57.77665 +/- 0.8305 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  50.09918 +/- 0.3736 deg
  Dec       = +58.60678 +/- 0.6297 deg
  Azimuth   =  38.59628 +/- 0.6449 deg
  Elevation = +36.24433 +/- 0.4065 deg
  Vavg      =  57.30876 +/- 0.9165 km/s
  Vinit     =  57.92243 +/- 0.8305 km/s
Radiant (geocentric, J2000):
  R.A.   =  50.58464 +/- 0.3678 deg
  Dec    = +58.39695 +/- 0.6454 deg
  Vg     =  56.70099 +/- 0.8462 km/s
  Vinf   =  57.77665 +/- 0.8305 km/s
  Zc     =  53.79365 +/- 0.4054 deg
  Zg     =  54.33983 +/- 0.4248 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  64.89730 +/- 0.3975 deg
  Bg     = +38.34531 +/- 0.5975 deg
  Vh     =  39.15619 +/- 1.0467 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  87.82318 +/- 0.6476 deg
  Bh     = +63.94723 +/- 0.2487 deg
  Vh_x   =  -0.65322 +/- 0.1881 km/s
  Vh_y   = -17.18494 +/- 0.3978 km/s
  Vh_z   = -35.17753 +/- 0.9845 km/s
Orbit:
  La Sun = 141.108074 +/- -0.0000 deg
  a      =   4.066065 +/- 16.8670 AU
  e      =   0.770608 +/- 0.0858
  i      = 111.399388 +/- 0.2701 deg
  peri   = 144.860425 +/- 2.2611 deg
  node   = 141.106870 +/- 0.0000 deg
  Pi     = 285.967294 +/- 2.2612 deg
  q      =   0.932722 +/- 0.0054 AU
  f      =  35.135575 +/- 2.2611 deg
  M      =   3.068411 +/- 1.9231 deg
  Q      =   7.199409 +/- 33.7316 AU
  n      =   0.120211 +/- 0.0622 deg/day
  T      =   8.199024 +/- 149.0613 years
  Last perihelion JD = 2459414.933075 (2021-07-19 10:23:37.644480) +/- 2.1131 days
  Tj     =   0.868851 +/- 0.4916
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +5.394270e-03, +2.850894e-04, +1.301296e-01, +1.798782e-08, +2.357033e-03, -2.411607e-04
q   , +2.850894e-04, +2.547519e-05, +8.754962e-03, +1.032881e-09, +1.718982e-04, -1.384135e-05
Tp  , +1.301296e-01, +8.754962e-03, +3.510810e+00, +4.303349e-07, +6.591367e-02, -5.767960e-03
node, +1.798782e-08, +1.032881e-09, +4.303349e-07, +1.115710e-13, +7.945969e-09, -1.495336e-09
peri, +2.357033e-03, +1.718982e-04, +6.591367e-02, +7.945969e-09, +1.253203e-03, -1.064964e-04
i   , -2.411607e-04, -1.384135e-05, -5.767960e-03, -1.495336e-09, -1.064964e-04, +2.004136e-05

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: UK000S
  Avg. res. = 2.237e-06 s
  Stddev    = 1.50e-03 s

Begin point on the trajectory:
  Lon =    -2.241369 +/- 0.0005 deg
  Lat =    52.150634 +/- 0.0010 deg
  Ht  = 108835.67 +/- 122.88 m
End point on the trajectory:
  Lon =    -2.359840 +/- 0.0001 deg
  Lat =    52.059111 +/- 0.0011 deg
  Ht  = 99154.55 +/- 137.72 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
    UK000S,   False,    -1.778230,    50.857470,   24.00,   0.000000,   0.000000,   108835.67,    99243.80,          0.010936,     19.70,     28.25,              40.81, 1.0000,    True,    True, {"ff_name": "FF_UK000S_20210813_225850_846_0254208.fits"}
    UK0027,   False,    -2.374601,    51.371449,   48.00,   0.000000,   0.000000,   108496.73,    99154.55,          0.018915,      6.06,     43.63,              27.60, 1.0000,    True,    True, {"ff_name": "FF_UK0027_20210813_225848_057_0248576.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,     UK000S,       0,  0.000000, 2459440.457580538001, 160.62592,  72.26971,              347.57695,  35.55062,       347.58224,       35.53482,    160.62592,     +72.26971,     160.59019,      +72.25749,  2292383.83, -3263971.04,  5099083.81,      52.150634,       -2.241369,  108835.67,  184240.94,       0.00,              144.47,    -3.04,      0.00,           57222.85,     43.19,     30.09,          58.92,  +4.94,  +3.61
