Nutations - Computed From Both IAU 1980 Series and Series 2000B
Date:   ±Y  M  D Time UT:   H M S ΔT:   ± H M S
Calendar Mode:   Julian            Gregorian

RAW DATA FOR THE IAU NUTATION SERIES 2000B (77 TERMS)

WITH FORMULAS FOR APPLICATION

In the nutation data table below, each data line represents one term in the
respective summation series.


******************************************************************************
NUTATION DATA TABLE FOR IAU NUTATION SERIES 2000B

The i column is NOT part of the actual data.  It is simply the reference index
number of the series terms to which the subsequent 11 data elements apply.

   ARGUMENT MULTIPLIERS       LONGITUDE COMPONENTS     OBLIQUITY COMPONENTS
    L   Lp  F   D   Om         ARC SEC * 10000000       ARC SEC * 10000000
i   m1  m2  m3  m4  m5        AA        BB      CC      DD       EE     FF
1    0   0   0   0   1   -172064161  -174666  33386  92052331   9086   15377
2    0   0   2  -2   2    -13170906    -1675  13696   5730336  -3015   -4587
3    0   0   2   0   2     -2276413     -234   2796    978459   -485    1374
4    0   0   0   0   2      2074554      207   -698   -897492    470    -291
5    0   1   0   0   0      1475877    -3633  11817     73871   -184   -1924
6    0   1   2  -2   2      -516821     1226   -524    224386   -677    -174
7    1   0   0   0   0       711159       73   -872     -6750      0     358
8    0   0   2   0   1      -387298     -367    380    200728     18     318
9    1   0   2   0   2      -301461      -36    816    129025    -63     367
10   0  -1   2  -2   2       215829     -494    111    -95929    299     132
11   0   0   2  -2   1       128227      137    181    -68982     -9      39
12  -1   0   2   0   2       123457       11     19    -53311     32      -4
13  -1   0   0   2   0       156994       10   -168     -1235      0      82
14   1   0   0   0   1        63110       63     27    -33228      0      -9
15  -1   0   0   0   1       -57976      -63   -189     31429      0     -75
16  -1   0   2   2   2       -59641      -11    149     25543    -11      66
17   1   0   2   0   1       -51613      -42    129     26366      0      78
18  -2   0   2   0   1        45893       50     31    -24236    -10      20
19   0   0   0   2   0        63384       11   -150     -1220      0      29
20   0   0   2   2   2       -38571       -1    158     16452    -11      68
21   0  -2   2  -2   2        32481        0      0    -13870      0       0
22  -2   0   0   2   0       -47722        0    -18       477      0     -25
23   2   0   2   0   2       -31046       -1    131     13238    -11      59
24   1   0   2  -2   2        28593        0     -1    -12338     10      -3
25  -1   0   2   0   1        20441       21     10    -10758      0      -3
26   2   0   0   0   0        29243        0    -74      -609      0      13
27   0   0   2   0   0        25887        0    -66      -550      0      11
28   0   1   0   0   1       -14053      -25     79      8551     -2     -45
29  -1   0   0   2   1        15164       10     11     -8001      0      -1
30   0   2   2  -2   2       -15794       72    -16      6850    -42      -5
31   0   0  -2   2   0        21783        0     13      -167      0      13
32   1   0   0  -2   1       -12873      -10    -37      6953      0     -14
33   0  -1   0   0   1       -12654       11     63      6415      0      26
34  -1   0   2   2   1       -10204        0     25      5222      0      15
35   0   2   0   0   0        16707      -85    -10       168     -1      10
36   1   0   2   2   2        -7691        0     44      3268      0      19
37  -2   0   2   0   0       -11024        0    -14       104      0       2
38   0   1   2   0   2         7566      -21    -11     -3250      0      -5
39   0   0   2   2   1        -6637      -11     25      3353      0      14
40   0  -1   2   0   2        -7141       21      8      3070      0       4
41   0   0   0   2   1        -6302      -11      2      3272      0       4
42   1   0   2  -2   1         5800       10      2     -3045      0      -1
43   2   0   2  -2   2         6443        0     -7     -2768      0      -4
44  -2   0   0   2   1        -5774      -11    -15      3041      0      -5
45   2   0   2   0   1        -5350        0     21      2695      0      12
46   0  -1   2  -2   1        -4752      -11     -3      2719      0      -3
47   0   0   0  -2   1        -4940      -11    -21      2720      0      -9
48  -1  -1   0   2   0         7350        0     -8       -51      0       4
49   2   0   0  -2   1         4065        0      6     -2206      0       1
50   1   0   0   2   0         6579        0    -24      -199      0       2
51   0   1   2  -2   1         3579        0      5     -1900      0       1
52   1  -1   0   0   0         4725        0     -6       -41      0       3
53  -2   0   2   0   2        -3075        0     -2      1313      0      -1
54   3   0   2   0   2        -2904        0     15      1233      0       7
55   0  -1   0   2   0         4348        0    -10       -81      0       2
56   1  -1   2   0   2        -2878        0      8      1232      0       4
57   0   0   0   1   0        -4230        0      5       -20      0      -2
58  -1  -1   2   2   2        -2819        0      7      1207      0       3
59  -1   0   2   0   0        -4056        0      5        40      0      -2
60   0  -1   2   2   2        -2647        0     11      1129      0       5
61  -2   0   0   0   1        -2294        0    -10      1266      0      -4
62   1   1   2   0   2         2481        0     -7     -1062      0      -3
63   2   0   0   0   1         2179        0     -2     -1129      0      -2
64  -1   1   0   1   0         3276        0      1        -9      0       0
65   1   1   0   0   0        -3389        0      5        35      0      -2
66   1   0   2   0   0         3339        0    -13      -107      0       1
67  -1   0   2  -2   1        -1987        0     -6      1073      0      -2
68   1   0   0   0   2        -1981        0      0       854      0       0
69  -1   0   0   1   0         4026        0   -353      -553      0    -139
70   0   0   2   1   2         1660        0     -5      -710      0      -2
71  -1   0   2   4   2        -1521        0      9       647      0       4
72  -1   1   0   1   1         1314        0      0      -700      0       0
73   0  -2   2  -2   1        -1283        0      0       672      0       0
74   1   0   2   2   1        -1331        0      8       663      0       4
75  -2   0   2   2   2         1383        0     -2      -594      0      -2
76  -1   0   0   0   2         1405        0      4      -610      0       2
77   1   1   2  -2   2         1290        0      0      -556      0       0
******************************************************************************

