Orbital Analysis for matched events on 20210813_002933.065_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 62.61° Bg 39.91° Vg 58.89km/s
mass 0.05449g, abs. mag -1.1
Path Details
------------
start 1.31° 52.01° 105.48km
end   1.21° 51.95° 94.94km

Orbit Details
-------------
Semimajor axis 47.19A.U., eccentricity 0.98, inclination 111.27°, Period 324.22Y, LA Sun 140.21°, 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: 2459439.520521595608
Time: 2021-08-13 00:29:33.065861 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK002C and UK0032
 Convergence angle = 70.78774 deg
 R.A. =  46.26198  Dec = +58.98665 deg

Best intersection: Stations UK002C and UK0032 with Qconv = 70.79 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   3476524.29 +/- 92.39 m
 Y =  -1977222.04 +/- 77.75 m
 Z =   5086301.99 +/- 111.73 m
 Vx =    21091.08 +/- 745.97 m/s
 Vy =    21903.80 +/- 600.49 m/s
 Vz =    51635.34 +/- 1127.37 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+2.866427e+03, +8.820050e+02, +5.580831e+02, +1.332274e+04, +5.204085e+03, +2.081409e+03
+8.820050e+02, +2.759879e+03, -3.859290e+02, -4.090851e+03, +4.305468e+03, -3.228484e+04
+5.580831e+02, -3.859290e+02, +8.824198e+02, +3.056604e+03, -4.907371e+02, +1.303177e+04
+1.332274e+04, -4.090851e+03, +3.056604e+03, +1.444261e+05, +2.612062e+04, +1.538888e+05
+5.204085e+03, +4.305468e+03, -4.907371e+02, +2.612062e+04, +1.864744e+04, -2.220625e+04
+2.081409e+03, -3.228484e+04, +1.303177e+04, +1.538888e+05, -2.220625e+04, +5.450734e+05

Timing offsets (from input data):
    UK000C: 0.000000 s
    UK002C: 0.000000 s
    UK0032: -0.000333 s

Reference point on the trajectory:
  Time: 2021-08-13 00:29:33.065861 UTC
  Lon     = ++1.313518 +/- 0.0015 deg
  Lat     = +52.005178 +/- 0.0006 deg
  Lat geo = +51.821374 +/- 0.0006 deg
  Ht      =  105458.75 +/- 105.47 m

  JD dynamic   = 2459439.521322336514 
  LST apparent = 330.3715825868 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  46.08293 +/- 0.5161 deg
  Dec       = +59.50670 +/- 0.3386 deg
  Azimuth   =  48.71669 +/- 0.5746 deg
  Elevation = +49.12717 +/- 0.2025 deg
  Vavg      =  57.69981 +/- 0.3251 km/s
  Vinit     =  59.92344 +/- 1.0965 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  46.21731 +/- 0.5161 deg
  Dec       = +59.27434 +/- 0.3386 deg
  Azimuth   =  48.99628 +/- 0.5746 deg
  Elevation = +48.96875 +/- 0.2025 deg
  Vavg      =  57.84376 +/- 0.3251 km/s
  Vinit     =  60.06739 +/- 1.0965 km/s
Radiant (geocentric, J2000):
  R.A.   =  46.32857 +/- 0.5216 deg
  Dec    = +59.26979 +/- 0.3386 deg
  Vg     =  58.88646 +/- 1.1160 km/s
  Vinf   =  59.92344 +/- 1.0965 km/s
  Zc     =  40.99430 +/- 0.2027 deg
  Zg     =  41.36818 +/- 0.2038 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  62.60997 +/- 0.4311 deg
  Bg     = +39.91487 +/- 0.2767 deg
  Vh     =  41.62082 +/- 0.9597 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  82.75426 +/- 1.6213 deg
  Bh     = +65.20793 +/- 0.7120 deg
  Vh_x   =  -2.20123 +/- 0.5896 km/s
  Vh_y   = -17.31334 +/- 0.7933 km/s
  Vh_z   = -37.78486 +/- 0.6843 km/s
Orbit:
  La Sun = 140.208205 +/- -0.0000 deg
  a      =  47.194198 +/- 1098.6916 AU
  e      =   0.979634 +/- 0.0850
  i      = 111.273863 +/- 0.9310 deg
  peri   = 153.652618 +/- 1.7047 deg
  node   = 140.207723 +/- 0.0001 deg
  Pi     = 293.860341 +/- 1.7047 deg
  q      =   0.961158 +/- 0.0047 AU
  f      =  26.343584 +/- 1.7048 deg
  M      =   0.056387 +/- nan deg
  Q      =  93.427238 +/- 2197.3823 AU
  n      =   0.003040 +/- 0.0279 deg/day
  T      = 324.215336 +/- 489897915.6970 years
  Last perihelion JD = 2459420.972812 (2021-07-25 11:20:50.992061) +/- 1.1111 days
  Tj     =  -0.328498 +/- 0.4892
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +4.416701e-03, +2.795787e-04, +9.451816e-02, -9.363373e-09, +1.864217e-03, +1.324044e-04
q   , +2.795787e-04, +2.366197e-05, +6.952656e-03, -1.656116e-09, +1.440642e-04, +2.339006e-05
Tp  , +9.451816e-02, +6.952656e-03, +2.180497e+00, -3.710917e-07, +4.413325e-02, +5.242961e-03
node, -9.363373e-09, -1.656116e-09, -3.710917e-07, +2.717089e-13, -8.564751e-09, -3.836217e-09
peri, +1.864217e-03, +1.440642e-04, +4.413325e-02, -8.564751e-09, +9.007415e-04, +1.209879e-04
i   , +1.324044e-04, +2.339006e-05, +5.242961e-03, -3.836217e-09, +1.209879e-04, +5.416335e-05

