Orbital Analysis for matched events on 20210904_041341.301_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 78.05° Bg 35.84° Vg 53.99km/s
mass 0.02201g, abs. mag -0.4
Path Details
------------
start -3.18° 50.61° 103.48km
end   -3.21° 50.59° 92.59km

Orbit Details
-------------
Semimajor axis 1.63A.U., eccentricity 0.40, inclination 113.81°, Period 2.08Y, LA Sun 161.57°, last Perihelion 2021-08-12

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: 2459461.676172465552
Time: 2021-09-04 04:13:41.315669 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK000H and UK003C
 Convergence angle = 9.55101 deg
 R.A. =  72.65268  Dec = +58.25045 deg

Best intersection: Stations UK000H and UK003C with Qconv = 9.55 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   2976975.47 +/- 175.62 m
 Y =   2850308.88 +/- 123.81 m
 Z =   4986010.77 +/- 107.64 m
 Vx =     9195.62 +/- 1362.22 m/s
 Vy =    27297.56 +/- 814.39 m/s
 Vz =    46989.49 +/- 524.33 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+2.018798e+04, -7.991059e+03, +2.239860e+03, +1.066544e+05, -3.313167e+04, +2.146629e+04
-7.991059e+03, +6.517669e+03, +3.702738e+03, -4.546402e+04, +1.813189e+04, -6.691063e+03
+2.239860e+03, +3.702738e+03, +7.156600e+03, +5.552383e+03, +2.008015e+03, +6.968427e+03
+1.066544e+05, -4.546402e+04, +5.552383e+03, +7.712002e+05, -2.529885e+05, +1.491049e+05
-3.313167e+04, +1.813189e+04, +2.008015e+03, -2.529885e+05, +1.714359e+05, +5.396255e+04
+2.146629e+04, -6.691063e+03, +6.968427e+03, +1.491049e+05, +5.396255e+04, +1.931243e+05

Timing offsets (from input data):
    UK000H: 0.000000 s
    UK003C: 0.000026 s

Reference point on the trajectory:
  Time: 2021-09-04 04:13:41.315669 UTC
  Lon     = +-3.175318 +/- 0.0028 deg
  Lat     = +50.608378 +/- 0.0006 deg
  Lat geo = +50.422529 +/- 0.0006 deg
  Ht      =  103463.31 +/- 116.08 m

  JD dynamic   = 2459461.676973375957 
  LST apparent = 43.7547684904 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  71.38308 +/- 2.7527 deg
  Dec       = +58.49149 +/- 0.2212 deg
  Azimuth   =  52.91315 +/- 1.6677 deg
  Elevation = +72.31319 +/- 1.3705 deg
  Vavg      =  53.59106 +/- 0.6094 km/s
  Vinit     =  55.11559 +/- 0.4836 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  71.91016 +/- 2.7527 deg
  Dec       = +58.36704 +/- 0.2212 deg
  Azimuth   =  53.52451 +/- 1.6677 deg
  Elevation = +72.07510 +/- 1.3705 deg
  Vavg      =  53.66467 +/- 0.6094 km/s
  Vinit     =  55.18920 +/- 0.4836 km/s
Radiant (geocentric, J2000):
  R.A.   =  71.26251 +/- 2.7825 deg
  Dec    = +58.50039 +/- 0.2251 deg
  Vg     =  53.98607 +/- 0.4937 km/s
  Vinf   =  55.11559 +/- 0.4836 km/s
  Zc     =  17.79948 +/- 1.3663 deg
  Zg     =  17.98525 +/- 1.3813 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  78.05118 +/- 1.7453 deg
  Bg     = +35.83740 +/- 0.4209 deg
  Vh     =  34.84436 +/- 0.4396 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  89.53929 +/- 4.8678 deg
  Bh     = +65.11812 +/- 1.0027 deg
  Vh_x   =  -0.11788 +/- 1.2945 km/s
  Vh_y   = -14.66025 +/- 0.5666 km/s
  Vh_z   = -31.61000 +/- 0.4569 km/s
Orbit:
  La Sun = 161.568145 +/- 0.0000 deg
  a      =   1.627441 +/- 0.0944 AU
  e      =   0.398783 +/- 0.0316
  i      = 113.805886 +/- 0.5166 deg
  peri   = 153.550153 +/- 8.0242 deg
  node   = 161.569341 +/- 0.0000 deg
  Pi     = 315.119494 +/- 8.0242 deg
  q      =   0.978446 +/- 0.0194 AU
  f      =  26.447834 +/- 8.0242 deg
  M      =  10.639304 +/- 3.4359 deg
  Q      =   2.276437 +/- 0.1815 AU
  n      =   0.474730 +/- 0.0399 deg/day
  T      =   2.076150 +/- 0.1827 years
  Last perihelion JD = 2459439.265667 (2021-08-12 18:22:33.607102) +/- 6.3647 days
  Tj     =   2.783834 +/- 0.1910
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +1.092601e-03, +6.840062e-05, +6.780955e-02, -8.722313e-09, +1.220657e-03, +2.272028e-04
q   , +6.840062e-05, +1.586693e-04, +5.507862e-02, +4.856536e-10, +1.201504e-03, -1.271191e-05
Tp  , +6.780955e-02, +5.507862e-02, +2.133577e+01, -1.918774e-07, +4.534902e-01, +4.962001e-03
node, -8.722313e-09, +4.856536e-10, -1.918774e-07, +9.981024e-14, -2.046447e-09, -2.599955e-09
peri, +1.220657e-03, +1.201504e-03, +4.534902e-01, -2.046447e-09, +9.699590e-03, +5.257434e-05
i   , +2.272028e-04, -1.271191e-05, +4.962001e-03, -2.599955e-09, +5.257434e-05, +6.772805e-05