Given the JD number corresponding to the date and time (TDB) in question:

---------------------------------------------------------------
Compute time in Julian centuries corresponding to the JD number
and reckoned from J2000.0 (2000 Jan 01 at 12:00:00 TDB)

T = (JD - 2451545.0) / 36525.0

-------------------
Compute powers of T

T2 = T * T
T3 = T * T2
T4 = T * T3

-----------------------------------------------------------------
Define conversion factor to convert degrees to radians.  Multiply
degrees by this factor to obtain the equivalent radians.

DegToRad = 3.141592653589793 / 180.0

-------------------------------------------
Compute mean anomaly of the Moon in radians

L  = DegToRad*((485868.249036 + 1717915923.2178*T + 31.8792*T2
   + 0.051635*T3 - 0.00024470*T4) / 3600.0)

------------------------------------------
Compute mean anomaly of the Sun in radians

Lp = DegToRad*((1287104.79305 + 129596581.0481*T
   - 0.5532*T2  + 0.000136*T3 - 0.00001149*T4) / 3600.0)

------------------------------------------------------------
Compute mean argument of the latitude of the Moon in radians

F  = DegToRad*((335779.526232 + 1739527262.8478*T
   - 12.7512*T2 - 0.001037*T3 + 0.00000417*T4) / 3600.0)

-----------------------------------------------------------
Compute mean elongation of the Moon from the Sun in radians

D  = DegToRad*((1072260.70369 + 1602961601.2090*T
   - 6.3706*T2  + 0.006593*T3 - 0.00003169*T4) / 3600.0)

-------------------------------------------------------------------
Compute mean longitude of the ascending node of the Moon in radians

Om = DegToRad*((450160.398036 - 6962890.5431*T
   + 7.4722*T2  + 0.007702*T3 - 0.00005939*T4) / 3600.0)


--------------
TERM FORMULAS:

Each data line contains the data for one term of
each nutation series.

