Orbital Analysis for matched events on 20210929_032550.447_UK

Summary for Event
-----------------
shower ID 210 BAU
Lg 94.59° Bg 24.94° Vg 65.91km/s
mass 0.01934g, abs. mag -0.8
Path Details
------------
start -3.22° 49.63° 109.93km
end   -3.33° 49.61° 93.36km

Orbit Details
-------------
Semimajor axis 9.47A.U., eccentricity 0.89, inclination 137.21°, Period 29.16Y, LA Sun 185.92°, last Perihelion 1992-08-06

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: 2459486.642944993451
Time: 2021-09-29 03:25:50.518526 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK002D and UK003E
 Convergence angle = 1.81050 deg
 R.A. =  31.82798  Dec =  -9.52703 deg
Intersection 2 - Stations: UK002D and UK003N
 Convergence angle = 17.75710 deg
 R.A. = 103.50063  Dec = +48.70272 deg
Intersection 3 - Stations: UK003E and UK003N
 Convergence angle = 17.99031 deg
 R.A. =  94.72075  Dec = +48.12930 deg

Best intersection: Stations UK003E and UK003N with Qconv = 17.99 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   2332738.99 +/- 514.31 m
 Y =   3508629.33 +/- 188.28 m
 Z =   4923221.51 +/- 49.43 m
 Vx =    -4955.85 +/- 2152.44 m/s
 Vy =    44172.38 +/- 768.62 m/s
 Vz =    49918.99 +/- 276.22 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+2.613524e+05, +8.832830e+04, +2.573485e+03, +1.036745e+06, +3.496942e+05, +1.420091e+04
+8.832830e+04, +3.422376e+04, +3.283318e+03, +3.681176e+05, +1.297642e+05, -1.132119e+03
+2.573485e+03, +3.283318e+03, +2.615971e+03, +1.568171e+04, +5.886498e+03, -4.083084e+02
+1.036745e+06, +3.681176e+05, +1.568171e+04, +4.599356e+06, +1.575299e+06, -1.230483e+03
+3.496942e+05, +1.297642e+05, +5.886498e+03, +1.575299e+06, +5.547186e+05, -1.522272e+04
+1.420091e+04, -1.132119e+03, -4.083084e+02, -1.230483e+03, -1.522272e+04, +1.891756e+04

Timing offsets (from input data):
    UK000H: 0.000000 s
    UK002D: 0.000000 s
    UK003E: 0.000150 s
    UK003N: -0.000326 s

Reference point on the trajectory:
  Time: 2021-09-29 03:25:50.518526 UTC
  Lon     = +-3.194846 +/- 0.0045 deg
  Lat     = +49.629508 +/- 0.0029 deg
  Lat geo = +49.442839 +/- 0.0029 deg
  Ht      =  114171.37 +/- 294.11 m

  JD dynamic   = 2459486.643746557180 
  LST apparent = 56.3817500610 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  96.40143 +/- 2.9327 deg
  Dec       = +48.31707 +/- 0.2056 deg
  Azimuth   =  77.38036 +/- 1.5955 deg
  Elevation = +64.00961 +/- 1.7685 deg
  Vavg      =  64.94654 +/- 0.0593 km/s
  Vinit     =  66.84059 +/- 0.1577 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  96.70338 +/- 2.9327 deg
  Dec       = +48.19044 +/- 0.2056 deg
  Azimuth   =  77.51033 +/- 1.5955 deg
  Elevation = +63.77900 +/- 1.7685 deg
  Vavg      =  65.07850 +/- 0.0593 km/s
  Vinit     =  66.97255 +/- 0.1577 km/s
Radiant (geocentric, J2000):
  R.A.   =  96.25260 +/- 2.9533 deg
  Dec    = +48.27420 +/- 0.2050 deg
  Vg     =  65.91391 +/- 0.1600 km/s
  Vinf   =  66.84059 +/- 0.1577 km/s
  Zc     =  26.03176 +/- 1.7734 deg
  Zg     =  26.21667 +/- 1.7878 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  94.58513 +/- 2.1381 deg
  Bg     = +24.93597 +/- 0.3690 deg
  Vh     =  40.95607 +/- 0.1448 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  92.35094 +/- 4.3115 deg
  Bh     = +42.73267 +/- 0.5173 deg
  Vh_x   =   1.23402 +/- 2.1178 km/s
  Vh_y   = -30.05805 +/- 0.6711 km/s
  Vh_z   = -27.79191 +/- 0.3311 km/s
Orbit:
  La Sun = 185.916507 +/- nan deg
  a      =   9.472869 +/- 1.3346 AU
  e      =   0.894478 +/- 0.0139
  i      = 137.211950 +/- 0.7600 deg
  peri   = 185.548480 +/- 6.4112 deg
  node   = 185.917720 +/- 0.0000 deg
  Pi     =  11.466200 +/- 6.4112 deg
  q      =   0.999594 +/- 0.0104 AU
  f      = 354.450624 +/- 6.4112 deg
  M      = 359.861594 +/- 0.1539 deg
  Q      =  17.946143 +/- 2.6768 AU
  n      =   0.033805 +/- 0.0064 deg/day
  T      =  29.155662 +/- 6.4782 years
  Last perihelion JD = 2448841.446846 (1992-08-06 22:43:27.457982) +/- 1940.9553 days
  Tj     =  -0.335988 +/- 0.0635
Shower association:
  IAU No.  =  210
  IAU code =  BAU

