Orbital Analysis for matched events on 20210929_205812.195_UK

Summary for Event
-----------------
shower ID -1 spo
Lg 84.61° Bg 12.80° Vg 67.97km/s
mass 0.02133g, abs. mag 0.2
Path Details
------------
start -2.18° 51.28° 113.89km
end   -2.63° 50.99° 104.71km

Orbit Details
-------------
Semimajor axis 8.15A.U., eccentricity 0.89, inclination 156.77°, Period 23.25Y, LA Sun 186.63°, last Perihelion 1998-07-28

Full details below
Click here to download a zip of the raw and processed data.

Detailed report below graphs

Click on an image to see a larger view


Input measurement type: Azimuth +east of due north for meas1, Elevation angle above the horizon for meas2

Uncertainties type:
 Purely geometric uncertainties

Reference JD: 2459487.373752264772
Time: 2021-09-29 20:58:12.236272 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK0006 and UK003Z
 Convergence angle = 24.66997 deg
 R.A. =  83.30351  Dec = +36.36161 deg

Best intersection: Stations UK0006 and UK003Z with Qconv = 24.67 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   3171550.92 +/- 16.38 m
 Y =  -2547036.38 +/- 46.89 m
 Z =   5043734.93 +/- 87.94 m
 Vx =     6310.76 +/- 39.93 m/s
 Vy =    54892.68 +/- 157.55 m/s
 Vz =    41110.38 +/- 197.87 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+2.856497e+02, -6.516761e+02, +1.263890e+03, +6.724580e+02, -1.890332e+03, +2.898929e+03
-6.516761e+02, +2.346433e+03, -4.223312e+03, -1.540063e+03, +5.872975e+03, -9.406492e+03
+1.263890e+03, -4.223312e+03, +8.258750e+03, +3.014612e+03, -1.136456e+04, +1.810167e+04
+6.724580e+02, -1.540063e+03, +3.014612e+03, +1.637969e+03, -4.674703e+03, +7.066640e+03
-1.890332e+03, +5.872975e+03, -1.136456e+04, -4.674703e+03, +1.703765e+04, -2.626087e+04
+2.898929e+03, -9.406492e+03, +1.810167e+04, +7.066640e+03, -2.626087e+04, +4.103012e+04

Timing offsets (from input data):
    UK0006: -0.000030 s
    UK003Z: 0.000000 s

Reference point on the trajectory:
  Time: 2021-09-29 20:58:12.236272 UTC
  Lon     = +-2.154965 +/- 0.0004 deg
  Lat     = +51.298975 +/- 0.0002 deg
  Lat geo = +51.114366 +/- 0.0002 deg
  Ht      =  114410.15 +/- 93.09 m

  JD dynamic   = 2459487.374553475529 
  LST apparent = 321.2324495697 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  83.44176 +/- 0.0536 deg
  Dec       = +36.65006 +/- 0.1909 deg
  Azimuth   =  43.83678 +/- 0.0722 deg
  Elevation = +11.44756 +/- 0.1826 deg
  Vavg      =  68.02466 +/- 0.0857 km/s
  Vinit     =  68.87014 +/- 0.0216 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  83.27856 +/- 0.0536 deg
  Dec       = +36.52568 +/- 0.1909 deg
  Azimuth   =  44.01784 +/- 0.0722 deg
  Elevation = +11.41369 +/- 0.1826 deg
  Vavg      =  68.22635 +/- 0.0857 km/s
  Vinit     =  69.07184 +/- 0.0216 km/s
Radiant (geocentric, J2000):
  R.A.   =  83.48923 +/- 0.0542 deg
  Dec    = +36.11723 +/- 0.1930 deg
  Vg     =  67.97108 +/- 0.0219 km/s
  Vinf   =  68.87014 +/- 0.0216 km/s
  Zc     =  78.68563 +/- 0.1824 deg
  Zg     =  79.30279 +/- 0.1848 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  84.61011 +/- 0.0368 deg
  Bg     = +12.80127 +/- 0.1947 deg
  Vh     =  40.77396 +/- 0.0606 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  74.47543 +/- 0.0714 deg
  Bh     = +21.67955 +/- 0.3141 deg
  Vh_x   = -10.14127 +/- 0.0397 km/s
  Vh_y   = -36.50741 +/- 0.0371 km/s
  Vh_z   = -15.06251 +/- 0.2295 km/s
Orbit:
  La Sun = 186.634311 +/- 0.0000 deg
  a      =   8.146981 +/- 0.3162 AU
  e      =   0.893074 +/- 0.0048
  i      = 156.769726 +/- 0.3412 deg
  peri   = 223.622312 +/- 0.1214 deg
  node   = 186.630509 +/- 0.0001 deg
  Pi     =  50.252822 +/- 0.1213 deg
  q      =   0.871126 +/- 0.0004 AU
  f      = 316.373840 +/- 0.1214 deg
  M      = 358.779911 +/- 0.0916 deg
  Q      =  15.422837 +/- 0.6322 AU
  n      =   0.042385 +/- 0.0030 deg/day
  T      =  23.253896 +/- 1.3045 years
  Last perihelion JD = 2451022.527256 (1998-07-28 00:39:14.953471) +/- 476.5816 days
  Tj     =  -0.395763 +/- 0.0278
Shower association:
  IAU No.  =   -1
  IAU code =  ...

