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The monthly variations are caused by the change in declination of the Moon as it travels (roughly) along the ecliptic. This is caused by the tilt of the Earth's rotation axis, which results in an angle of about 23° between the equator (declination = 0°) and the ecliptic. Around the constellations of Taurus and Gemini the ecliptic lies at much ...

6

There are many indeed. It may be specified from South westwards(0° to 360°), or from North eastwards and westwards(180° to -180°). The most popular one, as used by Roy and Clarke in "Astronomy : Principles and Practices" is to measure the azimuth from North eastwards 0° to 360°. For a southern hemisphere observer, this system changes to from South ...

5

Azimuth is conventionally calculated as a degree value between 0 (inclusive) and 360 (exclusive). North is assigned 0 (also by convention), which puts East at 90, South at 180, and West at 270. Sometimes 0 is set to South intead of North. This is the traditional means of measuring solar azimuth, even though North is the most accepted convention. Positive ...

4

The Sun's hour angle, measured around the celestial equator, changes at a nearly constant rate. The gnomon of a sundial is aligned with the polar axis to take advantage of this. The celestial equator is oblique to the horizon except at the Earth's equator and poles. The lines of azimuth converge at the observer's zenith and nadir, so the Sun's azimuth ...

3

Constant for every star with different declination's. Though you would have to assume the the declination is such that it can have an azimuth of 90 each, not all stars will. Depending on your latitude some stars will never get to an azimuth of 90, they will either be always be further north or south.

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The sundial translates the position of the sun to the time of day, so it depends on the path the sun takes across the sky, this is called the ecliptic. Because the earth's rotation is tilted with respect to its orbit around the sun, the ecliptic shifts across the sky during the year, which is also the cause of seasonal change on earth. Yet the highest ...

2

You know, the first time someone told me this, I was absolutely certain they were confused, ignorant, or otherwise mistaken, and I told him he had his facts wrong. To be precise, we were talking about an observer on the equator. I maintained that the Sun would rise due east and set due west, all year round. He said no. What gave me pause, though, is that ...

2

Your diagram is correct, your maths isn't. The bearing of the object's shadow is, as your diagram shows, away from the sun. If the bearing of the shadow is 75°, then the sun must have an azimuth of of 75°+180°, or 255°. Similarly if the bearing of the shadow was 300° (pointing towards the northwest) the sun would be at an azimuth of 300 - 180°, or 120° (in ...

2

The algorithm on that page is very simplistic and is probably the source of a good portion of that error. It's best to test your code using a very accurate ephemeris, even if your final goal is to have a much more simple ephemeris implementation. DE405, or VSOP87 would be good alternatives. A small error in GMST can have a big effect on Alt/Az ...

2

The NOAA formula sheet expresses some quantities in radians, some in degrees, and some in minutes of time. It does say which is which, but it's easy to miss. A few minor code changes can help expose bugs: Store angles in radians. Trigonometric expressions free of Math.toRadians calls are easier to verify against a reference document. Put that document's URL ...

2

Thanks to Ralf Kleberhoff for Pointing me in the right direction. Step 1: Find Summer Solstice Date For the accuracy needs of this question simply finding the hemisphere and picking the most common date will work. (June 21 in the Northern Hemisphere and December 22 for the Southern Hemisphere). If greater accuracy is required. There are many resources ...

1

This can be done using the Python package Skyfield fairly easily. Here is a shell of a script; I used some dictionaries to hold data, you may want to do something else. I've stored a lot of goodies but only printed azimuth, altitude and distance in kilometers. By default Skyfield's .altaz() method calculates atmospheric refraction for anything higher than -...

1

lat2 = 0 and lmst = 0 place the vernal equinox at the zenith, so most points on the ecliptic should have azimuth either obliq degrees north of east or obliq degrees south of west. Try other values for lat2 or lmst and see if the resulting azimuths make sense.

1

For the Sun at JD 2458599.125, RA = 32.8° and dec = 13.2° are correct regardless of geographic location. In the alt/az calculation, LHA should be 323.6° and converted to radians, and the expression for alt needs a call to Math.Asin. Trigonometric expressions are easier to verify if they are free of inline unit conversions. Store angles in ...

1

I've confirmed that this formula is in fact correct. I did have the wrong units in the code, which @Glorfindel suggested: sun's hour angle was in hours instead of radians. I did need to adjust the azimuth's angle offset based on the hour angle: // The angle offset needs to be adjusted based on whether the hour angle ...

1

The azimuth of the sunrise (or sunset, or any object) is a function of the Sun's declination and observer's latitude. It can be calculated from the following forumla: $$\cos(\theta_R)=-\frac{\sin(declination)}{\cos(latitude)}$$ where $\theta_R$ is measured from due south to the location where the object rises or sets. For example, at 55 degrees north ...

1

The azimuth angle from due south to the point where an object rises or sets is a function of the latitude (lat) and declination (decl), as follows: cos(angle) = -sin(decl)/cos(lat) This ignores refraction and the radius of the object, so it will introduce some inaccuracy for the Sun. (The refraction and radius of the Sun amount to 50 arcminutes. The change ...

1

You can use a package such as the pyephem package for python. It can calculate the position of any astronomical object. However for the sun since it moves along the ecliptic, roughly at a uniform rate, you can approximate the position by doing coordinate transformations. The sun's longitude moves by 365.24/360 degrees a day from 0 at the vernal equinox and ...

1

The actual equations used by NASA are located here: https://eclipse.gsfc.nasa.gov/SEcat5/deltatpoly.html I failed to find any pre-written code and consequently wrote my own in Swift. The equations are fairly straightforward and a list of the possible errors these equations may produce is linked to that page as well. Here are the polynomials: Using the ΔT ...

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Planetarium software, such as Stellarium, or astronomical computation software such as pyephem can compute the exact position of the sun at any date, time and location. It is then simple trigonometry to calculate the length of a shadow: if the sun is $\theta$ degrees above the horizon, a vertical building of height $h$ will cast a shadow on horizontal ...

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Any sundial that gives the same result as this is correct and any other is wrong (but sometimes close enough): _ /############ /| /############# skewer / /############## (central) v / /############### | north /################ | (S in S. /################# ...

1

The sun is not on the same Azimuth for the same hour (not even at noon!). You need to take the analema figure (http://en.wikipedia.org/wiki/Equation_of_time) into your accounts. If you do not, your clock will be exact only 4 times a year.

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