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 0.674404
 a2 = 27.746719

Mean time residuals from time vs. length:
  Station with reference time: UK002C
  Avg. res. = 2.547e-06 s
  Stddev    = 1.60e-03 s

Begin point on the trajectory:
  Lon =     1.313682 +/- 0.0013 deg
  Lat =    52.005267 +/- 0.0003 deg
  Ht  = 105476.26 +/- 65.58 m
End point on the trajectory:
  Lon =     1.214426 +/- 0.0007 deg
  Lat =    51.951928 +/- 0.0002 deg
  Ht  = 94940.87 +/- 36.42 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,    True,    -0.727590,    51.263100,   57.00,   0.000000,   0.000000,   110866.30,    95050.80,          0.042099,       nan,       nan,              17.33, 0.0000,    True,    True, {"ff_name": "FF_UK000C_20210813_002933_552_0389888.fits"}
    UK002C,   False,    -1.801980,    51.351940,  130.00,   1.313010,  24.320330,   105476.26,    94940.87,          0.012624,      3.29,     54.67,              29.11, 1.0000,    True,    True, {"ff_name": "FF_UK002C_20210813_002926_211_0384768.fits"}
    UK0032,   False,    -0.023645,    52.984073,    6.00,   0.041712,  40.749201,   104129.48,    95390.31,          0.015416,     43.82,     18.30,              63.84, 1.0000,    True,    True, {"ff_name": "FF_UK0032_20210813_002934_061_0386560.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,       1, -0.120367, 2459439.520520202350,  58.95429,  43.88330,               58.60239,  32.39807,        58.59209,       32.39388,     58.95429,     +43.88330,      58.96620,      +43.88693,  3479040.52, -1974608.85,  5092462.23,      52.032433,       +1.364372,  110866.30,  202627.92,       0.00,             7149.04, 14440.07,     -0.00,           60859.51,     32.68,     -9.87,          34.75,  +3.07,  +1.54
  1,     UK000C,       1, -0.080231, 2459439.520520667080,  59.03164,  43.69966,               58.71886,  32.23329,        58.68917,       32.22120,     59.03164,     +43.69966,      59.06705,      +43.71009,  3478247.40, -1975432.53,  5090520.52,      52.023850,       +1.348336,  109161.46,  200471.18,    2253.38,             4895.65,  9781.61,  56143.64,           60859.51,     93.38,    -28.10,         100.33,  +2.78,  +1.27
  2,     UK000C,       1, -0.040071, 2459439.520521131810,  59.11187,  43.47941,               58.86481,  32.04195,        58.80363,       32.01696,     59.11187,     +43.47941,      59.18536,      +43.50083,  3477332.39, -1976382.80,  5088280.39,      52.013939,       +1.329858,  107195.02,  197987.11,    4853.08,             2295.96,  4775.38,  64733.46,           60859.51,    190.59,    -57.02,         207.26,  +2.08,  +0.60
  3,     UK000C,       1,  0.000097, 2459439.520521596540,  59.24695,  43.28597,               58.95473,  31.83888,        58.91247,       31.82167,     59.24695,     +43.28597,      59.29774,      +43.30076,  3476478.38, -1977269.72,  5086189.58,      52.004680,       +1.312599,  105360.03,  195670.89,    7279.49,              130.46,   202.88,  60406.63,           60859.51,    130.22,    -39.11,         143.33,  +1.62,  +0.16
  4,     UK000C,       1,  0.040253, 2459439.520522061270,  59.35351,  43.09517,               59.05792,  31.65250,        59.01577,       31.63534,     59.35351,     +43.09517,      59.40428,      +43.10991,  3475681.86, -1978096.93,  5084239.55,      51.996038,       +1.296487,  103648.94,  193512.61,    9542.52,             2393.49,    59.62,  56356.04,           60042.60,    128.66,    -38.66,         143.20,  +1.48,  +0.05
  5,     UK000C,       1,  0.080413, 2459439.520522526465,  59.45996,  42.89848,               59.16537,  31.46180,        59.12141,       31.44392,     59.45996,     +42.89848,      59.51300,      +42.91382,  3474882.02, -1978927.59,  5082281.37,      51.987353,       +1.280307,  101931.02,  191347.91,   11815.01,             4665.98,   -74.41,  56585.85,           59315.36,    132.88,    -39.92,         149.56,  +1.42,  +0.01
