Orbital Analysis for matched events on 20210904_041516.475_UK

Summary for Event
-----------------
shower ID 856 EMO
Lg 98.60° Bg -21.60° Vg 61.64km/s
mass 0.00513g, abs. mag 0.5
Path Details
------------
start -0.26° 51.26° 106.93km
end   -0.48° 51.34° 98.72km

Orbit Details
-------------
Semimajor axis 7.09A.U., eccentricity 0.92, inclination 133.47°, Period 18.87Y, LA Sun 161.57°, last Perihelion 2021-07-25

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: 2459461.677274017129
Time: 2021-09-04 04:15:16.514911 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK0001 and UK000F
 Convergence angle = 75.87148 deg
 R.A. =  98.15883  Dec =  +2.32125 deg
Intersection 2 - Stations: UK0001 and UK002C
 Convergence angle = 14.28993 deg
 R.A. =  97.94224  Dec =  +1.75516 deg
Intersection 3 - Stations: UK000F and UK002C
 Convergence angle = 61.58242 deg
 R.A. =  98.01947  Dec =  +2.41893 deg

Best intersection: Stations UK0001 and UK000F with Qconv = 75.87 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   2769644.57 +/- 29.70 m
 Y =   2979144.10 +/- 110.30 m
 Z =   5035138.99 +/- 38.00 m
 Vx =    -8665.76 +/- 86.48 m/s
 Vy =    61985.46 +/- 217.66 m/s
 Vz =     2262.09 +/- 153.42 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+9.636918e+02, -1.453746e+03, -2.070909e+02, +3.074521e+03, +1.818240e+02, +3.801925e+02
-1.453746e+03, +1.257223e+04, +2.967062e+03, +4.423679e+02, -5.442149e+02, +7.155088e+03
-2.070909e+02, +2.967062e+03, +1.578866e+03, +6.980354e+02, +5.481024e+02, +5.153513e+03
+3.074521e+03, +4.423679e+02, +6.980354e+02, +1.481173e+04, -3.642915e+03, +7.243174e+03
+1.818240e+02, -5.442149e+02, +5.481024e+02, -3.642915e+03, +4.507717e+04, +8.880883e+03
+3.801925e+02, +7.155088e+03, +5.153513e+03, +7.243174e+03, +8.880883e+03, +2.457564e+04

Timing offsets (from input data):
    UK0001: 0.000303 s
    UK000F: 0.000000 s
    UK002C: 0.000497 s

Reference point on the trajectory:
  Time: 2021-09-04 04:15:16.514911 UTC
  Lon     = +-0.240765 +/- 0.0012 deg
  Lat     = +51.251382 +/- 0.0004 deg
  Lat geo = +51.066515 +/- 0.0004 deg
  Ht      =  107714.74 +/- 70.52 m