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +1.564586e-04, -7.490588e-05, -7.024976e+00, +1.982204e-09, -5.239021e-04, -9.278785e-05
q   , -7.490588e-05, +8.783514e-05, -3.809981e+00, -2.317934e-09, +9.331543e-04, +1.074777e-04
Tp  , -7.024976e+00, -3.809981e+00, +6.197012e+06, +3.274460e-04, -1.543211e+02, -1.473137e+01
node, +1.982204e-09, -2.317934e-09, +3.274460e-04, +8.309966e-14, -3.108129e-08, -3.816834e-09
peri, -5.239021e-04, +9.331543e-04, -1.543211e+02, -3.108129e-08, +1.281079e-02, +1.427703e-03
i   , -9.278785e-05, +1.074777e-04, -1.473137e+01, -3.816834e-09, +1.427703e-03, +1.753700e-04

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 0.000567
 a2 = 38.116690

Mean time residuals from time vs. length:
  Station with reference time: UK002D
  Avg. res. = 1.277e-06 s
  Stddev    = 1.13e-03 s

Begin point on the trajectory:
  Lon =    -3.222299 +/- 0.0037 deg
  Lat =    49.625512 +/- 0.0022 deg
  Ht  = 109930.55 +/- 150.43 m
End point on the trajectory:
  Lon =    -3.331110 +/- 0.0026 deg
  Lat =    49.609784 +/- 0.0018 deg
  Ht  = 93363.48 +/- 145.37 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,    True,    -1.778230,    50.857470,   24.00, 5152.819561,   0.146219,   113806.09,   104185.34,          0.069816,       nan,       nan,              80.36, 0.0000,    True,   False, {"ff_name": "FF_UK000H_20210929_032542_702_0811520.fits"}
    UK002D,   False,    -1.801980,    51.351940,  129.00,   0.000000,   0.000000,   109796.18,    93363.48,          0.047176,     87.46,    179.53,              83.17, 0.9858,    True,    True, {"ff_name": "FF_UK002D_20210929_032547_436_0811008.fits"}
    UK003E,   False,    -1.802002,    51.351948,  130.00,   0.000000,   0.000000,   109127.59,    94763.90,          0.046737,     86.74,    179.27,              83.17, 0.9858,    True,    True, {"ff_name": "FF_UK003E_20210929_032546_975_0810752.fits"}
    UK003N,   False,    -0.162561,    51.236425,  111.00,   0.000000,   0.000000,   109930.55,    95886.99,          0.006163,     22.70,     23.66,              94.22, 0.9946,    True,    True, {"ff_name": "FF_UK003N_20210929_032548_114_0822016.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,       1,  0.091441, 2459486.642946051899,  27.41290,  -0.24981,              216.97673,  32.76259,       217.08031,       32.78980,     27.41290,      -0.24981,      27.34308,       -0.19153,  2332769.12,  3508360.80,  4922918.05,      49.629164,       -3.197294,  113806.09,  205848.37,       0.00,              406.33, -5136.08,      0.00,           65206.41,   -267.58,   -189.35,         328.46,  +4.24,  +2.67
  1,     UK000H,       1,  0.131977, 2459486.642946520820,  26.96312,  -0.76488,              217.23706,  32.11504,       217.32364,       32.13777,     26.96312,      -0.76488,      26.90461,       -0.71584,  2332955.41,  3506700.31,  4921041.54,      49.627037,       -3.212081,  111547.64,  205278.06,    2512.61,             2918.95, -5332.91,  61984.76,           65206.41,   -224.44,   -158.92,         276.33,  +2.01,  +0.45
  2,     UK000H,       1,  0.172557, 2459486.642946990672,  26.47580,  -1.33232,              217.51059,  31.40420,       217.58564,       31.42388,     26.47580,      -1.33232,      26.42496,       -1.28950,  2333158.11,  3504893.61,  4918999.81,      49.624719,       -3.228165,  109090.53,  204690.36,    5246.46,             5652.79, -5311.46,  67369.19,           65206.41,   -195.35,   -138.39,         241.24,  +1.14,  -0.42
  3,     UK000H,       1,  0.213125, 2459486.642947460059,  25.99501,  -1.88387,              217.77986,  30.70995,       217.83812,       30.72522,     25.99501,      -1.88387,      25.95561,       -1.85040,  2333355.25,  3503136.49,  4917014.09,      49.622461,       -3.243822,  106701.04,  204152.58,    7905.29,             8311.62, -5364.22,  65540.18,           65206.41,   -152.20,   -107.89,         188.50,  +0.64,  -0.91