  6,     UK000C,       1,  0.120585, 2459439.520522991195,  59.57507,  42.68867,               59.27805,  31.25712,        59.23392,       31.23918,     59.57507,     +42.68867,      59.62842,      +42.70405,  3474046.79, -1979795.01,  5080236.56,      51.978277,       +1.263416,  100137.45,  189090.66,   14188.04,             7039.01,  -108.62,  59071.83,           59029.54,    132.04,    -39.68,         150.39,  +1.43,  +0.05
  7,     UK000C,       1,  0.160753, 2459439.520523456391,  59.67784,  42.46969,               59.40477,  31.05237,        59.34858,       31.02951,     59.67784,     +42.46969,      59.74576,      +42.48922,  3473212.03, -1980661.94,  5078192.88,      51.969198,       +1.246532,   98345.22,  186837.67,   16559.76,             9410.73,  -143.91,  59044.92,           58911.75,    166.49,    -49.93,         191.88,  +1.29,  -0.07
  8,     UK000C,       1,  0.200941, 2459439.520523921121,  59.81244,  42.24874,               59.51332,  30.82867,        59.46791,       30.81023,     59.81244,     +42.24874,      59.86752,      +42.26451,  3472360.58, -1981546.20,  5076108.36,      51.959930,       +1.229311,   96517.55,  184543.04,   18978.87,            11829.84,  -133.00,  60194.90,           58942.39,    133.05,    -40.00,         155.28,  +1.24,  -0.09
  9,     UK000C,       1,  0.241089, 2459439.520524385851,  59.90702,  42.06337,               59.61433,  30.65051,        59.56505,       30.63050,     59.90702,     +42.06337,      59.96685,      +42.08046,  3471677.15, -1982255.95,  5074435.19,      51.952486,       +1.215454,   95050.80,  182701.94,   20920.60,            13771.56,  -597.08,  48364.19,           58381.20,    143.20,    -43.03,         168.81,  +2.13,  +0.82
  0,     UK002C,       0,  0.000000, 2459439.520521595608,  56.74044,  30.50599,               70.15280,  23.65940,        70.14216,       23.65328,     56.74044,     +30.50599,      56.75356,      +30.50816,  3476532.48, -1977213.54,  5086322.03,      52.005267,       +1.313682,  105476.26,  252317.43,       0.00,               23.25,   101.50,      0.00,           59710.96,     50.60,     -3.01,          41.43,  +1.78,  -0.23
  1,     UK002C,       0,  0.040228, 2459439.520522061270,  56.83471,  30.25462,               70.27463,  23.41997,        70.29398,       23.43107,     56.83471,     +30.25462,      56.81107,      +30.25067,  3475719.01, -1978058.35,  5084330.49,      51.996441,       +1.297231,  103728.72,  250305.96,    2311.21,             2287.96,   -44.40,  57452.77,           59710.96,    -91.30,      5.52,          75.38,  +1.47,  -0.52
  2,     UK002C,       0,  0.080460, 2459439.520522526931,  56.89230,  29.98052,               70.43779,  23.18512,        70.45473,       23.19483,     56.89230,     +29.98052,      56.87184,      +29.97707,  3474868.96, -1978941.16,  5082249.39,      51.987212,       +1.280045,  101902.97,  248210.18,    4726.35,             4703.09,   -40.10,  60030.21,           59710.96,    -79.32,      4.79,          66.04,  +1.27,  -0.70
  3,     UK002C,       0,  0.120700, 2459439.520522992592,  56.94287,  29.69303,               70.61489,  22.94423,        70.62181,       22.94820,     56.94287,     +29.69303,      56.93487,      +29.69162,  3473997.32, -1979846.38,  5080115.44,      51.977739,       +1.262425,  100031.22,  246067.62,    7202.82,             7179.57,    25.06,  61542.72,           59710.96,    -32.22,      1.93,          27.06,  +1.30,  -0.66