  JD dynamic   = 2459461.678075219039 
  LST apparent = 47.0870708553 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  97.95854 +/- 0.1059 deg
  Dec       =  +2.06991 +/- 0.1337 deg
  Azimuth   = 121.18612 +/- 0.0937 deg
  Elevation = +25.01757 +/- 0.1478 deg
  Vavg      =  62.02727 +/- 0.2054 km/s
  Vinit     =  62.62914 +/- 0.2054 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  98.12927 +/- 0.1059 deg
  Dec       =  +2.06233 +/- 0.1337 deg
  Azimuth   = 121.03175 +/- 0.0937 deg
  Elevation = +24.91967 +/- 0.1478 deg
  Vavg      =  62.25750 +/- 0.2054 km/s
  Vinit     =  62.85937 +/- 0.2054 km/s
Radiant (geocentric, J2000):
  R.A.   =  97.99039 +/- 0.1069 deg
  Dec    =  +1.59739 +/- 0.1356 deg
  Vg     =  61.63808 +/- 0.2087 km/s
  Vinf   =  62.62914 +/- 0.2054 km/s
  Zc     =  64.88681 +/- 0.1478 deg
  Zg     =  65.46775 +/- 0.1501 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  98.59505 +/- 0.1187 deg
  Bg     = -21.60223 +/- 0.1325 deg
  Vh     =  40.42390 +/- 0.1928 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     = 121.55520 +/- 0.2505 deg
  Bh     = -34.14734 +/- 0.1969 deg
  Vh_x   =  17.50750 +/- 0.1171 km/s
  Vh_y   = -28.50796 +/- 0.2125 km/s
  Vh_z   =  22.69087 +/- 0.1390 km/s
Orbit:
  La Sun = 161.569213 +/- nan deg
  a      =   7.088704 +/- 1.0213 AU
  e      =   0.917541 +/- 0.0099
  i      = 133.472604 +/- 0.3236 deg
  peri   = 276.974051 +/- 0.6995 deg
  node   = 341.572990 +/- 0.0000 deg
  Pi     = 258.547041 +/- 0.6995 deg
  q      =   0.584527 +/- 0.0039 AU
  f      =  83.028483 +/- 0.6995 deg
  M      =   2.131957 +/- 0.4009 deg
  Q      =  13.592882 +/- 2.0396 AU
  n      =   0.052222 +/- 0.0095 deg/day
  T      =  18.873435 +/- 4.2584 years
  Last perihelion JD = 2459420.853218 (2021-07-25 08:28:38.060862) +/- 0.2883 days
  Tj     =   0.095579 +/- 0.0961
Shower association:
  IAU No.  =  856
  IAU code =  EMO

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +1.042450e-04, +3.148126e-05, +3.029665e-03, +1.097926e-09, +1.175729e-04, +1.776694e-05
q   , +3.148126e-05, +1.622545e-05, +9.917739e-04, +6.001712e-10, +4.942851e-05, +9.696721e-06
Tp  , +3.029665e-03, +9.917739e-04, +8.893345e-02, +3.479290e-08, +3.576339e-03, +5.628377e-04
node, +1.097926e-09, +6.001712e-10, +3.479290e-08, +1.386258e-13, +1.792669e-09, +2.239562e-09
peri, +1.175729e-04, +4.942851e-05, +3.576339e-03, +1.792669e-09, +1.614595e-04, +2.897717e-05
i   , +1.776694e-05, +9.696721e-06, +5.628377e-04, +2.239562e-09, +2.897717e-05, +3.618258e-05

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 0.004937
 a2 = 32.836834

Mean time residuals from time vs. length:
  Station with reference time: UK000F
  Avg. res. = 1.208e-06 s
  Stddev    = 1.10e-03 s