The 11 data elements of the 2000B series are:
5 fundamental argument multipliers  (m1, m2, m3, m4, m5)
3 coefficients for nutation in longitude (AA, BB, CC)
3 coefficients for nutation in obliquity (DD, EE, FF)

-------------------------------------------------
Compute the angular argument for the series term.
Angles are assumed to be in radians.

arg = m1*L  +  m2*Lp  +  m3*F  +  m4*D  +  m5*Om

--------------------------------------------------
Longitude terms use the AA,BB,CC coefficients from
the data table and take the general form:

DeltaPsiTerm = (AA + BB*T)*sin(arg) + CC*cos(arg)

--------------------------------------------------
Obliquity terms use the DD,EE,FF coefficients from
the data table and take the general form:

DeltaEpsTerm = (DD + EE*T)*cos(arg) + FF*sin(arg)


All terms in each respective series are summed and the result
divided by 36000000000.0 to obtain the nutation expressed in
decimal degrees.



===========================================================================
THE FOLLOWING ARE FUNCTION ALGORITHMS IN PSEUDO-CODE FOR THE NUTATION IN
ECLIPTICAL LONGITUDE AND IN OBLIQUITY OF THE ECLIPTIC FOR ANY GIVEN JD
NUMBER ARGUMENT CORRESPONDING TO THE DATE AND TIME (TDB) IN QUESTION.


--------------------------------------------------------------------
COMPUTE NUTATION IN LONGITUDE ACCORDING TO IAU 2000B NUTATION SERIES