  4,     UK002C,       0,  0.160924, 2459439.520523458254,  56.99398,  29.42614,               70.77563,  22.71783,        70.77678,       22.71849,     56.99398,     +29.42614,      56.99324,      +29.42591,  3473199.07, -1980675.40,  5078161.16,      51.969057,       +1.246272,   98317.41,  244110.24,    9470.79,             9447.54,  -117.33,  56383.51,           59239.46,     -5.32,      0.32,           4.50,  +1.43,  -0.51
  5,     UK002C,       0,  0.201160, 2459439.520523923915,  57.04065,  29.14046,               70.95249,  22.47990,        70.94136,       22.47352,     57.04065,     +29.14046,      57.05510,      +29.14271,  3472362.40, -1981544.30,  5076112.82,      51.959950,       +1.229346,   96521.47,  242065.08,   11847.91,            11824.65,  -151.30,  59079.26,           59081.85,     51.02,     -3.03,          43.55,  +1.18,  -0.74
  6,     UK002C,       0,  0.241380, 2459439.520524389576,  57.11132,  28.88993,               71.08616,  22.25340,        71.08796,       22.25443,     57.11132,     +28.88993,      57.11013,      +28.88957,  3471625.93, -1982309.16,  5074309.78,      51.951928,       +1.214426,   94940.87,  240268.75,   13940.37,            13917.11,  -468.96,  52025.34,           58269.75,     -8.20,      0.49,           7.05,  +3.63,  +1.73
  0,     UK0032,       0,  0.032174, 2459439.520521971863,   0.70735,   4.93773,              140.08004,  35.39389,       140.10953,       35.41911,      0.70735,      +4.93773,       0.67542,       +4.95166,  3475905.57, -1977864.60,  5084787.24,      51.998466,       +1.300998,  104129.48,  176894.83,       0.00,             1757.89,   -91.84,      0.00,           60336.19,    -41.48,    -99.26,         125.44,  +0.43,  -0.81
  1,     UK0032,       0,  0.072286, 2459439.520522436127,   0.37338,   4.25733,              140.77595,  34.89395,       140.78012,       34.89750,      0.37338,      +4.25733,       0.36916,       +4.25930,  3475002.13, -1978802.86,  5082575.42,      51.988658,       +1.282744,  102188.97,  175802.30,    2566.84,             4324.73,    71.35,  63991.85,           60336.19,     -5.81,    -13.94,          17.72,  +0.43,  -0.80
  2,     UK0032,       0,  0.112422, 2459439.520522900857,   0.08624,   3.60273,              141.39978,  34.39679,       141.40570,       34.40178,      0.08624,      +3.60273,       0.08030,       +3.60552,  3474159.21, -1979678.26,  5080511.78,      51.979499,       +1.265700,  100378.84,  174810.54,    4961.72,             6719.61,    61.14,  59669.18,           60336.19,     -8.20,    -19.65,          25.13,  +0.37,  -0.84
  3,     UK0032,       0,  0.152534, 2459439.520523365121, 359.78921,   2.97203,              142.01701,  33.92258,       142.00858,       33.91551,    359.78921,      +2.97203,     359.79897,       +2.96806,  3473346.42, -1980522.36,  5078521.91,      51.970660,       +1.249256,   98633.75,  173880.05,    7270.99,             9028.88,   -33.24,  57570.49,           60336.19,     11.60,     27.85,          35.79,  +0.37,  -0.83
  4,     UK0032,       0,  0.192666, 2459439.520523829386, 359.50699,   2.32102,              142.62011,  33.42122,       142.61545,       33.41733,    359.50699,      +2.32102,     359.51284,       +2.31883,  3472527.44, -1981372.90,  5076516.88,      51.961747,       +1.232686,   96875.71,  172968.78,    9597.85,            11355.75,  -111.22,  57980.26,           59566.14,      6.38,     15.32,          19.79,  +0.36,  -0.83
  5,     UK0032,       0,  0.232778, 2459439.520524293650, 359.26459,   1.76612,              143.13096,  32.99237,       143.12832,       32.99017,    359.26459,      +1.76612,     359.26843,       +1.76487,  3471835.36, -1982091.65,  5074822.51,      51.954210,       +1.218656,   95390.31,  172218.68,   11564.18,            13322.08,  -548.54,  49020.99,           57840.14,      3.61,      8.66,          11.24,  +1.19,  +0.01

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.