Begin point on the trajectory:
  Lon =    -0.260971 +/- 0.0005 deg
  Lat =    51.259054 +/- 0.0003 deg
  Ht  = 106932.61 +/- 55.35 m
End point on the trajectory:
  Lon =    -0.475752 +/- 0.0005 deg
  Lat =    51.339732 +/- 0.0002 deg
  Ht  = 98723.13 +/- 52.75 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
    UK0001,   False,    -1.778230,    50.857470,   24.00,   0.157672,  24.022079,   104907.32,    99749.57,          0.014529,     21.18,     31.30,              45.98, 0.5171,    True,    True, {"ff_name": "FF_UK0001_20210904_041510_699_0800000.fits"}
    UK000F,   False,    -1.306160,    51.883100,   80.00,   0.002266,  35.157607,   106932.61,    98723.13,          0.023971,     55.51,     19.33,              23.86, 0.1637,    True,    True, {"ff_name": "FF_UK000F_20210904_041510_197_0764672.fits"}
    UK002C,   False,    -1.801980,    51.351940,  130.00,  71.798429,   0.000000,   106655.47,    99239.11,          0.011659,     21.94,     19.48,              27.69, 0.2159,    True,    True, {"ff_name": "FF_UK002C_20210904_041514_742_0797184.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,     UK0001,       0,  0.113575, 2459461.677275327966, 120.55991,  45.99010,               64.88240,  42.16340,        64.88232,       42.16246,    120.55991,     +45.99010,     120.56154,      +45.98961,  2770563.98,  2972567.59,  5034898.99,      51.278932,       -0.313705,  104907.32,  154742.27,       0.00,             6644.80,   -58.71,      0.00,           61980.08,      2.10,     -1.42,           3.38,  +2.36,  +1.41
  1,     UK0001,       0,  0.153403, 2459461.677275788970, 121.14136,  46.62245,               63.87220,  42.19080,        63.87338,       42.20795,    121.14136,     +46.62245,     121.12067,      +46.63141,  2770934.33,  2969918.57,  5034802.31,      51.290023,       -0.343170,  103778.03,  152962.24,    2676.54,             9321.33,   123.43,  67202.36,           61980.08,    -37.97,     25.69,          61.82,  +1.40,  +0.48
  2,     UK0001,       0,  0.193211, 2459461.677276249509, 121.63121,  47.22236,               62.94834,  42.25201,        62.94779,       42.24213,    121.63121,     +47.22236,     121.64440,      +47.21715,  2771266.20,  2967544.69,  5034715.68,      51.299959,       -0.369612,  102766.80,  151389.00,    5075.07,            11719.87,    28.82,  60252.49,           61980.08,     21.63,    -14.66,          35.60,  +1.87,  +0.97
  3,     UK0001,       0,  0.233039, 2459461.677276710514, 122.17145,  47.80440,               62.02062,  42.27516,        62.02037,       42.26893,    122.17145,     +47.80440,     122.18027,      +47.80108,  2771591.67,  2965216.62,  5034630.72,      51.309700,       -0.395567,  101775.77,  149867.49,    7427.30,            14072.10,  -113.33,  59059.90,           61980.08,     13.49,     -9.14,          22.43,  +1.62,  +0.74
  4,     UK0001,       0,  0.272863, 2459461.677277171519, 122.79735,  48.42469,               61.00985,  42.27292,        61.01024,       42.28943,    122.79735,     +48.42469,     122.77755,      +48.43360,  2771938.67,  2962734.61,  5034540.14,      51.320083,       -0.423247,  100719.96,  148270.08,    9935.09,            16579.89,   -99.69,  62971.84,           61828.80,    -35.37,     23.94,          59.42,  +1.56,  +0.70
  5,     UK0001,       0,  0.312683, 2459461.677277632523, 123.38078,  49.01185,               60.06099,  42.27711,        60.06120,       42.30081,    123.38078,     +49.01185,     123.35182,      +49.02480,  2772257.81,  2960451.78,  5034456.83,      51.329630,       -0.448738,   99749.57,  146823.01,   12241.63,            18886.43,  -287.04,  57924.05,           61227.77,    -50.30,     34.03,          85.32,  +1.60,  +0.77
  0,     UK000F,       1,  0.000000, 2459461.677274017129,  77.90522,  15.73760,              133.09004,  45.87978,       133.15713,       45.85344,     77.90522,     +15.73760,      77.87514,      +15.69246,  2769650.27,  2979103.31,  5035137.50,      51.251553,       -0.241049,  107697.31,  148820.11,       0.00,               41.21,   450.79,      0.00,           59898.41,     45.70,    131.59,         193.07,  +5.09,  +4.23
