Anonymous
Anonymous asked in Science & MathematicsAstronomy & Space · 1 decade ago

# how many degrees does the sunset move each day?

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I presume you're asking about the point of the horizon at which the sun sets. Points on the horizon can be measured by azimuth -- 180 for due south, 270 for due west, and 360 (or 0) for due north.

The answer to your question depends on both your latitude and the time of year. Here are some azimuths for sunset in 2007 for a person who lives at latitude 40 degrees north:

March 16 268.68 degrees (before vernal equinox)

March 26 273.83 degrees (after vernal equinox)

June 21 302.11 degrees (summer solstice)

Dec 21 239.53 degrees (winter solstice)

Between the solstices, the sunset point changes by about 62.6 degrees in half a year (about 183 days), for an average of 0.34 degrees per day. Near the equinoxes, the sunset point changes about 0.51 degrees per day; near the solstices, it hardly changes at all.

If you live south of 40 degrees, the change from solstice to solstice is less; if you live north of 40 degrees, the change is greater.

The earth's axis is inclined to its orbit by 23.5 degrees. The shift in the sunset point between solstices is roughly given (in degrees) by

2 * 23.5 / cos (latitude)

but this is only an approximation. For a precise calculation, you need to use spherical trigonometry.

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• Pure simple logic will tell you it all depends on what latitude you're at. On Dec. 21 or Dec. 22 - depending on the year - 1 of the poles will not see a sunset. It will be daylight for a full 24 hours. Hence no sunset. The same at the opposite pole on June 21 or June 22. But at the equator it will move 360 degrees each day.

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• It depends on the time of year. Near the Summer and Winter Solstice (about June 21 and December 21), the sunset point changes very little from day to day. Near the Vernal and Autumnal Equinoxes (Equinoxi?) ( about March 21 and September 21) the motion is at its greatest.

Another way to look at this is that the sunset point swings back and forth like a pendulum. This means we can use the mathematics of simple harmonic motion to estimate the travel of the sunset point at any time of the year.

Sunset Point = ( 23.5 degrees ) cos ( ω t )

where ω = 2π / ( 365.25 days / year ) and t is the time (in days) since the most recent solstice.

Velocity of Sunset Point, in degrees per day = - ( 23.5 degrees ) ω sin ( ω t )

So to find the maximum velocity of the sunset point, let the trig function have a value of 1 and multiply 23.5 degrees by ω by to get the speed in degrees moved per day.

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• When you say "sunset," I suppose you are talking about the point where it sets, on the horizon.

This will vary throughout the year. Hold a pendulum at arm's length and allow it to swing parallel to the horizon. Watch the string as it intersects the horizon. At the extremes, it slows down and covers less distance per given period of time. But when it is in the middle, it is moving its fastest and covers more of the horizon in that same unit of time.

This is how the sun behaves during the course of the year. At the equinoxes it is moving the greatest distance each day. At the solstices it is at its northernmost or southernmost limits and has slowed to the point where it will reverse direction, north or south.

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• I'm assuming you mean as we see it setting, it moves slightly north or south...

That's a hard question. As we get close to a solstice, as we are now, it's moving less & less south, until December 21st, then it'll begin to slowly move northward again. Then, during the equinoxes, it moves the fastest (In the vernal equinox, it's moving north, in the autumnal equinox, it's moving south). The number of degrees per day changes, because the rate at which it changes varies.

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