  1,     UK000S,       0,  0.040088, 2459440.457581001800, 161.74904,  71.92254,              347.00616,  35.39684,       347.00326,       35.40533,    161.74904,     +71.92254,     161.76852,      +71.92900,  2291596.62, -3264917.34,  5097047.74,      52.137344,       -2.258602,  107425.73,  182440.84,    2379.24,             2523.71,    60.05,  59350.40,           57222.85,    -23.02,    -16.06,          31.73,  +2.12,  +0.81
  2,     UK000S,       0,  0.080156, 2459440.457581465598, 162.85390,  71.59132,              346.44243,  35.26342,       346.43808,       35.27586,    162.85390,     +71.59132,     162.88264,      +71.60065,  2290840.66, -3265826.09,  5095092.47,      52.124574,       -2.275155,  106072.26,  180725.02,    4664.05,             4808.53,    29.87,  57023.43,           57222.85,    -33.47,    -23.35,          46.58,  +2.18,  +0.89
  3,     UK000S,       0,  0.120224, 2459440.457581929397, 163.90794,  71.25708,              345.88680,  35.12818,       345.88074,       35.14521,    163.90794,     +71.25708,     163.94739,      +71.26965,  2290106.74, -3266708.32,  5093194.25,      52.112169,       -2.291228,  104758.76,  179071.62,    6882.21,             7026.68,   -66.97,  55359.80,           57222.85,    -45.45,    -31.72,          63.84,  +2.08,  +0.81
  4,     UK000S,       0,  0.160276, 2459440.457582393195, 165.02203,  70.91034,              345.29557,  34.99986,       345.29391,       35.00440,    165.02203,     +70.91034,     165.03312,      +70.91365,  2289345.62, -3267623.27,  5091225.63,      52.099297,       -2.307887,  103397.07,  177369.98,    9182.62,             9327.09,   -80.62,  57435.61,           57072.44,    -12.05,     -8.40,          17.08,  +1.56,  +0.32
  5,     UK000S,       0,  0.200344, 2459440.457582856994, 166.13434,  70.52645,              344.67453,  34.84824,       344.67320,       34.85183,    166.13434,     +70.52645,     166.14340,      +70.52901,  2288553.01, -3268576.06,  5089175.60,      52.085884,       -2.325227,  101979.60,  175612.53,   11578.17,            11722.64,    -0.07,  59787.13,           57417.25,     -9.43,     -6.58,          13.50,  +1.57,  +0.35
  6,     UK000S,       0,  0.240408, 2459440.457583320327, 167.24466,  70.13561,              344.04143,  34.70001,       344.04395,       34.69335,    167.24466,     +70.13561,     167.23041,      +70.13094,  2287762.36, -3269526.50,  5087130.64,      52.072496,       -2.342520,  100566.20,  173874.77,   13967.80,            14112.27,    74.80,  59645.31,           57779.11,     17.37,     12.11,          25.12,  +2.13,  +0.93
  7,     UK000S,       0,  0.280484, 2459440.457583784126, 168.21395,  69.74067,              343.44795,  34.53276,       343.44552,       34.53908,    168.21395,     +69.74067,     168.22956,      +69.74503,  2287022.35, -3270416.07,  5085216.63,      52.059958,       -2.358715,   99243.80,  172262.76,   16204.40,            16348.87,    -4.06,  55808.85,           57765.67,    -16.36,    -11.41,          23.88,  +2.57,  +1.39