  4,     UK000H,       1,  0.253729, 2459486.642947929911,  25.49920,  -2.47852,              218.04149,  29.96962,       218.10122,       29.98527,     25.49920,      -2.47852,      25.45866,       -2.44395,  2333562.82,  3501286.40,  4914923.31,      49.620079,       -3.260310,  104185.34,  203622.13,   10704.80,            11111.14, -5278.70,  68946.74,           66060.69,   -156.73,   -111.11,         194.61,  +0.58,  -0.96
  0,     UK002D,       1,  0.000000, 2459486.642944993451,  32.83020,  -8.12953,              207.87501,  26.75302,       207.80800,       26.73103,     32.83020,      -8.12953,      32.88142,       -8.16818,  2332727.80,  3508729.05,  4923334.21,      49.629636,       -3.193671,  114307.01,  245604.48,       0.00,              150.90,   720.45,      0.00,           62373.26,    245.77,    119.56,         229.53,  +5.34,  +3.39
  1,     UK002D,       1,  0.040488, 2459486.642945461906,  32.45857,  -8.67251,              208.08756,  26.12551,       208.06186,       26.11708,     32.45857,      -8.67251,      32.47849,       -8.68742,  2332938.70,  3506849.24,  4921209.85,      49.627228,       -3.210387,  111750.27,  245092.33,    2844.48,             2693.58,   556.89,  70254.99,           62373.26,     94.53,     45.91,          88.44,  +5.33,  +3.38
  2,     UK002D,       0,  0.080864, 2459486.642945929430,  32.17566,  -9.09139,              208.24516,  25.64231,       208.25546,       25.64569,     32.17566,      -9.09139,      32.16805,       -9.08539,  2333099.91,  3505412.42,  4919586.10,      49.625385,       -3.223211,  109796.18,  244723.68,    5018.65,             4867.75,    32.30,  53848.04,           62373.26,    -37.96,    -18.41,          35.56,  +1.96,  +0.02
  3,     UK002D,       0,  0.121296, 2459486.642946397420,  31.78632,  -9.57416,              208.48997,  25.06636,       208.49051,       25.06654,     31.78632,      -9.57416,      31.78641,       -9.57384,  2333297.24,  3503653.53,  4917598.39,      49.623126,       -3.238880,  107404.25,  244296.97,    7680.16,             7529.26,    -8.69,  65826.86,           62373.26,     -1.99,     -0.97,           1.87,  +1.12,  -0.82
  4,     UK002D,       0,  0.161748, 2459486.642946865410,  31.38778, -10.07562,              208.73442,  24.46936,       208.73080,       24.46817,     31.38778,     -10.07562,      31.39127,      -10.07775,  2333500.30,  3501843.61,  4915553.02,      49.620797,       -3.255010,  104943.15,  243887.38,   10418.88,            10267.98,    26.19,  67702.82,           63501.19,     13.40,      6.51,          12.60,  +0.48,  -1.46
  5,     UK002D,       0,  0.202204, 2459486.642947333865,  30.98545, -10.57908,              208.97833,  23.86884,       208.97011,       23.86615,     30.98545,     -10.57908,      30.99272,      -10.58395,  2333703.82,  3500029.65,  4913503.07,      49.618459,       -3.271186,  102476.75,  243507.18,   13163.72,            13012.82,    66.93,  67847.61,           64444.70,     30.52,     14.82,          28.74,  +0.46,  -1.47
  6,     UK002D,       0,  0.242632, 2459486.642947801854,  30.57836, -11.05344,              209.23315,  23.29407,       209.19971,       23.28314,     30.57836,     -11.05344,      30.60566,      -11.07337,  2333900.20,  3498279.24,  4911524.93,      49.616199,       -3.286811,  100096.94,  243169.40,   15812.40,            15661.50,    13.38,  65516.04,           64896.31,    124.45,     60.49,         117.37,  +0.76,  -1.17
  7,     UK002D,       0,  0.283032, 2459486.642948269378,  30.21170, -11.49535,              209.45450,  22.76201,       209.40910,       22.74718,     30.21170,     -11.49535,      30.24872,      -11.52255,  2334080.16,  3496675.24,  4909712.27,      49.614125,       -3.301152,   97916.36,  242885.35,   18239.53,            18088.63,  -259.85,  60077.47,           64683.27,    169.32,     82.34,         159.89,  +0.61,  -1.32