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +2.463951e-05, +1.119856e-06, -2.441799e+00, +5.402046e-09, -9.383859e-06, -3.007377e-05
q   , +1.119856e-06, +1.817667e-07, -1.133411e-01, +2.254918e-10, -8.285909e-07, -1.261994e-06
Tp  , -2.441799e+00, -1.133411e-01, +2.428680e+05, -5.353814e-04, +9.369718e-01, +2.983343e+00
node, +5.402046e-09, +2.254918e-10, -5.353814e-04, +1.223826e-12, -1.995685e-09, -6.814531e-09
peri, -9.383859e-06, -8.285909e-07, +9.369718e-01, -1.995685e-09, +4.809323e-06, +1.112988e-05
i   , -3.007377e-05, -1.261994e-06, +2.983343e+00, -6.814531e-09, +1.112988e-05, +3.795446e-05

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 0.000000
 a2 = 0.000000

Mean time residuals from time vs. length:
  Station with reference time: UK003Z
  Avg. res. = 5.778e-06 s
  Stddev    = 2.40e-03 s

Begin point on the trajectory:
  Lon =    -2.180222 +/- 0.0004 deg
  Lat =    51.282477 +/- 0.0002 deg
  Ht  = 113886.22 +/- 84.33 m
End point on the trajectory:
  Lon =    -2.631132 +/- 0.0006 deg
  Lat =    50.986930 +/- 0.0001 deg
  Ht  = 104714.54 +/- 66.90 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
    UK0006,   False,    -1.306160,    51.883100,   80.00,   0.000000,   0.000000,   111622.57,   105190.52,          0.015813,     38.23,     25.12,             116.33, 1.0000,    True,    True, {"ff_name": "FF_UK0006_20210929_205812_412_0220928.fits"}
    UK003Z,   False,    -1.639327,    51.011519,   64.00,   0.000000,  53.263379,   113886.22,   104714.54,          0.005794,      6.76,     10.53,              80.95, 1.0000,    True,    True, {"ff_name": "FF_UK003Z_20210929_205811_432_0235776.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,     UK0006,       0,  0.205743, 2459487.373754646163, 293.40205,  15.49334,              222.75145,  47.05653,       222.77277,       47.05704,    293.40205,     +15.49334,     293.38956,      +15.50011,  3170257.31, -2558288.53,  5035307.94,      51.210732,       -2.290440,  111622.57,  151258.40,       0.00,            14117.31,   189.69,      0.00,           65854.83,     21.02,    -32.09,          52.31,  +1.85,  +0.95
  1,     UK0006,       0,  0.246531, 2459487.373755118344, 292.95381,  14.69637,              222.81513,  46.15070,       222.82259,       46.15087,    292.95381,     +14.69637,     292.95010,      +14.69877,  3170000.46, -2560522.71,  5033634.70,      51.193183,       -2.317325,  111072.53,  152713.50,    2803.09,            16920.39,   183.70,  68723.29,           65854.83,      7.55,    -11.52,          18.61,  +2.01,  +1.09
  2,     UK0006,       0,  0.287247, 2459487.373755589593, 292.54121,  13.97826,              222.88551,  45.33030,       222.86668,       45.32986,    292.54121,     +13.97826,     292.55452,      +13.97214,  3169763.44, -2562584.39,  5032090.67,      51.176982,       -2.342133,  110565.98,  154089.96,    5389.74,            19507.04,   -33.77,  63529.08,           65854.83,    -19.54,     29.78,          47.68,  +1.92,  +0.98
  3,     UK0006,       0,  0.327971, 2459487.373756060842, 292.16610,  13.22213,              222.88829,  44.49086,       222.91023,       44.49137,    292.16610,     +13.22213,     292.15320,      +13.22935,  3169516.84, -2564729.31,  5030484.29,      51.160117,       -2.367922,  110040.01,  155554.77,    8080.82,            22198.13,  -147.35,  66081.03,           65854.83,     23.31,    -35.57,          56.39,  +1.98,  +1.02
  4,     UK0006,       0,  0.368659, 2459487.373756532092, 291.78037,  12.52647,              222.94309,  43.70105,       222.95033,       43.70122,    291.78037,     +12.52647,     291.77715,      +12.52888,  3169280.12, -2566788.40,  5028942.19,      51.143920,       -2.392672,  109536.08,  156991.98,   10664.22,            24781.52,  -366.14,  63492.85,           65328.11,      7.87,    -12.00,          18.85,  +2.44,  +1.46