  1,     UK000F,       0,  0.039828, 2459461.677274478134,  77.62424,  15.85388,              133.35583,  46.10896,       133.36572,       46.10505,     77.62424,     +15.85388,      77.62000,      +15.84723,  2769900.53,  2977313.22,  5035072.17,      51.259054,       -0.260971,  106932.61,  147164.18,    1808.68,             1849.89,  -234.92,  45412.27,           59898.41,      6.69,     19.13,          28.40,  +3.31,  +2.47
  2,     UK000F,       0,  0.079520, 2459461.677274937276,  77.25364,  16.09854,              133.64727,  46.49140,       133.67864,       46.47900,     77.25364,     +16.09854,      77.24007,      +16.07752,  2770264.12,  2974712.54,  5034977.26,      51.269949,       -0.289858,  105822.36,  144767.93,    4436.37,             4477.58,   -93.11,  66202.05,           59898.41,     20.73,     59.42,          89.67,  +2.60,  +1.80
  3,     UK000F,       0,  0.119216, 2459461.677275396883,  76.86021,  16.33455,              133.97552,  46.87573,       134.00585,       46.86370,     76.86021,     +16.33455,      76.84735,      +16.31429,  2770626.86,  2972117.85,  5034882.57,      51.280815,       -0.318702,  104715.53,  142385.64,    7058.00,             7099.21,    42.40,  66042.64,           59898.41,     19.63,     56.25,          86.30,  +1.37,  +0.60
  4,     UK000F,       0,  0.158904, 2459461.677275856491,  76.49843,  16.59179,              134.25273,  47.26418,       134.32692,       47.23479,     76.49843,     +16.59179,      76.46660,      +16.54249,  2770966.32,  2969689.72,  5034793.96,      51.290981,       -0.345726,  103680.52,  140163.96,    9511.34,             9552.55,    10.11,  61815.70,           61105.86,     46.82,    134.74,         209.92,  +1.38,  +0.65
  5,     UK000F,       0,  0.198636, 2459461.677276316099,  76.09608,  16.77912,              134.63121,  47.60782,       134.64888,       47.60076,     76.09608,     +16.77912,      76.08923,      +16.76738,  2771291.59,  2967363.12,  5034709.05,      51.300719,       -0.371647,  102689.48,  138042.58,   11862.11,            11903.31,  -127.51,  59165.49,           61173.93,     11.01,     31.50,          49.86,  +1.54,  +0.84
  6,     UK000F,       0,  0.238312, 2459461.677276775241,  75.66216,  17.02340,              135.01447,  48.01501,       135.01816,       48.01353,     75.66216,     +17.02340,      75.66156,      +17.02096,  2771647.99,  2964813.76,  5034616.02,      51.311386,       -0.400054,  101604.34,  135727.65,   14437.94,            14479.15,   -36.54,  64921.81,           61599.35,      2.26,      6.44,          10.37,  +0.87,  +0.21
  7,     UK000F,       0,  0.277980, 2459461.677277234383,  75.21154,  17.27402,              135.41881,  48.43412,       135.40632,       48.43915,     75.21154,     +17.27402,      75.21804,      +17.28226,  2772004.26,  2962265.45,  5034523.02,      51.322045,       -0.428473,  100520.48,  133423.57,   17012.72,            17053.93,    53.86,  64908.06,           62052.05,     -7.47,    -21.29,          34.89,  +0.95,  +0.32
  8,     UK000F,       0,  0.317676, 2459461.677277693991,  74.80888,  17.50344,              135.78011,  48.81260,       135.76098,       48.82033,     74.80888,     +17.50344,      74.81834,      +17.51603,  2772313.86,  2960050.90,  5034442.20,      51.331306,       -0.453210,   99579.23,  131429.00,   19250.26,            19291.47,  -194.72,  56367.09,           61884.55,    -11.24,    -32.00,          53.23,  +1.08,  +0.49
  9,     UK000F,       0,  0.357384, 2459461.677278153598,  74.44043,  17.73339,              136.10013,  49.17607,       136.09865,       49.17667,     74.44043,     +17.73339,      74.44255,      +17.73436,  2772595.62,  2958035.45,  5034368.65,      51.339732,       -0.475752,   98723.13,  129620.44,   21286.64,            21327.85,  -645.22,  51283.75,           61220.99,     -0.85,     -2.44,           4.11,  +2.29,  +1.73