  8,     UK002D,       0,  0.323508, 2459486.642948737834,  29.76160, -12.02098,              209.72785,  22.12433,       209.65847,       22.10168,     29.76160,     -12.02098,      29.81797,      -12.06279,  2334296.28,  3494748.88,  4907535.29,      49.611630,       -3.318352,   95297.77,  242574.93,   21154.46,            21003.56,   -50.36,  72016.17,           65073.22,    259.39,    126.30,         245.32,  +0.75,  -1.17
  9,     UK002D,       0,  0.363856, 2459486.642949204892,  29.41522, -12.40092,              209.94359,  21.65648,       209.84233,       21.62344,     29.41522,     -12.40092,      29.49732,      -12.46223,  2334455.94,  3493325.83,  4905927.11,      49.609784,       -3.331110,   93363.48,  242369.34,   23307.78,            23156.88,  -593.92,  53368.80,           64634.73,    379.29,    184.95,         359.12,  +3.15,  +1.23
  0,     UK003E,       0,  0.092500, 2459486.642946062144,  32.12797,  -9.27224,              208.23492,  25.45566,       208.32083,       25.48383,     32.12797,      -9.27224,      32.06195,       -9.22212,  2333155.06,  3504920.79,  4919030.51,      49.624754,       -3.227590,  109127.59,  244601.20,       0.00,             5611.67,    -1.52,      0.00,           66228.89,   -317.14,   -153.29,         297.04,  +1.17,  -0.77
  1,     UK003E,       0,  0.133064, 2459486.642946531996,  31.71624,  -9.75778,              208.50137,  24.87044,       208.56107,       24.89000,     31.71624,      -9.75778,      31.67043,       -9.72275,  2333357.16,  3503119.43,  4916994.81,      49.622439,       -3.243638,  106677.98,  244172.55,    2725.76,             8337.43,    12.93,  67196.62,           66228.89,   -220.88,   -106.89,         207.29,  +0.36,  -1.58
  2,     UK003E,       0,  0.173628, 2459486.642947001383,  31.32131, -10.24835,              208.74495,  24.28490,       208.79663,       24.30183,     31.32131,     -10.24835,      31.28170,      -10.21784,  2333556.54,  3501342.39,  4914986.59,      49.620152,       -3.259481,  104261.63,  243778.98,    5414.74,            11026.41,    -9.42,  66289.73,           66228.89,   -191.69,    -92.81,         180.20,  -0.22,  -2.15
  3,     UK003E,       0,  0.214188, 2459486.642947470769,  30.92959, -10.73092,              208.98428,  23.70748,       209.02686,       23.72141,     30.92959,     -10.73092,      30.89711,      -10.70565,  2333752.55,  3499595.28,  4913012.18,      49.617899,       -3.275070,  101886.16,  243420.57,    8058.44,            13670.11,   -76.78,  65179.90,           66228.89,   -158.30,    -76.68,         149.04,  +0.02,  -1.91
  4,     UK003E,       0,  0.254776, 2459486.642947940622,  30.51147, -11.23927,              209.23812,  23.09705,       209.26813,       23.10686,     30.51147,     -11.23927,      30.48891,      -11.22136,  2333959.38,  3497751.77,  4910928.85,      49.615517,       -3.291521,   99379.86,  243072.81,   10847.98,            16459.65,    -0.16,  68728.28,           66626.21,   -111.81,    -54.20,         105.44,  +0.09,  -1.84
  5,     UK003E,       0,  0.295352, 2459486.642948410008,  30.08659, -11.72562,              209.50227,  22.50492,       209.50223,       22.50491,     30.08659,     -11.72562,      30.08786,      -11.72564,  2334161.30,  3495952.05,  4908894.99,      49.613189,       -3.307595,   96933.27,  242763.98,   13571.28,            19182.95,    11.02,  67116.05,           66809.69,      0.13,      0.06,           0.13,  +0.32,  -1.61
