How to convert heliocentric coordinates to geocentric coordinates?

Answer 1

Heliocentric Ecliptic Rectangular to Geocentric Ecliptic Spherical coordinates

lon and lat are in radians; X, Y, Z and dist are in Astronomical Units

Pl is planet of interest;

PlX is Heliocentric X coord, PlY is Heliocentric Y coord, PlZ Heliocentric Z coord

Ea is Earth;

EaX is Helio X, EaY is Helio Y, EaZ is Helio z

geocentric longitude = ArcTangent2( (PlY-EaY) , (PlX-EaX) )

geocentric latitude = ArcSine( (PlZ-EaZ) / ( (PlX-EaX)^2 + (PlY-EaY)^2 + (PlZ-EaZ)^2)^1/2 )

geocentric distance = ((PlX-EaX)^2 + (PlY-EaY)^2 + (PlZ-EaZ)^2)^1/2

Note: ArcTangent2 function

Function ArcTangent2 (numerator, denominator)

'theta is the angle, in this case longitude ,

' 0 <= theta < (2 * 3.14159265358979323846)

If numerator = 0 Then

If denominator < 0 Then

theta = 3 * 3.14159265358979323846 / 2

Else

theta = 3.14159265358979323846 / 2

End If

Else

theta =ArcTangent(numerator/denominator)

'this is the conventional ArcTangent function

End If

If numerator < 0 Then

theta = theta + 3.14159265358979323846 / 2

ElseIf numerator > 0 And denominator < 0 Then

theta = theta + 2 * 3.14159265358979323846

End If

Return theta

End Function