Question 1

Pre-published Ephemerides

Accepted Answer

, such as the astronomical almanacs published by the US Naval Observatory, represent the traditional alternative. These are massive databases where the math has already been done by supercomputers. The advantage of an ephemeris is absolute, unquestionable accuracy, accounting for minute gravitational wobbles of the Earth (nutation) that simplified formulas ignore. Furthermore, looking up a value in a database requires almost zero processing power. The massive disadvantage is storage space and inflexibility; if you need data for a coordinate that isn't in the table, you must perform complex mathematical interpolation, defeating the purpose of the lookup table.

Question 2

Why does the earliest sunset of the year not occur on the winter solstice?

Accepted Answer

The winter solstice is the shortest total day of the year, but the earliest sunset occurs roughly two weeks prior. This happens because the Earth's orbit is an ellipse, not a circle, and its axis is tilted. These two factors cause solar noon to shift later by the clock every day during December. Because solar noon is moving later, the entire day shifts later, pulling the sunset time with it. Therefore, the sun sets earliest by the clock in early December, even though the total hours of daylight continue to shrink until the solstice.

Question 3

How exactly does elevation change the time of sunrise and sunset?

Accepted Answer

Elevation changes the angle of your visible horizon. When you are at sea level, your horizon is effectively at 0 degrees relative to your position. When you climb a mountain, the curvature of the Earth falls away from you, creating a "dip" in the horizon. Because you can see slightly "over" the curve of the Earth, the sun will appear to rise earlier and set later. As a general rule of thumb, for every 1,500 meters (roughly 5,000 feet) of elevation gained, sunrise occurs approximately 5 minutes earlier, and sunset occurs 5 minutes later, depending on your latitude.

Question 4

What is the difference between Civil, Nautical, and Astronomical twilight?

Accepted Answer

Twilight phases are strictly defined by the angle of the sun's center below the geometric horizon. Civil twilight occurs when the sun is between 0 and 6 degrees below the horizon; during this time, there is enough natural light for most outdoor activities without artificial illumination. Nautical twilight occurs when the sun is between 6 and 12 degrees below the horizon; the horizon is still visible for sailors to take navigational sightings, but artificial light is needed for tasks. Astronomical twilight occurs between 12 and 18 degrees below the horizon; the sky is quite dark, but residual scattered light will still interfere with viewing the faintest stars and galaxies.

Question 5

Why is the sun still visible after the calculator says it has set?

Accepted Answer

This is primarily due to atmospheric refraction. The Earth's atmosphere acts like a giant magnifying glass, bending the light of the sun around the curvature of the planet. By the time you see the bottom edge of the sun touch the horizon, the physical sphere of the sun is actually already entirely below the geometric horizon. Standard calculators account for an average atmospheric bending of 34 arcminutes, but if the air is exceptionally cold or dense, the atmosphere will bend the light even more, keeping the visual image of the sun in the sky minutes after the mathematical sunset.

Question 6

Can these formulas be used to calculate sunrise on other planets?

Accepted Answer

Yes, the fundamental spherical trigonometry used in these calculators applies universally to any spherical body in space. However, to calculate sunrise on Mars, for example, you must replace the Earth-specific constants with Martian constants. You would need to use the Martian axial tilt (25.19 degrees), the Martian orbital eccentricity, the length of a Martian day (a "sol," which is 24 hours and 39 minutes), and entirely remove the Earth's atmospheric refraction constant, replacing it with the much smaller refractive index of the thin Martian atmosphere.

Question 7

What is the Equation of Time, and why is it necessary?

Accepted Answer

The Equation of Time is the mathematical difference between time tracked by a perfect mechanical clock (mean solar time) and time tracked by the actual position of the sun in the sky (apparent solar time). Because the Earth speeds up when it is closer to the sun in its elliptical orbit and slows down when it is further away, the length of a true solar day is rarely exactly 24 hours. The Equation of Time corrects this discrepancy, which can fluctuate from -14 minutes in February to +16 minutes in November. Without applying this correction, any calculated sunrise time could be off by over a quarter of an hour.

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