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I am struggling to understand the how the coordinates work.

Example: At vernal equinox RA=0 DEC=0, Does this mean the Sun is at its highest point at the equator?

If my mean solar time is 2h 30min, does this mean it's 2:30am on my watch?

I calculated the Hour angle which gives me how far away is the sun at this time, so HA= MST - 12h = -10h 30m, meaning 10h 30m away from me, right?

How do I know how far below the horizon the Sun is? I know for every hour the sun rises by 15degrees. As it's 2:30am it must be below horizon, but I don't know how to find how far is the sun below the horizon.

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    $\begingroup$ You have 4 questions that are only somewhat related. You should split them up so that each question and answer can cover one topic. $\endgroup$
    – JohnHoltz
    May 18, 2022 at 16:53
  • $\begingroup$ In this case I think these really are part of working the same basic problem and so not really unrelated. It would not do any good to break them up into four separate question posts - they're much easier to answer together as steps in solving a single problem, so voting to leave open because closing and preventing answers doesn't allow for a better outcome than allowing answers. $\endgroup$
    – uhoh
    May 19, 2022 at 21:49

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The vernal equinox is defined as the time the Sun's DEC changes from south to north. At that time the Sun is directly over some point on the equator.

If it's 2;30 on your watch and you happen to be in the middle of your time zone, and Daylight Saving Time is not in effect, yes. You probably noted that your mean solar time depends on your longitude. Getting it accurate to 1 minute of time requires knowing your longitude to 1/4 of a degree. For your watch to agree with your mean solar time, you need to be within 1/4 of a degree of longitude of the meridian passing through the center of that time zone, which will be a multiple of 15 degrees. For the Eastern Time zone the meridian 1s 75 degrees west longitude.

Calculating the Sun's angular distance below the horizon is complicated. There's more than mean solar time that determines the Sun's DEC and RA, and you need to know both as well as your latitude and longitude to work the spherical trigonometry to find that angle. Then you have to consider complications like refraction - the Sun is actually below the geometric horizon at sunrise and sunset.

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    $\begingroup$ Actually at the vernal equinox the RA is a particular value of 0. $\endgroup$
    – d_e
    May 18, 2022 at 20:33
  • $\begingroup$ If say eastern time zone is 30° East. You might want to refine your wording. $\endgroup$ May 19, 2022 at 6:23
  • $\begingroup$ I'll also add that the Equation of Time is more than -7 minutes on the vernal equinox (celestialprogramming.com/snippets/equationoftime-simple.html). I think the question asks what should be several different questions, so trying to sum them all up in one answer is going to be complicated. $\endgroup$ May 19, 2022 at 15:00
  • $\begingroup$ @d_e Thanks - edited. $\endgroup$
    – stretch
    May 20, 2022 at 11:30
  • $\begingroup$ @planetmaker Eastern Time zone in North America means the time zone of the eastern United States, most of eastern Canada and the state Quintana Roo in Mexico. The zone is more or less centered on 75 W, and its time in autumn and winter is UTC-5. $\endgroup$
    – stretch
    May 20, 2022 at 12:09

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