Orbital Analysis for matched events on 20210813_000650.745_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 63.11° Bg 37.08° Vg 59.27km/s
mass 0.01653g, abs. mag -0.7
Path Details
------------
start -1.35° 53.23° 107.97km
end   -1.46° 53.17° 99.29km

Orbit Details
-------------
Semimajor axis 9.87A.U., eccentricity 0.90, inclination 115.03°, Period 31.01Y, LA Sun 140.19°, last Perihelion 2021-07-22

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: 2459439.504753997084
Time: 2021-08-13 00:06:50.780431 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK001L and UK0027
 Convergence angle = 31.32168 deg
 R.A. =  51.14941  Dec = +56.88660 deg
Intersection 2 - Stations: UK001L and UK002Z
 Convergence angle = 74.86791 deg
 R.A. =  50.25894  Dec = +55.96197 deg
Intersection 3 - Stations: UK001L and UK003B
 Convergence angle = 15.23347 deg
 R.A. =  45.64329  Dec = +50.22863 deg
Intersection 4 - Stations: UK0027 and UK002Z
 Convergence angle = 73.81541 deg
 R.A. =  49.50823  Dec = +56.34498 deg
Intersection 5 - Stations: UK0027 and UK003B
 Convergence angle = 46.46500 deg
 R.A. =  47.06421  Dec = +55.46704 deg
Intersection 6 - Stations: UK002Z and UK003B
 Convergence angle = 59.73821 deg
 R.A. =  47.63756  Dec = +57.24807 deg

Best intersection: Stations UK001L and UK002Z with Qconv = 74.87 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   3067292.29 +/- 25.58 m
 Y =  -2394336.54 +/- 84.91 m
 Z =   5173508.45 +/- 57.34 m
 Vx =    21667.83 +/- 177.40 m/s
 Vy =    24610.90 +/- 638.09 m/s
 Vz =    50609.27 +/- 321.26 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+7.126622e+02, -2.203661e+03, +1.521071e+03, +4.252638e+03, -1.281285e+04, +7.227663e+03
-2.203661e+03, +7.861914e+03, -5.205527e+03, -1.371819e+04, +4.614472e+04, -2.648610e+04
+1.521071e+03, -5.205527e+03, +3.582570e+03, +9.135717e+03, -3.048457e+04, +1.766718e+04
+4.252638e+03, -1.371819e+04, +9.135717e+03, +3.073708e+04, -9.609439e+04, +5.088596e+04
-1.281285e+04, +4.614472e+04, -3.048457e+04, -9.609439e+04, +3.422732e+05, -1.817524e+05
+7.227663e+03, -2.648610e+04, +1.766718e+04, +5.088596e+04, -1.817524e+05, +1.010274e+05

Timing offsets (from input data):
    UK001L: -0.000053 s
    UK0027: 0.001628 s
    UK002Z: 0.000000 s
    UK003B: -0.000127 s

Reference point on the trajectory:
  Time: 2021-08-13 00:06:50.780431 UTC
  Lon     = +-1.342028 +/- 0.0008 deg
  Lat     = +53.233604 +/- 0.0002 deg
  Lat geo = +53.052009 +/- 0.0002 deg
  Ht      =  109005.10 +/- 88.35 m