  0,     UK0027,       0,  0.012076, 2459440.457580674440,  43.04359,  86.26633,                5.84193,  50.69879,         5.84265,       50.69999,     43.04359,     +86.26633,      43.02406,      +86.26615,  2292194.62, -3264198.49,  5098594.43,      52.147440,       -2.245521,  108496.73,  139367.69,       0.00,              716.34,  -128.89,      0.00,           58479.52,     -3.10,     -0.43,           4.64,  +2.23,  +1.51
  1,     UK0027,       0,  0.051912, 2459440.457581135444,  41.18466,  86.75090,                5.12602,  50.90579,         5.10633,       50.87208,     41.18466,     +86.75090,      41.81041,      +86.75695,  2291350.32, -3265213.43,  5096410.68,      52.133184,       -2.263989,  106984.69,  137107.67,    2551.80,             3268.14,   121.32,  64057.75,           58479.52,     85.18,     11.78,         129.36,  +1.68,  +0.99
  2,     UK0027,       0,  0.091804, 2459440.457581597380,  39.88982,  87.19044,                4.45481,  51.04451,         4.44206,       51.02210,     39.88982,     +87.19044,      40.36728,      +87.19500,  2290617.89, -3266093.88,  5094516.29,      52.120810,       -2.280031,  105673.52,  135155.63,    4765.47,             5481.81,    30.17,  55491.57,           58479.52,     55.62,      7.72,          85.70,  +1.38,  +0.73
  3,     UK0027,       0,  0.131692, 2459440.457582058851,  38.11111,  87.65319,                3.73975,  51.18226,         3.73648,       51.17633,     38.11111,     +87.65319,      38.26096,      +87.65460,  2289867.01, -3266996.51,  5092574.20,      52.108116,       -2.296469,  104329.82,  133163.12,    7034.90,             7751.24,    -5.00,  56894.95,           58479.52,     14.43,      2.01,          22.57,  +1.30,  +0.68
  4,     UK0027,       0,  0.171560, 2459440.457582520321,  34.70812,  88.14149,                2.97595,  51.34153,         2.97365,       51.33724,     34.70812,     +88.14149,      34.84274,      +88.14276,  2289084.62, -3267937.02,  5090550.58,      52.094881,       -2.313588,  102930.25,  131096.77,    9399.58,            10115.92,    56.24,  59312.78,           58388.10,     10.25,      1.43,          16.29,  +1.81,  +1.22
  5,     UK0027,       0,  0.211452, 2459440.457582981791,  30.07685,  88.60339,                2.23422,  51.46884,         2.24289,       51.48560,     30.07685,     +88.60339,      29.40634,      +88.59698,  2288362.94, -3268804.54,  5088684.00,      52.082666,       -2.329389,  101639.77,  129200.00,   11580.76,            12297.10,   -67.41,  54677.04,           57831.58,    -39.32,     -5.52,          63.39,  +2.17,  +1.61
  6,     UK0027,       0,  0.251284, 2459440.457583442796,  16.33334,  89.06701,                1.42546,  51.66066,         1.41838,       51.64656,     16.33334,     +89.06701,      17.08615,      +89.07536,  2287577.84, -3269748.31,  5086653.38,      52.069370,       -2.346561,  100236.41,  127147.13,   13953.63,            14669.97,     4.10,  59571.96,           57819.13,     32.47,      4.52,          53.18,  +1.92,  +1.40
  7,     UK0027,       0,  0.291168, 2459440.457583904732, 353.40655,  89.36565,                0.76760,  51.78964,         0.75810,       51.77014,    353.40655,     +89.36565,     354.41719,      +89.38277,  2286972.41, -3270476.10,  5085087.46,      52.059111,       -2.359840,   99154.55,  125571.86,   15783.48,            16499.82,  -470.41,  45879.31,           56818.71,     44.20,      6.15,          73.31,  +3.58,  +3.09

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.