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 1.278955
 a2 = 27.361449

Mean time residuals from time vs. length:
  Station with reference time: UK000H
  Avg. res. = 1.144e-06 s
  Stddev    = 1.07e-03 s

Begin point on the trajectory:
  Lon =    -3.175243 +/- 0.0021 deg
  Lat =    50.608414 +/- 0.0003 deg
  Ht  = 103484.53 +/- 156.30 m
End point on the trajectory:
  Lon =    -3.214657 +/- 0.0026 deg
  Lat =    50.589845 +/- 0.0006 deg
  Ht  = 92590.57 +/- 141.08 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
    UK000H,   False,    -1.778230,    50.857470,   24.00,   0.035769,  47.718154,   103484.53,    93257.52,          0.008074,     19.65,      5.07,              61.95, 1.0000,    True,    True, {"ff_name": "FF_UK000H_20210904_041339_300_0795904.fits"}
    UK003C,   False,    -4.949858,    50.224871,   55.00,  94.087092,   0.000005,   100957.85,    92590.57,          0.006113,     17.31,      1.42,              34.71, 1.0000,    True,    True, {"ff_name": "FF_UK003C_20210904_041340_641_0781312.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,     UK000H,       0,  0.000000, 2459461.676172635052, 355.68361,  25.27210,              254.83446,  44.59381,       254.85037,       44.59240,    355.68361,     +25.27210,     355.67331,      +25.27870,  2976979.18,  2850319.91,  4986029.76,      50.608414,       -3.175243,  103484.53,  146183.62,       0.00,               22.27,   -74.07,      0.00,           56449.58,     -7.29,    -28.21,          41.11,  +2.57,  +1.75
  1,     UK000H,       0,  0.040660, 2459461.676173105836, 355.15073,  24.60711,              254.71068,  43.77662,       254.71238,       43.77647,    355.15073,     +24.60711,     355.14979,      +24.60782,  2976584.74,  2849148.99,  4984014.16,      50.604581,       -3.183380,  101232.13,  145070.28,    2364.16,             2341.89,     4.55,  58144.64,           56449.58,     -0.78,     -3.04,           4.46,  +1.50,  +0.69
  2,     UK000H,       0,  0.081292, 2459461.676173576154, 354.64971,  23.96312,              254.58661,  42.99230,       254.58347,       42.99257,    354.64971,     +23.96312,     354.65214,      +23.96179,  2976211.48,  2848040.97,  4982106.83,      50.600951,       -3.191094,   99100.77,  144045.08,    4601.34,             4579.07,     2.26,  55059.47,           56449.58,      1.45,      5.64,           8.34,  +0.99,  +0.20
  3,     UK000H,       0,  0.121952, 2459461.676174046472, 354.12470,  23.29421,              254.47175,  42.17276,       254.45234,       42.17447,    354.12470,     +23.29421,     354.13819,      +23.28597,  2975827.48,  2846901.03,  4980144.55,      50.597213,       -3.199028,   96908.08,  143019.03,    6902.96,             6880.69,    62.89,  56606.51,           56449.58,      9.02,     35.02,          52.16,  +0.47,  -0.31
  4,     UK000H,       0,  0.162560, 2459461.676174516790, 353.66786,  22.67180,              254.34394,  41.42765,       254.33594,       41.42836,    353.66786,     +22.67180,     353.67395,      +22.66838,  2975482.13,  2845875.87,  4978379.86,      50.593849,       -3.206184,   94936.22,  142122.74,    8972.82,             8950.55,  -105.38,  50971.84,           55324.50,      3.74,     14.52,          21.76,  +1.02,  +0.26