  JD dynamic   = 2459439.505555144046 
  LST apparent = 322.0243067135 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  48.63879 +/- 0.8504 deg
  Dec       = +57.06051 +/- 0.4258 deg
  Azimuth   =  48.71519 +/- 0.1292 deg
  Elevation = +43.75093 +/- 0.6266 deg
  Vavg      =  56.98487 +/- 0.0783 km/s
  Vinit     =  60.30332 +/- 0.0878 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  48.66782 +/- 0.8504 deg
  Dec       = +56.83522 +/- 0.4258 deg
  Azimuth   =  48.96024 +/- 0.1292 deg
  Elevation = +43.61094 +/- 0.6266 deg
  Vavg      =  57.13936 +/- 0.0783 km/s
  Vinit     =  60.45781 +/- 0.0878 km/s
Radiant (geocentric, J2000):
  R.A.   =  48.86332 +/- 0.8487 deg
  Dec    = +56.74367 +/- 0.4335 deg
  Vg     =  59.27348 +/- 0.0893 km/s
  Vinf   =  60.30332 +/- 0.0878 km/s
  Zc     =  46.36904 +/- 0.6263 deg
  Zg     =  46.79171 +/- 0.6338 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  63.11463 +/- 0.3894 deg
  Bg     = +37.08182 +/- 0.5596 deg
  Vh     =  40.75784 +/- 0.2612 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  81.78290 +/- 0.6215 deg
  Bh     = +61.26808 +/- 0.8166 deg
  Vh_x   =  -2.80029 +/- 0.1690 km/s
  Vh_y   = -19.39164 +/- 0.3984 km/s
  Vh_z   = -35.73967 +/- 0.5093 km/s
Orbit:
  La Sun = 140.193065 +/- -0.0000 deg
  a      =   9.869625 +/- 1.3642 AU
  e      =   0.904191 +/- 0.0213
  i      = 115.031156 +/- 0.5962 deg
  peri   = 149.248237 +/- 1.8538 deg
  node   = 140.192067 +/- 0.0000 deg
  Pi     = 289.440303 +/- 1.8539 deg
  q      =   0.945598 +/- 0.0074 AU
  f      =  30.747756 +/- 1.8538 deg
  M      =   0.692399 +/- 0.3681 deg
  Q      =  18.793652 +/- 2.7213 AU
  n      =   0.031787 +/- 0.0129 deg/day
  T      =  31.006420 +/- 5.7031 years
  Last perihelion JD = 2459417.723263 (2021-07-22 05:21:29.965135) +/- 1.2948 days
  Tj     =   0.029549 +/- 0.1180
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +4.832225e-04, +1.605710e-04, +2.866689e-02, +1.765302e-08, +7.117339e-04, -2.258170e-04
q   , +1.605710e-04, +5.670396e-05, +9.982262e-03, +6.164408e-09, +2.494261e-04, -7.883047e-05
Tp  , +2.866689e-02, +9.982262e-03, +1.763211e+00, +1.087828e-06, +4.399215e-02, -1.391281e-02
node, +1.765302e-08, +6.164408e-09, +1.087828e-06, +6.912531e-13, +2.715093e-08, -8.841226e-09
peri, +7.117339e-04, +2.494261e-04, +4.399215e-02, +2.715093e-08, +1.098338e-03, -3.472345e-04
i   , -2.258170e-04, -7.883047e-05, -1.391281e-02, -8.841226e-09, -3.472345e-04, +1.130827e-04

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 0.004560
 a2 = 46.553232

Mean time residuals from time vs. length:
  Station with reference time: UK002Z
  Avg. res. = 1.757e-06 s
  Stddev    = 1.33e-03 s