s = 0
s = s + (-172064161 - 174666*T)*sin(Om) + 33386*cos(Om)
s = s + (-13170906 - 1675*T)*sin(2*(F - D + Om)) - 13696*cos(2*(F - D + Om))
s = s + (-2276413 - 234*T)*sin(2*(F + Om)) + 2796*cos(2*(F + Om))
s = s + (2074554 + 207*T)*sin(2*Om) - 698*cos(2*Om)
s = s + (1475877 - 3633*T)*sin(Lp) + 11817*cos(Lp)
s = s + (-516821 + 1226*T)*sin(Lp + 2*(F - D + Om)) - 524*cos(Lp + 2*(F - D + Om))
s = s + (711159 + 73*T)*sin(L) - 872*cos(L)
s = s + (-387298 - 367*T)*sin(2*F + Om) + 380*cos(2*F + Om)
s = s + (-301461 - 36*T)*sin(L + 2*(F + Om)) + 816*cos(L + 2*(F + Om))
s = s + (215829 - 494*T)*sin(2*(F - D + Om) - Lp) + 111*cos(2*(F - D + Om) - Lp)
s = s + (128227 + 137*T)*sin(2*(F - D) + Om) + 181*cos(2*(F - D) + Om)
s = s + (123457 + 11*T)*sin(2*(F + Om) - L) + 19*cos(2*(F + Om) - L)
s = s + (156994 + 10*T)*sin(2*D - L) - 168*cos(2*D - L)
s = s + (63110 + 63*T)*sin(L + Om) + 27*cos(L + Om)
s = s + (-57976 - 63*T)*sin(Om - L) - 189*cos(Om - L)
s = s + (-59641 - 11*T)*sin(2*(F + D + Om) - L) + 149*cos(2*(F + D + Om) - L)
s = s + (-51613 - 42*T)*sin(L + 2*F + Om) + 129*cos(L + 2*F + Om)
s = s + (45893 + 50*T)*sin(2*(F - L) + Om) + 31*cos(2*(F - L) + Om)
s = s + (63384 + 11*T)*sin(2*D) - 150*cos(2*D)
s = s + (-38571 - T)*sin(2*(F + D + Om)) + 158*cos(2*(F + D + Om))
s = s + 32481*sin(2*(F - Lp - D + Om))
s = s - 47722*sin(2*(D - L)) + 18*cos(2*(D - L))
s = s + (-31046 - T)*sin(2*(L + F + Om)) + 131*cos(2*(L + F + Om))
s = s + 28593*sin(L + 2*(F - D + Om)) - cos(L + 2*(F - D + Om))
s = s + (20441 + 21*T)*sin(2*F + Om - L) + 10*cos(2*F + Om - L)
s = s + 29243*sin(2*L) - 74*cos(2*L)
s = s + 25887*sin(2*F) - 66*cos(2*F)
s = s + (-14053 - 25*T)*sin(Lp + Om) + 79*cos(Lp + Om)
s = s + (15164 + 10*T)*sin(-L + 2*D + Om) + 11*cos(-L + 2*D + Om)
s = s + (-15794 + 72*T)*sin(2*(Lp + F - D + Om)) - 16*cos(2*(Lp + F - D + Om))
s = s + 21783*sin(2*(D - F)) + 13*cos(2*(D - F))
s = s + (-12873 - 10*T)*sin(L - 2*D + Om) - 37*cos(L - 2*D + Om)
s = s + (-12654 + 11*T)*sin(-Lp + Om) + 63*cos(-Lp + Om)
s = s - 10204*sin(2*(F + D) + Om - L) - 25*cos(2*(F + D) + Om - L)
s = s + (16707 - 85*T)*sin(2*Lp) - 10*cos(2*Lp)
s = s - 7691*sin(L + 2*(F + D + Om)) - 44*cos(L + 2*(F + D + Om))
s = s - 11024*sin(2*(F - L)) + 14*cos(2*(F - L))
