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107

=1- . 02516 - . 00 074 3. The Suns mean anomaly at time JDE.

M = 2.5534 + 29.10535669» - O.O0UO2I87- - 0.0000001 IP

FIGURE 14-23 TradeStation function to calculate the moons phases. IMOOHPHASES

Returns the mean phases of the moon, corrected for the suns aberratiorl VARS: k(0), HO), next(O), 1(01; ARRAY fullmoon[6Z](OI. newmoon[62](01; next - 62;

for t - 1 to 62 begin

= 2000 + next; (newmoons relative tc the year ZDOOI T = / 1236.85; Itime in Julian centuries! newmoonCi] - 2i52550.09765 + 29.53CbBBBS3*k ♦ O.C001337«epoi«er(T,2);

-0.00C000150*epoiier(T,3) + 0.00000000073* « (1,4); - 2000 + next + .5; {full moons relative to the year 20001 T - / 1236.85;

fullmocnm = 2452550.09765 + 29.530588853*k + 0.0001337*®power(T,21

-0.000000150«epouer(T,31 + 0.000OOO0OO73*@po»er(T,41; next next + 1; end;



[> «0001239/" - ooooooosay*

+ 390 67050274* - 00103417-»

( the d-rf.-incliiig nnde of rht lunar urbii

il («>ni<.-> = 124.77-46 - 1. 6375580* + O.traZOftgiy + . 02 5 »

I*it- fi>Ili>wing ciilituliun. biis«l an t- and 11. tfivf thtr hofits fcir Ihe solar or lunar ct-lipse, and if differs from O", « ", 360" by less than 3".9 iJien an eclipse is cei-lain 1 is nni-ii-e (han 21° from these phases, there is no eclipsf. If F feiils be-

A, = 2W 77 + 0= 07«(>M (> 000173»»

9 Then to find the esiact time of thr hjll solar (or lunar> eclipse. 4te folionlnK corrections <in days) should he addend to the time of the mean eonjunction fiven hy JOE In (lie first fonriula al>ove (smaller quantities have been umined)

Time of maximum eclipse

= JDE + fjunar OF solar componen* helow)

-f- O.OIGI sin 2 / - O.OOS>7 sin 2/--. + O.O073 E n sin - )

sin <Af -«- - 0023sln (Af- 21--,) +0.««2 x £ x sm £J4 (Af + 2/-.> + OOtNi x x sin (2 *- + *> - OOt>4 sin * x s.n ( / + 2/-V» + «003 sin A. - 0.0002 x £ x s.n ( / - Zf-.y xsin <2 *-- *>-<1

OSi>2 sltl n* + Ol

- 73 xi x sin < * + *> 0 0067 * x sin ( * - AO + «11; II. = +5 2207 - 004 x x cos /+ «020 x x cos 2Af - 33V9C

- 0.0060x£xeos -1- *> -1-0.004 x £ x cos (Af - *> 2. W= I cosF, 1

13. Otamma» - (/> eos / , + f sin f=V> x (1 - O.OO4RW0 14 = ( >59 + 0.004 COS .

Solar Eclipses

For a solar eclipse, represents the shortest distance from the axis of the moons shadow to the center of the Earth in units of the equatorial radius of the Earth (the distance from the center to the surface of the Earth at the equator). Its value is positive if the axis of the shadow is passing north of the Earths center, and negative if it is passing south. When is less than +.9912 and greater than -9972, the solar eclipse is cenfral, that is, there is a line of cenfral eclipse on the surface of the Earth (see Figure 14-24).

The value u gives the radius of the moons umbral cone on the fundamental plane, which passes through the center of the Earth pe endicular to the axis of the moons shadow (in units of Earths equatorial radius). The radius of the penumbral cone in the fundamental plane is u .5460.

Based on these values, the following situations exist:



I Y I is between 0.9972 and 1.5432 + The eclipse is not central

Part of the eclipse may touch the polar rcons.

I Y I is between 0.9972 and 1.0260 0.9972< I Yl <0.9972 + « y>1-5432 + «

For a central eclipse, <0

> 0.0047 < < 0.0047

The combination of a noncentral total or annular eclipse.

No eclipse is vuoble from the Eanhs sur-fece.

The echpse is total

The eclipse is annular.

The ecbpse is either annular or annular-

total.

To remove the ambiguity of this last situation, calculate

(0 = 0.00464 cos W, where sin IF = If u < (0 then Ihe eclipse is annular-total; otherwise, it is annular.

FIGURE 14-24 Geomehj of a solar eclipse.

The greatest magnitude for a partial solar eclipse is reached at the point on the Earths surface that comes closest to the a.xis of the shadow at



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