  5,     UK0006,       0,  0.409527, 2459487.373757005204, 291.31461,  11.64115,              222.98457,  42.70592,       222.99812,       42.70623,    291.31461,     +11.64115,     291.30728,      +11.64572,  3168975.48, -2569438.19,  5026957.70,      51.123065,       -2.424454,  108889.06,  158882.93,   13988.74,            28106.04,   143.79,  81347.75,           67474.19,     15.15,    -23.10,          35.86,  +2.11,  +1.10
  6,     UK0006,       0,  0.450299, 2459487.373757476918, 290.89436,  10.85532,              223.03175,  41.81924,       223.03981,       41.81942,    290.89436,     +10.85532,     290.89080,      +10.85807,  3168697.70, -2571854.41,  5025148.14,      51.104037,       -2.453430,  108300.47,  160648.55,   17020.20,            31137.51,   367.29,  74351.70,           68977.23,      9.24,    -14.09,          21.64,  +2.63,  +1.60
  7,     UK0006,       0,  0.490895, 2459487.373757946771, 290.56875,  10.25048,              223.07172,  41.13557,       223.07205,       41.13558,    290.56875,     +10.25048,     290.57058,      +10.25059,  3168479.34, -2573753.81,  5023725.63,      51.089071,       -2.476231,  107838.68,  162064.25,   19403.25,            33520.56,   -45.52,  58701.53,           68750.03,      0.39,     -0.59,           0.90,  +1.77,  +0.72
  8,     UK0006,       0,  0.531607, 2459487.373758418020, 290.19030,   9.51933,              223.10340,  40.31519,       223.10896,       40.31532,    290.19030,      +9.51933,     290.18868,       +9.52126,  3168212.11, -2576078.28,  5021984.79,      51.070748,       -2.504081,  107274.72,  163826.30,   22319.60,            36436.90,    66.98,  71633.56,           68835.97,      6.66,    -10.15,          15.28,  +1.55,  +0.48
  9,     UK0006,       0,  0.572291, 2459487.373758888803, 289.80665,   8.83186,              223.16661,  39.53181,       223.14351,       39.53129,    289.80665,      +8.83186,     289.82512,       +8.82378,  3167951.15, -2578348.14,  5020284.83,      51.052845,       -2.531265,  106725.21,  165578.83,   25167.45,            39284.75,   112.92,  69999.25,           68943.10,    -28.29,     43.06,          64.18,  +1.89,  +0.79
 10,     UK0006,       0,  0.612971, 2459487.373759359587, 289.44543,   8.13574,              223.19979,  38.74978,       223.17713,       38.74927,    289.44543,      +8.13574,     289.46392,       +8.12774,  3167685.19, -2580661.56,  5018552.27,      51.034590,       -2.558950,  106166.37,  167396.12,   28069.93,            42187.24,   213.77,  71349.17,           69110.75,    -28.37,     43.18,          63.66,  +2.63,  +1.51
 11,     UK0006,       0,  0.653547, 2459487.373759829439, 289.13911,   7.54293,              223.22728,  38.08416,       223.20566,       38.08368,    289.13911,      +7.54293,     289.15715,       +7.53523,  3167454.22, -2582670.56,  5017047.68,      51.018728,       -2.583000,  105682.04,  168999.89,   30590.49,            44707.80,   -60.15,  62119.51,           68939.72,    -27.57,     41.96,          61.28,  +2.51,  +1.37
 12,     UK0006,       0,  0.694127, 2459487.373760298826, 288.81446,   6.96148,              223.28214,  37.42090,       223.23355,       37.41983,    288.81446,      +6.96148,     288.85208,       +6.94406,  3167219.37, -2584713.35,  5015517.78,      51.002593,       -2.607439,  105190.52,  170653.47,   33153.44,            47270.75,  -291.94,  63158.03,           68646.46,    -63.21,     96.08,         139.00,  +2.60,  +1.44
  0,     UK003Z,       1,  0.000000, 2459487.373752264772, 283.59191,  61.57689,              311.74421,  66.78894,       311.75810,       66.74271,    283.59191,     +61.57689,     283.49798,      +61.58990,  3171550.20, -2547042.63,  5043730.24,      51.298926,       -2.154870,  114408.59,  124257.87,       0.00,                7.85,   249.80,      0.00,           64115.23,     84.90,    -54.65,         167.60,  +4.43,  +3.96