s = s + (7566 - 21*T)*sin(Lp + 2*(F + Om)) - 11*cos(Lp + 2*(F + Om))
s = s + (-6637 - 11*T)*sin(2*(F + D) + Om) + 25*cos(2*(F + D) + Om)
s = s + (-7141 + 21*T)*sin(2*(F + Om) - Lp) + 8*cos(2*(F + Om) - Lp)
s = s + (-6302 - 11*T)*sin(2*D + Om) + 2*cos(2*D + Om)
s = s + (5800 + 10*T)*sin(L + 2*(F - D) + Om) + 2*cos(L + 2*(F - D) + Om)
s = s + 6443*sin(2*(L + F - D + Om)) - 7*cos(2*(L + F - D + Om))
s = s + (-5774 - 11*T)*sin(2*(D - L) + Om) - 15*cos(2*(D - L) + Om)
s = s - 5350*sin(2*(L + F) + Om) - 21*cos(2*(L + F) + Om)
s = s + (-4752 - 11*T)*sin(2*(F - D) + Om - Lp) - 3*cos(2*(F - D) + Om - Lp)
s = s + (-4940 - 11*T)*sin(Om - 2*D) - 21*cos(Om - 2*D)
s = s + 7350*sin(2*D - L - Lp) - 8*cos(2*D - L - Lp)
s = s + 4065*sin(2*(L - D) + Om) + 6*cos(2*(L - D) + Om)
s = s + 6579*sin(L + 2*D) - 24*cos(L + 2*D)
s = s + 3579*sin(Lp + 2*(F - D) + Om) + 5*cos(Lp + 2*(F - D) + Om)
s = s + 4725*sin(L - Lp) - 6*cos(L - Lp)
s = s - 3075*sin(2*(F + Om - L)) + 2*cos(2*(F + Om - L))
s = s - 2904*sin(3*L + 2*(F + Om)) - 15*cos(3*L + 2*(F + Om))
s = s + 4348*sin(2*D - Lp) - 10*cos(2*D - Lp)
s = s - 2878*sin(L - Lp + 2*(F + Om)) - 8*cos(L - Lp + 2*(F + Om))
s = s - 4230*sin(D) - 5*cos(D)
s = s - 2819*sin(2*(F + D + Om) - L - Lp) - 7*cos(2*(F + D + Om) - L - Lp)
s = s - 4056*sin(2*F - L) - 5*cos(2*F - L)
s = s - 2647*sin(2*(F + D + Om) - Lp) - 11*cos(2*(F + D + Om) - Lp)
s = s - 2294*sin(Om - 2*L) + 10*cos(Om - 2*L)
s = s + 2481*sin(L + Lp + 2*(F + Om)) - 7*cos(L + Lp + 2*(F + Om))
s = s + 2179*sin(2*L + Om) - 2*cos(2*L + Om)
s = s + 3276*sin(Lp + D - L) + cos(Lp + D - L)
s = s - 3389*sin(L + Lp) - 5*cos(L + Lp)
s = s + 3339*sin(L + 2*F) - 13*cos(L + 2*F)
s = s - 1987*sin(2*(F - D) + Om - L) + 6*cos(2*(F - D) + Om - L)
s = s - 1981*sin(L + 2*Om)
s = s + 4026*sin(D - L) - 353*cos(D - L)
s = s + 1660*sin(2*F + D + 2*Om) - 5*cos(D + 2*(F + Om))
s = s - 1521*sin(2*(F + 2*D + Om) - L) - 9*cos(2*(F + 2*D + Om) - L)
s = s + 1314*sin(Lp + D + Om - L)
s = s - 1283*sin(2*(F - D - Lp) + Om)
s = s - 1331*sin(L + 2*F + 2*D + Om) - 8*cos(L + 2*(F + D) + Om)
s = s + 1383*sin(2*(F - L + D + Om)) - 2*cos(2*(F - L + D + Om))
s = s + 1405*sin(2*Om - L) + 4*cos(2*Om - L)
s = s + 1290*sin(L + Lp + 2*(F - D + Om))

