Thread about DST made me recall a conversation i had with someone a while ago.
Apparently this friend of mine noted sunrise and sunset times throughout the year and found to his surprise that the day of the latest sunrise did not coincide with the day of the earliest sunset and vice versa. Apparently they are offset by a few days.
Of course I understand why the length of days change due to the earths axis being offset etc but i was also lost for an explanation as to why the sunrise/sunset times didn’t match up.
Only thing i could think of was that this was due to the amount of travel of the earths orbit during each day. By that i mean, if the earth advanced 1/365th of its orbit in one leap then stayed there a day the earliest sunrise and latest sunset would match up (ignoring the fact that a day is different depending on where you are). But as it moves progressively without stopping i can maybe understand why they don’t although i lack the mathematical skill to prove this.
Is my thinking right? If so, can someone explain how to prove this by geometry or whatever?
You actually have the explanation almost there. The Earth does not travel along exactly 1/365 of its orbit every day, because its orbit around the Sun is not a circle, but an ellipse. So one part of the year it travels less than 1/365 of its orbit in a day, and the other part of the year it travels more than 1/365.
The Sun is not a point source - you have to factor in the effect on sunrise and sunset times of appearance and disappearance of the leading and trailing edges of the Sun.
To amplify Giles’s comment, this is easier to understand if instead of focusing on sunrise/sunset, you think about the position of the Sun in the sky at 12:00 noon each day.
The latest sunrise/earliest sunset days will occur around the date of the winter solstice in late December. Daylight time around the solstice will be nearly the same length for each of these days. However, consider the position of the Sun at noon on day X vs. the position of the Sun at noon on day Y. Suppose the daylight time on each of these days is fairly equal. If the noontime sun on day X is further east than it is at noontime on day Y, then sunrise is earlier on day X than day Y, while sunset is later. Although there is some slight variation in the length of daylight for days around a solstice, this variance (around the solstice only) is somewhat smaller than the change in noontime position from day to day.
Over the course of a year (not accounting for DST here), the noontime position of the Sun varies by as much as 45 minutes, and as Giles points out this is because the elliptical orbit of the Earth means it does not move exactly 1/365th of the way around the sun each day. It so happens that the Earth’s perihelion–point it is closest to the sun–occurs in the winter, meaning the Earth is moving faster in its orbit in the winter, meaning the noontime Sun appears to drift eastward from day to day in the dead of winter.
At some point, the natural lengthening of daylight after a solstice increases at a rate greater than the noontime drift due to the Earth’s orbit, and of course this eastward drift ends after a short while. By the last few days of December, sunrise/sunset comes earlier/later each subsequent day.
As a point of clarification to CJJ’s* comments, the reference point being used is for the northern hemisphere. For example, a December winter solstice refers to the northern hemisphere, as does the Earth’s perihelion also occurs during the northern hemisphere winter. Those who live south of the equator have an equally different perspective.
Wonderful answers, and it helped clear up my own misconceptions on this.
I’ll just add that in any elliptical orbit, the orbiting body spends more time in the geometric “outer” half of the orbit than in the “inner” half. On a near-circular ellipse like Earth’s orbit, the difference is miniscule but does affect things to a very small degree; on a more elongated ellipse like that of a periodic comet, it’s very significant. (A comet that has a 100 year period will pass from Mars’s orbit around the sun and back to Mars’s orbit in something like a year.) The explanation behind this lies in one of Kepler’s Laws, and I’ll let an astrophysicist explain it better.
Have you ever noticed an odd figure 8 on some globes. They are usually located somewhere in the Pacific where there are no inhabited islands. It is called the analemma and marks the deviation of the transit of the meridian from clock noon, as measured at the Greenwich observatory. (Well it used to be; I assume there are more modern ways of measuring it now.) The figure 8 shows how it varies during the year. And yes, it is the result of the eccentricity of the earth’s orbit. FWIW, the earliest sunset comes in early Dec. and the latest sunrise is in early January. This is at 40 deg N latitude, since these dates vary with the latitude. It is similar in the summer with the latest sunset in early July and the earliest sunrise in early June. At 40 deg N, the passage of the meridian can be as much 16 minutes before or after noon.
There is another oddity. One would think that at the equinoxes, the interval between sunrise and sunset ought to be exactly 12 hours, anywhere on earth. It isn’t. At 40 N, it is several minutes more. Although I have never seen an explanation of this, I have intuited that it there are two reasons. One that is often cited is refraction. I don’t know if that is true or how important it is, but the second accounts for about 4 minutes and I have verified that it is correct. If you compare stated sunrise and sunset times with the actual appearance and disappearance of the sun, you will find that the sunrise time is when the first light of the sun actually appears and the sunset time is when the last light disappears. Thus the partial light of the rising or setting sun is not distinguished from full light. This lengthens the reported day by the length of time it takes the sun to go from first tangent to the horizon to last tangent. At the equator this is about 2 minutes, but is 4 at mid-latitudes (and about a day, I believe, at the pole).
Also the tilt of the Earth’s axis. Even if the Earth’s orbit were a perfect circle, if the axis were still tilted, the sun would be at different points in the sky at the same time of day at different times of year.
You can photograph the analemma- what you do is take a picture of the sun from the same location at the same time every day (or every few days) throughout the year, and then superimpose the images so all the suns appear in the same image.
It is caused by the eccentricity of the earth’s orbit and the inclination of the earth.
Earliest sunrise about second week of July
Latest sunrise about the second week of January
Latest sunset about the second week of June
Earliest sunset about the second week of December
Spring equinox about March 21st.
Summer solstice about June 21st.
Fall equinox about September 21st.
Winter solstice about December 21st.
Halloween Tuesday October 31st, 2006