  0,     UK002C,       1,  0.010577, 2459461.677274133544, 101.53633,  29.95412,               95.28503,  43.82515,        95.23964,       43.78089,    101.53633,     +29.95412,     101.59937,      +29.94682,  2769656.62,  2979057.90,  5035135.84,      51.251743,       -0.241592,  107677.91,  154058.86,       0.00,               87.09,  -165.77,      0.00,           63600.60,     98.18,   -110.85,         198.26,  +5.17,  +4.23
  1,     UK002C,       0,  0.050377, 2459461.677274594083, 101.65666,  30.37498,               94.76419,  44.04254,        94.75936,       44.03777,    101.65666,     +30.37498,     101.66364,      +30.37418,  2769991.26,  2976664.23,  5035048.49,      51.261773,       -0.268178,  106655.47,  151921.17,    2418.53,             2505.62,  -239.88,  60767.11,           63600.60,     10.38,    -11.68,          21.21,  +3.62,  +2.71
  2,     UK002C,       0,  0.090093, 2459461.677275054157, 101.72257,  30.88454,               94.19529,  44.35322,        94.18232,       44.34031,    101.72257,     +30.88454,     101.74130,      +30.88239,  2770377.60,  2973900.82,  5034947.64,      51.273348,       -0.298869,  105476.02,  149465.60,    5210.63,             5297.72,    64.85,  70301.64,           63600.60,     27.54,    -31.01,          57.23,  +2.18,  +1.31
  3,     UK002C,       0,  0.129881, 2459461.677275514696, 101.82104,  31.31014,               93.68030,  44.58381,        93.69051,       44.59409,    101.82104,     +31.31014,     101.80699,      +31.31186,  2770694.26,  2971635.77,  5034864.98,      51.282833,       -0.324075,  104509.98,  147460.55,    7499.20,             7586.30,  -138.47,  57519.15,           63600.60,    -21.53,     24.20,          45.31,  +2.10,  +1.26
  4,     UK002C,       0,  0.169605, 2459461.677275974303, 101.89046,  31.81670,               93.10177,  44.88582,        93.10565,       44.88976,    101.89046,     +31.81670,     101.88557,      +31.81736,  2771056.52,  2969044.54,  5034770.42,      51.293681,       -0.352909,  103405.62,  145178.58,   10117.35,            10204.44,    -8.21,  65908.40,           63676.42,     -8.09,      9.10,          17.29,  +1.79,  +0.98
  5,     UK002C,       0,  0.209329, 2459461.677276433911, 101.95419,  32.31967,               92.52612,  45.18652,        92.51984,       45.18008,    101.95419,     +32.31967,     101.96422,      +32.31860,  2771404.83,  2966553.07,  5034679.49,      51.304108,       -0.380661,  102344.59,  142995.34,   12634.68,            12721.78,    21.25,  63370.63,           63654.45,     12.95,    -14.58,          28.13,  +1.38,  +0.60
  6,     UK002C,       0,  0.249065, 2459461.677276893985, 102.01456,  32.79655,               91.97525,  45.46938,        91.95913,       45.45271,    102.01456,     +32.79655,     102.03932,      +32.79378,  2771725.44,  2964259.78,  5034595.80,      51.313703,       -0.406237,  101368.65,  140995.22,   14951.79,            15038.88,  -150.28,  58312.49,           63074.48,     32.88,    -37.07,          72.49,  +1.59,  +0.84
  7,     UK002C,       0,  0.288777, 2459461.677277353592, 102.11225,  33.34765,               91.31013,  45.77602,        91.30033,       45.76576,    102.11225,     +33.34765,     102.12807,      +33.34594,  2772087.15,  2961672.48,  5034501.38,      51.324525,       -0.435093,  100268.39,  138751.92,   17565.96,            17653.05,   -23.24,  65828.15,           63062.02,     19.82,    -22.33,          44.38,  +1.56,  +0.85
  8,     UK002C,       0,  0.328501, 2459461.677277813200, 102.21320,  33.87934,               90.65707,  46.06478,        90.65701,       46.06471,    102.21320,     +33.87934,     102.21466,      +33.87933,  2772425.79,  2959250.28,  5034412.99,      51.334653,       -0.462140,   99239.11,  136663.52,   20013.31,            20100.40,   -63.76,  61608.94,           62959.38,      0.11,     -0.13,           0.26,  +2.14,  +1.46

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.