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I've learned about Orbits recently, and there are 6 orbital elements. Now, I've heard of three coordinate systems whereas, they can help you measure positions of stars in the night sky. The Altazimuth, the Equatorial, and the Ecliptic coordinate systems. Now, I can't quite grasp what they mean, and how to use them. This is what I am asking for from an answer to this question. From night to night, I know that star and planet positions may vary, because we're rotating, and the start move due to it, and even in the day, we're still spinning, and the star positions keep changing, whether or not we can see them, or they're blocked by the sun's brightness, so the next night, they'll be in a new place. That being said, I don't want an answer that says there can't be a coordinate system that doesn't relate to my position on Earth, because I want an explanation for those three coordinate systems that includes my position (preferably using latitude and longitude).

Assuming this can be feasibly explained in a post, thanks in advance!

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    $\begingroup$ You might want to play with Stellarium (stellarium.org). You can enable or disable equatorial and azimuthal grids, you can select the observer position on Earth, and you can let time pass as fast as you want. $\endgroup$ Apr 28 at 14:54
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    $\begingroup$ Thanks for your help, @EricDuminil. The Stellarium helps me practice what I learned from the posted answer. $\endgroup$
    – Questioner
    Apr 28 at 15:00
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The altazimuth system is directly linked to your position on the Earth. It is the “left-right/up-down” coordinates system; the azimuth being the “left-right” (with 0° for North, 90° East, etc.), and the altitude is the “up-down” (with 0° being the horizon, 90° being overhead, also called zenith). Of course, a star’s (or planet’s, comet’s, galaxy’s, etc.) position will change during the night and over the year.

The equatorial system is independent of any location on the Earth. It is akin to the longitude and latitude of the Earth, but for the sky. As you can guess from the name, its reference is the celestial equator, which is the projection of Earth’s equator on the celestial sphere. There’s an imaginary point along it, where the Sun crosses it from south to north (near March 20), that’s the reference point, to be more specific; it’s called the vernal point. Like longitude, right ascension is measured (in hours, minutes, and seconds of time) eastward from that point, from 0 h at this point to 12 h opposite it to 24 h back at this point. Like latitude, declination is measured north (+) or south (−) from the equator to the poles (+90° North, −90° South). Celestial bodies virtually keep the same right ascension and declination over a human lifetime, except for planets, asteroids, and comets, which keep moving.

Finally, the ecliptic system is used mostly for bodies of the Solar System. As you can guess by the name, it’s measured along the ecliptic instead of the equator. The ecliptic is the apparent path of the Sun in the sky over the year—it corresponds to the plane of the Earth’s orbit around the Sun. Coordinates in the ecliptic system are ecliptic longitude, measured eastward from the vernal point mentioned in the previous paragraph, from 0° at it to 180° opposite it to 360° back at it; and the ecliptic latitude, measured perpendicularly to the ecliptic, from 0° along it to +90° at the ecliptic north pole and −90° at the ecliptic south pole.

There are indeed formulas for converting from one system to the other. Between the equatorial and ecliptic system, it’s a fixed conversion, but between any of these and the altazimuth system, there’s a time factor, so you need to account for it. And as time zones vary from country to country (and sometimes within the same country!), we don’t rely on them but instead on true local sidereal time, which is basically the right ascension of the point in the sky that is due south (or north, in the southern hemisphere) of your location.

You also mentioned, in the beginning of your question, orbital elements, but these are completely independent of the coordinates system being used, although it is standard to consider them in the ecliptic reference system.

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    $\begingroup$ The angular orbital elements certainly depend on the coordinate system. Ecliptic coordinates are commonly used in spacecraft attitude operations, since the Sun is the easiest reference point to detect, and you often need to point solar panels toward it while pointing instruments and radiators away. $\endgroup$
    – John Doty
    Apr 28 at 12:28
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    $\begingroup$ What I meant is that orbital elements, e.g. the eccentricity of a planet, remain the same no matter which coordinate system is used. Orbital elements are semi-major axis (no link with coordinates systems), eccentricity (no link), inclination (relative to an arbitrary plane that may or may not be the ecliptic), argument or longitude of periastron (relative to arbitrary planes), longitude of node (relative to arbitrary plane), and a six pertaining to the body’s position on its orbit (relative to periastron)… $\endgroup$ Apr 28 at 20:23
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    $\begingroup$ But the elements "relative to arbitrary plane" depend on the choice of plane and reference direction within the plane. In other words, they depend on the coordinate system defined by those choices. For example, NORAD "TLE" elements for Earth-orbiting objects use equatorial coordinates to define inclination, longitude of ascending node, and argument of perigee. $\endgroup$
    – John Doty
    Apr 28 at 20:42
  • $\begingroup$ How does the Altazimuth Coordinate System relate to my position on Earth? Isn't it just telling you where a star is, using it's angle in the sky, and the direction you face it at? $\endgroup$
    – Questioner
    Apr 29 at 14:10
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    $\begingroup$ The altazimuth coordinate system relates to your position on the Earth because an object that might be high in the sky for you might be set for another observer elsewhere. Yes, the celestial equator does cut through “the middle” of the sky, i.e. halfway between the North and South celestial poles. And yes, the Sun’s path across the sky; as it takes a year to complete, that’s why I mentioned “over the year.” $\endgroup$ Apr 29 at 21:49

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