  1,     UK003Z,       0,  0.040600, 2459487.373752734624, 282.81886,  60.42979,              308.74453,  66.57319,       308.74652,       66.56848,    282.81886,     +60.42979,     282.80970,      +60.43107,  3171308.81, -2549142.31,  5042157.75,      51.282477,       -2.180222,  113886.22,  123850.26,    2634.32,             2642.17,    88.00,  64884.74,           64115.23,      8.70,     -5.59,          17.22,  +4.31,  +3.85
  2,     UK003Z,       0,  0.081208, 2459487.373753204476, 282.12874,  59.22625,              305.67506,  66.31908,       305.67050,       66.32745,    282.12874,     +59.22625,     282.14524,      +59.22403,  3171059.64, -2551309.65,  5040534.58,      51.265490,       -2.206370,  113348.07,  123487.30,    5353.53,             5361.38,    10.53,  66962.44,           64115.23,    -15.53,      9.97,          30.82,  +2.32,  +1.86
  3,     UK003Z,       0,  0.121736, 2459487.373753673863, 281.60325,  58.14256,              302.97638,  66.06886,       302.98104,       66.06172,    281.60325,     +58.14256,     281.59021,      +58.14442,  3170838.53, -2553232.89,  5039094.22,      51.250409,       -2.229579,  112871.43,  123215.31,    7766.50,             7774.35,  -367.67,  59538.32,           64115.23,     13.37,     -8.59,          26.61,  +1.80,  +1.35
  4,     UK003Z,       0,  0.162460, 2459487.373754145112, 280.90880,  56.71571,              299.52382,  65.64240,       299.52401,       65.64216,    280.90880,     +56.71571,     280.90902,      +56.71577,  3170547.79, -2555761.85,  5037200.22,      51.230567,       -2.260028,  112245.98,  122928.02,   10939.42,            10947.26,     0.58,  77912.71,           66522.18,      0.47,     -0.30,           0.93,  +1.54,  +1.09
  5,     UK003Z,       0,  0.203100, 2459487.373754615430, 280.35003,  55.46294,              296.59765,  65.21091,       296.59648,       65.21222,    280.35003,     +55.46294,     280.35326,      +55.46261,  3170294.38, -2557966.07,  5035549.44,      51.213264,       -2.286572,  111702.04,  122744.88,   13704.89,            13712.74,   -32.83,  68048.15,           67426.93,     -2.51,      1.61,           5.02,  +1.29,  +0.84
  6,     UK003Z,       0,  0.243808, 2459487.373755086679, 279.78987,  54.06407,              293.44904,  64.67818,       293.45746,       64.66989,    279.78987,     +54.06407,     279.77589,      +54.06611,  3170013.20, -2560411.84,  5033717.74,      51.194055,       -2.315988,  111099.80,  122614.29,   16773.44,            16781.28,   232.15,  75379.32,           68603.95,     16.27,    -10.45,          32.54,  +1.32,  +0.88
  7,     UK003Z,       0,  0.284376, 2459487.373755556066, 279.34544,  52.98163,              291.11554,  64.20073,       291.11177,       64.20416,    279.34544,     +52.98163,     279.35278,      +52.98080,  3169795.49, -2562305.60,  5032299.46,      51.179173,       -2.338790,  110634.41,  122567.18,   19149.41,            19157.26,  -185.80,  58567.75,           68258.71,     -6.84,      4.39,          13.68,  +1.38,  +0.94
  8,     UK003Z,       0,  0.325072, 2459487.373756027315, 278.86633,  51.63713,              288.31978,  63.58406,       288.32504,       63.57967,    278.86633,     +51.63713,     278.85986,      +51.63819,  3169526.51, -2564645.25,  5030547.25,      51.160778,       -2.366906,  110060.61,  122571.86,   22084.81,            22092.66,   -53.14,  72129.84,           68356.10,      8.95,     -5.75,          17.91,  +1.33,  +0.89
  9,     UK003Z,       0,  0.365760, 2459487.373756498098, 278.40195,  50.32735,              285.72936,  62.91917,       285.72726,       62.92080,    278.40195,     +50.32735,     278.40637,      +50.32696,  3169264.04, -2566928.28,  5028837.43,      51.142819,       -2.394329,  109501.90,  122644.65,   24949.17,            24957.02,     9.03,  70398.27,           68517.23,     -3.40,      2.18,           6.80,  +1.33,  +0.89
