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Can anyone help me with the formulas to convert Equatorial coordinates (Right Ascension / Declination) into Heliocentric coordinates (Angle and Distance in relation to the Sun) ?

i.e. Ra/Dec of 6.7659/18.4563 ---> 281.98 degrees and 0.4562 AUs

It feels like this is possible with no other inputs, but I can't figure it out.

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  • $\begingroup$ Its not possible because the Earth moves relative to the sun. So you will need a date at least. Moreover, you need two angles (eg RA and Dec) to determine a direction. You can't convert a direction into one angle and a distance. $\endgroup$
    – James K
    Jul 2 '20 at 18:24
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No, this is not possible. Equatorial coordinates only specify the direction of a certain point in space (as seen from Earth), not the distance. During a solar eclipse, the Moon and the Sun have (approximately) the same equatorial coordinates, but the distance to the Sun is 0 or almost 1 AU.

It is possible to define equatorial or ecliptic coordinates with the Sun as center, but even then there is no general formula. You'll need the full position (i.e. three coordinates) of the Earth (relative to the Sun) or vice versa, and the full position of the object under observation to be able to convert the coordinates.

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  • $\begingroup$ Thanks for trying to help! Good counter example of the sun/moon on an eclipse. $\endgroup$
    – user2191367
    Jul 2 '20 at 21:20
  • $\begingroup$ Hi, I have a follow-up question that I believe is answerable... I would like to convert Ra/Dec to Heliocentric Longitude. I realize from your reply that I can't get the Heliocentric Radius, but I would still like to convert Ra/Dec to the angle around the sun. How would I do that? $\endgroup$
    – user2191367
    Aug 10 '20 at 16:06
  • $\begingroup$ That depends on where you put the origin/center of your heliocentric system. $\endgroup$
    – Glorfindel
    Aug 10 '20 at 16:26
  • $\begingroup$ It would be with respect to the Sun being at the center of the circle, and the angle given by the calculation would be the angle around the Sun. Where would i be able to find the math to make that calculation of Ra/Dec -> angle around the Sun? $\endgroup$
    – user2191367
    Aug 10 '20 at 16:56
  • $\begingroup$ That still depends entirely on where you put the 0 angle. There is no standard definition, except perhaps the galactic coordinate system. And it will only work for objects that are far away because of the stellar parallax. $\endgroup$
    – Glorfindel
    Aug 10 '20 at 17:11

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