dPsiDeg = s / 36000000000.0



===========================================================================
COMPUTE NUTATION IN OBLIQUITY (dEps) ACCORDING TO IAU 2000B NUTATION SERIES

s = 0
s = s + (92052331 + 9086*T)*cos(Om) + 15377*sin(Om)
s = s + (5730336 - 3015*T)*cos(2*(F - D + Om)) - 4587*sin(2*(F - D + Om))
s = s + (978459 - 485*T)*cos(2*(F + Om)) + 1374*sin(2*(F + Om))
s = s + (-897492 + 470*T)*cos(2*Om) - 291*sin(2*Om)
s = s + (73871 - 184*T)*cos(Lp) - 1924*sin(Lp)
s = s + (224386 - 677*T)*cos(Lp + 2*(F - D + Om)) - 174*sin(Lp + 2*(F - D + Om))
s = s - 6750*cos(L) - 358*sin(L)
s = s + (200728 + 18*T)*cos(2*F + Om) + 318*sin(2*F + Om)
s = s + (129025 - 63*T)*cos(L + 2*(F + Om)) + 367*sin(L + 2*(F + Om))
s = s + (-95929 + 299*T)*cos(2*(F - D + Om) - Lp) + 132*sin(2*(F - D + Om) - Lp)
s = s + (-68982 - 9*T)*cos(2*(F - D) + Om) + 39*sin(2*(F - D) + Om)
s = s + (-53311 + 32*T)*cos(2*(F + Om) - L) - 4*sin(2*(F + Om) - L)
s = s - 1235*cos(2*D - L) - 82*sin(2*D - L)
s = s - 33228*cos(L + Om) + 9*sin(L + Om)
s = s + 31429*cos(Om - L) - 75*sin(Om - L)
s = s + (25543 - 11*T)*cos(2*(F + D + Om) - L) + 66*sin(2*(F + D + Om) - L)
s = s + 26366*cos(L + 2*F + Om) + 78*sin(L + 2*F + Om)
s = s + (-24236 - 10*T)*cos(2*(F - L) + Om) + 20*sin(2*(F - L) + Om)
s = s - 1220*cos(2*D) - 29*sin(2*D)
s = s + (16452 - 11*T)*cos(2*(F + D + Om)) + 68*sin(2*(F + D + Om))
s = s - 13870*cos(2*(F - Lp - D + Om))
s = s + 477*cos(2*(D - L)) - 25*sin(2*(D - L))
s = s + (13238 - 11*T)*cos(2*(L + F + Om)) + 59*sin(2*(L + F + Om))
s = s + (-12338 + 10*T)*cos(L + 2*(F - D + Om)) - 3*sin(L + 2*(F - D + Om))
s = s - 10758*cos(2*F + Om - L) + 3*sin(2*F + Om - L)
s = s - 609*cos(2*L) - 13*sin(2*L)
s = s - 550*cos(2*F) - 11*sin(2*F)
s = s + (8551 - 2*T)*cos(Lp + Om) - 45*sin(Lp + Om)
s = s - 8001*cos(2*D - L + Om) + sin(2*D - L + Om)
s = s + (6850 - 42*T)*cos(2*(Lp + F - D + Om)) - 5*sin(2*(Lp + F - D + Om))
s = s - 167*cos(2*(D - F)) - 13*sin(2*(D - F))
s = s + 6953*cos(L - 2*D + Om) - 14*sin(L - 2*D + Om)
s = s + 6415*cos(Om - Lp) + 26*sin(Om - Lp)
s = s + 5222*cos(2*(F + D) + Om - L) + 15*sin(2*(F + D) + Om - L)
s = s + (168 - T)*cos(2*Lp) + 10*sin(2*Lp)
s = s + 3268*cos(L + 2*(F + D + Om)) + 19*sin(L + 2*(F + D + Om))
s = s + 104*cos(2*(F - L)) + 2*sin(2*(F - L))
s = s - 3250*cos(Lp + 2*(F + Om)) + 5*sin(Lp + 2*(F + Om))
s = s + 3353*cos(2*(F + D) + Om) + 14*sin(2*(F + D) + Om)
s = s + 3070*cos(2*(F + Om) - Lp) + 4*sin(2*(F + Om) - Lp)
s = s + 3272*cos(2*D + Om) + 4*sin(2*D + Om)
s = s - 3045*cos(L + 2*(F - D) + Om) + sin(L + 2*(F - D) + Om)
s = s - 2768*cos(2*(L + F - D + Om)) + 4*sin(2*(L + F - D + Om))
s = s + 3041*cos(2*(D - L) + Om) - 5*sin(2*(D - L) + Om)
s = s + 2695*cos(2*(L + F) + Om) + 12*sin(2*(L + F) + Om)
s = s + 2719*cos(2*(F - D) + Om - Lp) - 3*sin(2*(F - D) + Om - Lp)
s = s + 2720*cos(Om - 2*D) - 9*sin(Om - 2*D)
s = s - 51*cos(2*D - L - Lp) - 4*sin(2*D - L - Lp)
s = s - 2206*cos(2*(L - D) + Om) - sin(2*(L - D) + Om)
s = s - 199*cos(L + 2*D) - 2*sin(L + 2*D)
s = s - 1900*cos(Lp + 2*(F - D) + Om) - sin(Lp + 2*(F - D) + Om)
s = s - 41*cos(L - Lp) - 3*sin(L - Lp)
s = s + 1313*cos(2*(F - L + Om)) - sin(2*(F - L + Om))
s = s + 1233*cos(3*L + 2*(F + Om)) + 7*sin(3*L + 2*(F + Om))
s = s - 81*cos(-Lp + 2*D) - 2*sin(-Lp + 2*D)
s = s + 1232*cos(L - Lp + 2*(F + Om)) + 4*sin(L - Lp + 2*(F + Om))
s = s - 20*cos(D) + 2*sin(D)
s = s + 1207*cos(2*(F + D + Om) - L - Lp) + 3*sin(2*(F + D + Om) - L - Lp)
s = s + 40*cos(2*F - L) - 2*sin(2*F - L)
s = s + 1129*cos(2*(F + D + Om) - Lp) + 5*sin(2*(F + D + Om) - Lp)
s = s + 1266*cos(Om - 2*L) - 4*sin(Om - 2*L)
s = s - 1062*cos(L + Lp + 2*(F + Om)) + 3*sin(L + Lp + 2*(F + Om))
s = s - 1129*cos(2*L + Om) + 2*sin(2*L + Om)
s = s - 9*cos(Lp + D - L)
s = s + 35*cos(L + Lp) - 2*sin(L + Lp)
s = s - 107*cos(L + 2*F) - sin(L + 2*F)
s = s + 1073*cos(2*(F - D) + Om - L) - 2*sin(2*(F - D) + Om - L)
s = s + 854*cos(L + 2*Om)
s = s - 553*cos(D - L) + 139*sin(D - L)
s = s - 710*cos(2*(F + Om) + D) + 2*sin(2*(F + Om) + D)
s = s + 647*cos(2*(F + 2*D + Om) - L) + 4*sin(2*(F + 2*D + Om) - L)
s = s - 700*cos(Lp + D + Om - L)
s = s + 672*cos(2*(F - Lp - D) + Om)
s = s + 663*cos(L + 2*(F + D) + Om) + 4*sin(L + 2*(F + D) + Om)
s = s - 594*cos(2*(F - L + D + Om)) + 2*sin(2*(F - L + D + Om))
s = s - 610*cos(2*Om - L) - 2*sin(2*Om - L)
s = s - 556*cos(L + Lp + 2*(F - D + Om))

dEpsDeg = s / 36000000000.0

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© Jay Tanner - PHP Science Labs - 2017