  6,     UK003E,       0,  0.335868, 2459486.642948878929,  29.73613, -12.17915,              209.69928,  21.96641,       209.70890,       21.96956,     29.73613,     -12.17915,      29.72989,      -12.17334,  2334340.35,  3494356.12,  4907091.44,      49.611120,       -3.321877,   94763.90,  242516.06,   15986.20,            21597.87,  -282.18,  59603.95,           66104.25,    -36.05,    -17.49,          34.08,  +0.79,  -1.13
  0,     UK003N,       0,  0.070782, 2459486.642945816275,  11.54216,  -5.74624,              231.68417,  19.86532,       231.68891,       19.86625,     11.54216,      -5.74624,      11.53903,       -5.74322,  2333088.82,  3505511.22,  4919697.76,      49.625512,       -3.222299,  109930.55,  304579.03,       0.00,             4718.24,   556.67,      0.00,           62786.58,    -17.47,    -16.75,          16.39,  +3.86,  +1.44
  1,     UK003N,       0,  0.111050, 2459486.642946282402,  11.29941,  -6.00744,              231.77007,  19.51891,       231.76809,       19.51852,     11.29941,      -6.00744,      11.30131,       -6.00870,  2333228.65,  3504264.93,  4918289.33,      49.623912,       -3.233449,  108235.68,  304622.76,    1885.86,             6604.10,  -249.01,  46832.68,           62786.58,      7.32,      7.02,           6.87,  +1.83,  -0.59
  2,     UK003N,       0,  0.151486, 2459486.642946750391,  10.90822,  -6.43178,              231.90534,  18.95767,       231.89464,       18.95556,     10.90822,      -6.43178,      10.91664,       -6.43864,  2333455.25,  3502245.21,  4916006.86,      49.621314,       -3.251426,  105489.22,  304713.13,    4942.05,             9660.29,   104.42,  75580.87,           62786.58,     39.65,     38.05,          37.20,  +0.90,  -1.52
  3,     UK003N,       0,  0.191838, 2459486.642947217450,  10.59666,  -6.78276,              232.00508,  18.49936,       231.99717,       18.49780,     10.59666,      -6.78276,      10.60323,       -6.78784,  2333639.54,  3500602.55,  4914150.50,      49.619198,       -3.266087,  103255.68,  304810.89,    7427.68,            12145.92,  -107.10,  61598.69,           62786.58,     29.39,     28.20,          27.56,  +0.73,  -1.69
  4,     UK003N,       0,  0.232254, 2459486.642947685439,  10.23330,  -7.19142,              232.12042,  17.96543,       232.11568,       17.96449,     10.23330,      -7.19142,      10.23774,       -7.19448,  2333854.43,  3498687.20,  4911985.97,      49.616726,       -3.283166,  100651.58,  304949.08,   10325.94,            15044.18,    89.73,  71710.73,           64881.68,     17.68,     16.96,          16.57,  +0.87,  -1.55
  5,     UK003N,       0,  0.272618, 2459486.642948152497,   9.91085,  -7.55471,              232.22125,  17.49108,       232.22047,       17.49092,      9.91085,      -7.55471,       9.91256,       -7.55521,  2334045.38,  3496985.25,  4910062.61,      49.614526,       -3.298370,   98337.81,  305095.97,   12901.29,            17619.53,   -32.88,  63803.16,           65325.68,      2.92,      2.80,           2.73,  +1.02,  -1.40
  6,     UK003N,       0,  0.313006, 2459486.642948620021,   9.57221,  -7.94159,              232.32311,  16.98828,       232.33066,       16.98978,      9.57221,      -7.94159,       9.56796,       -7.93668,  2334247.65,  3495182.35,  4908025.16,      49.612192,       -3.314476,   95886.99,  305274.75,   15629.39,            20347.64,    -4.33,  67547.45,           65722.35,    -28.35,    -27.19,          26.54,  +1.00,  -1.42
  7,     UK003N,       1,  0.353214, 2459486.642949085217,   9.38659,  -8.14792,              232.38140,  16.71765,       232.39050,       16.71945,      9.38659,      -8.14792,       9.38136,       -8.14200,  2334356.74,  3494209.98,  4906926.29,      49.610931,       -3.323244,   94565.21,  305385.33,   17100.76,            21819.00, -1220.49,  36593.83,           63471.17,    -34.22,    -32.82,          32.03,  +4.69,  +2.27

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.