  5,     UK000H,       0,  0.203084, 2459461.676174985711, 353.27858,  22.13371,              254.23453,  40.78556,       254.23809,       40.78524,    353.27858,     +22.13371,     353.27701,      +22.13524,  2975188.13,  2845003.11,  4976877.52,      50.590984,       -3.212303,   93257.52,  141380.42,   10734.98,            10712.70,  -576.74,  43484.17,           53316.58,     -1.67,     -6.49,           9.78,  +3.57,  +2.82
  0,     UK003C,       1,  0.006468, 2459461.676172614563, 118.44881,  39.17495,               70.64636,  36.98017,        70.63688,       36.97885,    118.44881,     +39.17495,     118.45626,      +39.18002,  2976945.48,  2850219.86,  4985857.52,      50.608087,       -3.175916,  103292.06,  169281.86,       0.00,              179.75,  -273.06,      0.00,           57521.66,     -1.85,    -22.63,          27.67,  +4.39,  +3.25
  1,     UK003C,       0,  0.046912, 2459461.676173082553, 118.86807,  38.81668,               70.73768,  36.50144,        70.73904,       36.50163,    118.86807,     +38.81668,     118.86717,      +38.81595,  2976536.71,  2849006.40,  4983768.71,      50.604114,       -3.184343,  100957.85,  167283.12,    2450.04,             2629.79,   -52.12,  60578.56,           57521.66,      0.26,      3.21,           3.97,  +1.55,  +0.43
  2,     UK003C,       0,  0.087356, 2459461.676173550542, 119.27614,  38.45352,               70.83543,  36.02471,        70.83971,       36.02530,    119.27614,     +38.45352,     119.27308,      +38.45123,  2976138.21,  2847823.45,  4981732.40,      50.600238,       -3.192566,   98682.38,  165346.15,    4838.50,             5018.24,   107.25,  59055.92,           57521.66,      0.83,     10.11,          12.65,  +1.23,  +0.14
  3,     UK003C,       0,  0.127760, 2459461.676174018532, 119.62794,  38.11378,               70.94086,  35.59532,        70.92972,       35.59377,    119.62794,     +38.11378,     119.63732,      +38.11974,  2975784.89,  2846774.61,  4979926.95,      50.596799,       -3.199879,   96664.93,  163637.78,    6956.17,             7135.92,    -1.97,  52412.52,           57521.66,     -2.14,    -26.14,          33.06,  +0.48,  -0.59
  4,     UK003C,       0,  0.168156, 2459461.676174486056, 120.00340,  37.79419,               71.00857,  35.16319,        71.01826,       35.16454,    120.00340,     +37.79419,     119.99632,      +37.78898,  2975440.61,  2845752.60,  4978167.67,      50.593445,       -3.207013,   94699.11,  161982.24,    9019.69,             9199.44,  -164.90,  51082.28,           55775.45,      1.87,     22.65,          28.94,  +0.32,  -0.73
  5,     UK003C,       0,  0.208596, 2459461.676174954046, 120.38992,  37.42838,               71.10840,  34.69323,        71.11431,       34.69405,    120.38992,     +37.42838,     120.38601,      +37.42520,  2975071.32,  2844656.35,  4976280.61,      50.589845,       -3.214657,   92590.57,  160217.73,   11233.09,            11412.84,  -180.37,  54732.99,           55127.19,      1.13,     13.75,          17.76,  +1.21,  +0.19

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.