Begin point on the trajectory:
  Lon =    -1.354026 +/- 0.0005 deg
  Lat =    53.227282 +/- 0.0001 deg
  Ht  = 107967.09 +/- 86.60 m
End point on the trajectory:
  Lon =    -1.455305 +/- 0.0010 deg
  Lat =    53.174264 +/- 0.0005 deg
  Ht  = 99290.09 +/- 22.65 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
    UK001L,   False,    -1.306160,    51.883100,   80.00,   0.000000,   0.000000,   107967.09,    99981.17,          0.034998,     77.28,     80.67,              38.74, 0.3915,    True,    True, {"ff_name": "FF_UK001L_20210813_000643_136_0333056.fits"}
    UK0027,   False,    -2.374601,    51.371449,   48.00,   0.201975,  29.337211,   107659.97,    99290.09,          0.031584,    124.81,     34.08,              28.66, 0.2301,    True,    True, {"ff_name": "FF_UK0027_20210813_000648_818_0346112.fits"}
    UK002Z,   False,    -0.382830,    53.537790,   34.00,   0.000000,   0.000000,   107692.23,    99590.03,          0.005173,      6.41,      9.83,              80.74, 0.9741,    True,    True, {"ff_name": "FF_UK002Z_20210813_000646_556_0346368.fits"}
    UK003B,   False,    -1.072290,    52.276980,  129.00,   0.000000,   0.000000,   104026.33,    99640.55,          0.044643,     50.67,    101.22,              41.78, 0.4438,   False,    True, {"ff_name": "FF_UK003B_20210813_000645_007_0350720.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,     UK001L,       0,  0.035022, 2459439.504754403140, 145.44867,  72.96419,              358.79060,  34.86937,       358.77564,       34.89333,    145.44867,     +72.96419,     145.49435,      +72.98758,  3066752.92, -2394949.18,  5172248.64,      53.227282,       -1.354026,  107967.09,  185479.40,       0.00,             1501.12,   154.43,      0.00,           58478.19,    -62.96,    -60.25,          96.91,  +1.95,  +0.61
  1,     UK001L,       0,  0.075302, 2459439.504754869267, 146.71497,  72.70439,              358.31973,  34.62963,       358.28346,       34.68710,    146.71497,     +72.70439,     146.82754,      +72.75991,  3065917.70, -2395897.85,  5170297.82,      53.217485,       -1.372774,  106360.07,  183664.04,    2324.49,             3825.61,    49.91,  57708.35,           58478.19,   -149.83,   -143.65,         233.11,  +1.20,  -0.12
  2,     UK001L,       0,  0.115546, 2459439.504755334929, 148.09194,  72.48312,              357.80220,  34.43765,       357.77976,       34.47290,    148.09194,     +72.48312,     148.16304,      +72.51679,  3065075.35, -2396854.60,  5168330.37,      53.207598,       -1.391681,  104739.77,  181845.09,    4668.81,             6169.93,   -32.62,  58252.53,           58478.19,    -91.27,    -87.38,         143.32,  +1.32,  +0.02
  3,     UK001L,       0,  0.155810, 2459439.504755801056, 149.48162,  72.23739,              357.26815,  34.22974,       357.25696,       34.24716,    149.48162,     +72.23739,     149.51798,      +72.25383,  3064213.83, -2397833.14,  5166318.12,      53.197477,       -1.411015,  103083.03,  179997.46,    7066.49,             8567.61,   -62.99,  59549.16,           58478.19,    -44.78,    -42.82,          71.00,  +1.48,  +0.20
  4,     UK001L,       0,  0.196082, 2459439.504756267183, 150.98265,  71.97241,              356.68023,  34.01515,       356.69088,       33.99873,    150.98265,     +71.97241,     150.94904,      +71.95711,  3063294.85, -2398876.94,  5164171.68,      53.186672,       -1.431628,  101316.30,  178041.20,    9624.08,            11125.20,    66.06,  63507.81,           59583.99,     41.92,     39.99,          67.12,  +2.02,  +0.77
  5,     UK001L,       0,  0.236318, 2459439.504756732844, 152.04212,  71.72983,              356.24985,  33.81471,       356.25587,       33.80550,    152.04212,     +71.72983,     152.02351,      +71.72134,  3062600.21, -2399665.94,  5162549.20,      53.178498,       -1.447251,   99981.17,  176572.95,   11557.34,            13058.46,  -427.05,  48047.93,           58253.01,     23.37,     22.31,          37.75,  +3.78,  +2.55