 10,     UK003Z,       0,  0.406440, 2459487.373756968882, 277.97838,  49.05046,              283.31913,  62.23106,       283.31273,       62.23573,    277.97838,     +49.05046,     277.98835,      +49.04934,  3169008.20, -2569153.66,  5027170.79,      51.125305,       -2.421047,  108958.45,  122780.38,   27741.21,            27749.06,    -0.57,  68634.10,           68610.40,     -9.99,      6.41,          19.94,  +1.43,  +0.98
 11,     UK003Z,       0,  0.447120, 2459487.373757439665, 277.59038,  47.76054,              280.98918,  61.50735,       280.99221,       61.50526,    277.59038,     +47.76054,     277.58855,      +47.76104,  3168749.79, -2571401.34,  5025487.45,      51.107605,       -2.448016,  108410.72,  122981.99,   30561.22,            30569.07,    17.81,  69321.93,           68691.53,      4.58,     -2.94,           9.14,  +1.55,  +1.10
 12,     UK003Z,       0,  0.487772, 2459487.373757910449, 277.22690,  46.53937,              278.89388,  60.77936,       278.89513,       60.77853,    277.22690,     +46.53937,     277.22747,      +46.53957,  3168504.16, -2573537.93,  5023887.31,      51.090772,       -2.473646,  107891.12,  123233.78,   33241.86,            33249.71,  -101.26,  65941.00,           68649.85,      1.86,     -1.20,           3.70,  +1.69,  +1.24
 13,     UK003Z,       0,  0.528480, 2459487.373758381233, 276.86617,  45.20711,              276.70697,  59.96123,       276.72060,       59.95259,    276.86617,     +45.20711,     276.85303,      +45.20917,  3168235.53, -2575874.55,  5022137.37,      51.072354,       -2.501642,  107324.10,  123575.00,   36173.45,            36181.30,    26.76,  72015.19,           68719.97,     19.98,    -12.82,          39.63,  +1.34,  +0.88
 14,     UK003Z,       0,  0.569208, 2459487.373758852948, 276.49216,  43.87912,              274.65730,  59.09265,       274.65590,       59.09351,    276.49216,     +43.87912,     276.49607,      +43.87891,  3167965.52, -2578223.18,  5020378.42,      51.053831,       -2.529765,  106755.43,  123987.25,   39120.12,            39127.97,   168.49,  72349.95,           68856.47,     -2.04,      1.31,           4.04,  +1.37,  +0.90
 15,     UK003Z,       0,  0.609944, 2459487.373759324197, 276.14027,  42.54187,              272.69329,  58.19280,       272.68365,       58.19848,    276.14027,     +42.54187,     276.15300,      +42.54051,  3167692.08, -2580601.56,  5018597.20,      51.035063,       -2.558223,  106180.86,  124474.74,   42104.11,            42111.96,   346.99,  73251.90,           69044.97,    -13.94,      8.94,          27.44,  +1.64,  +1.16
 16,     UK003Z,       0,  0.650528, 2459487.373759794049, 275.88996,  41.45354,              271.14999,  57.45540,       271.15774,       57.45095,    275.88996,     +41.45354,     275.88467,      +41.45462,  3167468.80, -2582543.73,  5017142.66,      51.019730,       -2.581480,  105712.59,  124925.69,   44540.82,            44548.67,   -11.33,  60041.22,           68998.03,     11.20,     -7.18,          21.97,  +1.98,  +1.50
 17,     UK003Z,       0,  0.691192, 2459487.373760264833, 275.60288,  40.23613,              269.51085,  56.59891,       269.52135,       56.59302,    275.60288,     +40.23613,     275.59512,      +40.23756,  3167216.59, -2584737.53,  5015499.68,      51.002402,       -2.607714,  105184.73,  125489.59,   47293.23,            47301.08,   -59.45,  67686.69,           68942.09,     15.22,     -9.76,          29.71,  +1.72,  +1.23
 18,     UK003Z,       0,  0.731792, 2459487.373760734685, 275.34616,  39.15989,              268.13317,  55.81770,       268.13534,       55.81650,    275.34616,     +39.15989,     275.34705,      +39.16018,  3166991.50, -2586695.41,  5014033.37,      50.986930,       -2.631132,  104714.54,  126042.47,   49749.66,            49757.51,  -399.16,  60503.05,           68769.03,      3.16,     -2.03,           6.15,  +3.26,  +2.76

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.