Hello
Yves and all !Thank for the information.
However, these formulas are known for me.
I would like to receive the formulas of immediate passage of ecliptic heliocentric rectangular coordinates of comets, from standart epoch (1950.0 and 2000.0) to epoch t.
Really it cannot be made not resorting to equatorial rectangular coordinates?
Now I and student of mathematical faculty
Yaroslav Mihalin try to simulate driving comets and cometary trains. This information would be for us valuable.Sergey
ShanovRUSSIA
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I put in attachment the calculus you asked for. I hope this will help
you. If something is unclear, ask me.
Yves.You want to pass from rectangular ecliptic heliocentric coordinates (X,Y,Z) at the epoque t, to the epoque J 2000.0 (vector (X4,Y4,Z4).
First, you must know the rectangular geocentric coordinates of the Sun (or the heliocentric position of the Earth and you change all the signs).
(XS,YS,ZS) is this vector position.
a) geocentric coordinates (X1,Y1,Z1):
(X1,Y1,Z1) = (XS,YS,ZS) + (X,Y,Z) = (XS+X,YS+Y,ZS+Z)
b) Calculus of the Earth obliquity, epsilon, at the date t
epsilon = 23.439291 - 0.0130042*T – 0.00000016*T*T (degrees)
T = (JD – 2451545.0)/36525
JD is the Julian Day of the date t
c) Transformation ecliptic -> equatorial (X2,Y2,Z2)
X2 = X1 :
Y2 = Y1*cos(epsilon) + Z1*sin(epsilon) :
Z2 = - Y1*sin(epsilon) + Z1*cos(epsilon) :
d) Passage at the epoque J 2000.0 (XJ2000,YJ2000,ZJ2000)
XJ2000 = P11*X2 + P21*Y2 + P31*Z2
YJ2000 = P12*X2 + P22*Y2 + P32*Z2
ZJ2000 = P13*X2 + P23*Y2 + P33*Z2
P11 = 1 – 0.00029724*T*T – 0.00000013*T*T*T
P12 = -0.02236172*T – 0.00000677*T*T + 0.00000222*T*T*T
P13 = -0.00971717*T + 0.00000207*T*T + 0.00000096*T*T*T
P21 = -P12
P22 = 1 – 0.00025002*T*T – 0.00000015*T*T*T
P23 = -0.00010865*T*T
P31 = -P13
P32 = P23
P33 = 1 – 0.00004721*T*T
e) Passage at the ecliptic geocentric coordinates (J 2000.0) (X3,Y3,Z3)
X3 = X2
Y3 = Z2*sin(epsilon2) + Y2*cos(epsilon2)
Z3 = Z2*cos(epsilon2) – Y2*sin(epsilon2) epsilon2 = 23.439291111 (degrees)
f) Return at the ecliptic heliocentric coordinates.
You must know the geocentric position of the Sun (J 2000.0)
(Xgo,Ygo,Zgo). You can find it on the server...
Let be (X4,Y4,Z4) these coordinates.
(X4,Y4,Z4) = (X3,Y3,Z3) – (Xgo,Ygo,Zgo) = (X3 – Xgo,Y3 – Ygo,Z3 – Zgo)