  0,     UK0027,       0,  0.049765, 2459439.504754554015, 106.19042,  60.29963,               18.19963,  25.12537,        18.18609,       25.13868,    106.19042,     +60.29963,     106.20281,      +60.31669,  3066593.32, -2395130.46,  5171875.86,      53.225410,       -1.357631,  107659.97,  244428.19,       0.00,             1945.31,  -290.45,      0.00,           64112.91,    -20.09,    -74.51,          65.12,  +2.75,  +0.81
  1,     UK0027,       0,  0.089977, 2459439.504755019676, 106.79541,  60.20351,               17.93599,  24.91974,        17.92903,       24.92657,    106.79541,     +60.20351,     106.80218,      +60.21226,  3065615.96, -2396240.57,  5169593.05,      53.213944,       -1.379541,  105779.61,  242052.44,    2720.07,             4665.38,     4.70,  67643.28,           64112.91,    -10.25,    -37.95,          33.50,  +2.32,  +0.40
  2,     UK0027,       0,  0.130173, 2459439.504755484872, 107.34235,  60.10681,               17.69997,  24.72597,        17.69396,       24.73185,    107.34235,     +60.10681,     107.34852,      +60.11433,  3064736.85, -2397239.09,  5167539.72,      53.203622,       -1.399265,  104088.76,  239921.55,    5166.71,             7112.02,    27.39,  60867.74,           64112.91,     -8.77,    -32.46,          28.91,  +2.48,  +0.58
  3,     UK0027,       0,  0.170381, 2459439.504755950067, 107.93557,  60.00302,               17.44145,  24.51806,        17.43960,       24.51987,    107.93557,     +60.00302,     107.93804,      +60.00533,  3063799.11, -2398304.20,  5165349.46,      53.192602,       -1.420295,  102285.67,  237655.61,    7776.51,             9721.82,   212.51,  64907.49,           64112.91,     -2.67,     -9.88,           8.89,  +1.95,  +0.07
  4,     UK0027,       0,  0.210541, 2459439.504756415263, 108.39125,  59.92601,               17.24032,  24.36178,        17.24478,       24.35742,    108.39125,     +59.92601,     108.38779,      +59.92045,  3063093.23, -2399105.95,  5163700.76,      53.184300,       -1.436167,  100928.75,  235953.94,    9741.01,            11686.32,  -244.77,  48916.81,           61048.35,      6.42,     23.70,          21.47,  +4.38,  +2.52
  5,     UK0027,       0,  0.250705, 2459439.504756879993, 108.98902,  59.88262,               16.95170,  24.21170,        17.00697,       24.15763,    108.98902,     +59.88262,     108.93560,      +59.81394,  3062240.58, -2400074.41,  5161709.23,      53.174264,       -1.455305,   99290.09,  233904.70,   12114.02,            14059.32,  -293.78,  59082.90,           59891.69,     79.59,    291.12,         266.14,  +5.25,  +3.40
  0,     UK002Z,       1,  0.000000, 2459439.504753997084, 287.68929,  30.77115,              242.36034,  55.91777,       242.43739,       55.91057,    287.68929,     +30.77115,     287.64444,      +30.79194,  3067291.38, -2394337.58,  5173506.32,      53.233593,       -1.341902,  109003.34,  131081.35,       0.00,                2.54,   767.80,      0.00,           53729.16,     83.83,    -54.80,         157.60,  +5.51,  +4.92
  1,     UK002Z,       0,  0.040620, 2459439.504754467402, 287.19560,  30.06986,              242.20045,  55.10239,       242.20644,       55.10182,    287.19560,     +30.06986,     287.19223,      +30.07150,  3066610.08, -2395111.42,  5171915.02,      53.225607,       -1.357227,  107692.23,  130741.75,    1896.11,             1898.65,   214.39,  46679.23,           53729.16,      6.63,     -4.33,          12.49,  +1.10,  +0.52
