What is an equal-sun-elevation "day" called?

[dotancohen]

What is the "day" called such that the sun's elevation (distance above the horizon) is constant? Thanks.

It's not a solar day, though that is what I was expecting.

[dotancohen]

For instance, if on 2011-05-16 at 15:00 the sun is at 62.3 degrees elevation, then what is the term for the period of time until 2011-05-17 with the sun is at 62.3 degrees elevation (which would be near but not exactly 15:00)?

[dotancohen]

I think that I found what I'm looking for, it's the "apparent solar day":
http://en.wikipedia.org/wiki/Solar_time

[russ_watters]

Sorry, your question doesn't make much sense to me. The only place I can think of when the sun would be at a constant elevation all day (roughly) is at the poles, where it slowly rises and sets once over the course of the year. Everywhere else on earth, it rises in the morning and falls in the afternoon. It's never at constant elevation.

[dotancohen]

I do not mean that the sun would be in a constant elevation all day. I mean to ask what is the name of the period in time from which the elevation of the sun above the horizon is equal to it's elevation the previous "day". I now know that this is called the Apparent Solar Day.

When one says 15:00 one day and 15:00 the next day, the sun is at a different elevation. This is because the colloquial "day" is an average of the lengths of all the days in the year. This time period, according to Wikipedia, is the "Mean Solar Day". The relationship between the Mean Solar Day and the Apparent Solar Day is the analemma.

[russ_watters]

Ok, I see what you're getting at, but it still isn't quite right. The sun's elevation won't be the same even from one day to the next. It gets successively higher through the spring and successively lower through the fall. From the definition on the wiki: Apparent solar time or true solar time is given by the daily apparent motion of the true, or observed, Sun. It is based on the apparent solar day, which is the interval between two successive returns of the Sun to the local meridian. So that's when it crosses the same vertical plane every day, not when it rises to a certain elevation.

[HallsofIvy]

No, that's not what he is asking. Lets say that you go out and measure the elevation of the sun at 9:00 A.M. The next day, you go out a little before 9:00 A.M. and wait until the sun is at exactly the same elevation as the previous day. That will NOT be at exactly 9:00 A.M.- the time interval will be a little different from 24 hours. His question is "what is that time interval called?"

[russ_watters]

Maybe im still missing something: what if it doesn't get back to that elevation the next day?

It doesn't look to me like that has anything to do with a solar day.

[russ_watters]

[very late addition:] Or to put it another way: since the sun's path through the sky is different every day, getting back to the same elevation won't get you back to the same meridian, so you can't measure a solar day based on elevation.

[dotancohen]

No, that's not what he is asking. Lets say that you go out and measure the elevation of the sun at 9:00 A.M. The next day, you go out a little before 9:00 A.M. and wait until the sun is at exactly the same elevation as the previous day. That will NOT be at exactly 9:00 A.M.- the time interval will be a little different from 24 hours. His question is "what is that time interval called?"

Yes, Halls, that is exactly what I am asking! Is that not the apparent solar day?

[D H]

Yes, Halls, that is exactly what I am asking! Is that not the apparent solar day?
No, it is not. You are talking about something slightly different. Solar time is a function of the Sun's azimuth, not its elevation. Suppose you measure the azimuth of the Sun one day, then on the next day determine the time at which the Sun reaches the same azimuth. The time difference between those events is one apparent solar day. The difference between apparent and mean solar time is the equation of time. It is also the east-west variation in an analemma. You are talking about the vertical variations in an analemma. That is something different from a solar day, and I don't know if what you are asking about has a name.

[dotancohen]

No, it is not. You are talking about something slightly different. Solar time is a function of the Sun's azimuth, not its elevation.

I see. So at 9:00 on one day and 9:00 the next day, the sun is at the same azimuth?

[D H]

I see. So at 9:00 on one day and 9:00 the next day, the sun is at the same azimuth?
Not at all! Over the course of a year, apparent solar time varies from over 14 minutes behind mean solar time to over 16 minutes ahead of mean solar time. And that's just apparent versus mean solar time.

Your watch, or whatever you use to say that it is 9:00 AM, is based on Coordinated Universal Time (UTC). UTC seconds are equal to TAI seconds, except for discontinuities when leap seconds are added/subtracted to keep UTC and UT1 within one second of each other. Mean solar time is closest in concept to the now obsolete UT2 time scale. Speaking of obsolete: Mean solar time is also an outdated and obsolete concept. The concept of a mean fictitious Sun just has too many problems now that we can measure time with the incredible accuracy available nowadays.

[dotancohen]

So the 9:00 to 9:00 time is now completely independent of the rotation of the Earth? I know that it is now based upon the decay of cesium atoms, but I thought that it was still intended to approximate the rotation of the Earth.

[dotancohen]

In any case, the reason that I am interested in the period of time between [sun is at elevation x] and the following [sun is at elevation x] is to determine the ideal day for observing planets (especially Mercury) in the early morning. If I could observe the positions of the planets in Stellarium for several days, with the sun at the same elevation for each day, the I could determine which day would give the best view of the planets.

A different metric which would let me make the same determination would be the following: [the elevation of a particular planet] minus [the elevation of the sun]. Does such a metric exist? In Stellarium I can in fact pause time, measure the altitude (elevation) of the sun and any planet, and then do the math. Is there a name for this metric?

[russ_watters]

Oh, I see what you're after. When I do that (I use Starry Night, not Stellarium), I just manually adjust the time as I scroll through the days to hold the sun at the same elevation (just below the horizon). A different metric which would let me make the same determination would be the following: [the elevation of a particular planet] minus [the elevation of the sun]. Does such a metric exist? In Stellarium I can in fact pause time, measure the altitude (elevation) of the sun and any planet, and then do the math. Is there a name for this metric? It surely can be calculated, but probably doesn't have a name. A similar metric, though, is elongation which is a measure of how far in degrees the planet is away from the sun. That's not vertical, though.