  2,     UK002Z,       0,  0.081332, 2459439.504754938651, 286.67170,  29.21011,              241.93008,  54.14217,       241.94313,       54.14095,    286.67170,     +29.21011,     286.66420,      +29.21372,  3065804.91, -2396025.96,  5170034.38,      53.216162,       -1.375308,  106143.09,  130374.01,    4136.97,             4139.51,     0.18,  55041.85,           53729.16,     14.75,     -9.62,          27.86,  +0.72,  +0.14
  3,     UK002Z,       0,  0.122116, 2459439.504755410366, 286.10194,  28.28626,              241.67490,  53.10288,       241.67192,       53.10316,    286.10194,     +28.28626,     286.10427,      +28.28542,  3064940.38, -2397007.91,  5168015.10,      53.206013,       -1.394711,  104480.18,  130020.79,    6543.04,             6545.58,   -53.17,  58995.26,           53729.16,     -3.44,      2.25,           6.52,  +0.67,  +0.10
  4,     UK002Z,       0,  0.162924, 2459439.504755882546, 285.53748,  27.31291,              241.39199,  52.02255,       241.40283,       52.02153,    285.53748,     +27.31291,     285.53142,      +27.31601,  3064044.39, -2398025.60,  5165922.36,      53.195485,       -1.414814,  102757.25,  129700.82,    9036.63,             9039.17,   -20.43,  61105.60,           55779.11,     12.79,     -8.35,          24.29,  +0.62,  +0.06
  5,     UK002Z,       0,  0.203740, 2459439.504756355193, 284.97329,  26.34237,              241.13813,  50.94068,       241.14662,       50.93989,    284.97329,     +26.34237,     284.96877,      +26.34483,  3063152.96, -2399038.10,  5163840.27,      53.185003,       -1.434817,  101043.57,  129429.65,   11517.55,            11520.09,    -0.85,  60782.82,           57080.04,     10.23,     -6.67,          19.46,  +0.98,  +0.42
  6,     UK002Z,       0,  0.244440, 2459439.504756826442, 284.49224,  25.51749,              240.94330,  50.01752,       240.93828,       50.01799,    284.49224,     +25.51749,     284.49648,      +25.51602,  3062396.67, -2399897.12,  5162073.81,      53.176102,       -1.451813,   99590.03,  129237.59,   13622.37,            13624.91,  -350.38,  51715.54,           56969.90,     -6.16,      4.02,          11.74,  +2.08,  +1.52
  0,     UK003B,       0,  0.129108, 2459439.504755492788, 190.35548,  78.40030,              348.03250,  43.83638,       348.01197,       43.87489,    190.35548,     +78.40030,     190.53429,      +78.42078,  3064704.38, -2397275.96,  5167463.89,      53.203241,       -1.399990,  104026.33,  148629.68,       0.00,             7202.37,   182.01,      0.00,           53476.82,    -95.73,    -47.87,         148.53,  +0.90,  +0.04
  1,     UK003B,       0,  0.169248, 2459439.504755957518, 191.87804,  77.87681,              347.23705,  43.63245,       347.22490,       43.65470,    191.87804,     +77.87681,     191.97905,      +77.88817,  3063880.08, -2398212.22,  5165538.59,      53.193554,       -1.418496,  102441.34,  146950.58,    2294.09,             9496.46,    55.52,  57152.17,           53476.82,    -54.89,    -27.42,          86.12,  +0.61,  -0.23
  2,     UK003B,       0,  0.209412, 2459439.504756422248, 193.34039,  77.29658,              346.38796,  43.39524,       346.37955,       43.41028,    193.34039,     +77.29658,     193.40707,      +77.30393,  3063008.14, -2399202.60,  5163502.01,      53.183299,       -1.438063,  100765.21,  145192.84,    4720.76,            11923.14,    60.17,  60419.17,           53476.82,    -36.79,    -18.37,          58.42,  +1.31,  +0.50
  3,     UK003B,       0,  0.249576, 2459439.504756886978, 194.02356,  76.86622,              345.84150,  43.17100,       345.80268,       43.23907,    194.02356,     +76.86622,     194.31629,      +76.89865,  3062422.97, -2399867.25,  5162135.23,      53.176412,       -1.451250,   99640.55,  144024.86,    6349.35,            13551.72,  -733.27,  40548.38,           53476.82,   -165.68,    -82.99,         265.38,  +4.63,  +3.84

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.