[_ Old Earth _] Help! My sundial is losing time and getting slower!

[tim-from-pa]

:biglol Yes, it is losing time, but not because the thing's not set up right, but because right now the day is over 24 hours long. This is quite normal. It will be 24 hours again later this month, and then it will perhaps 20 seconds faster than 24 hours mid-September, and this variation of the day going several seconds slow, then fast will average out over any given year. This average length of the day is what we call "mean solar time".

So, to set up a sundial, it is not technically correct to say the sun is "due South" at noon. If we did have a nice, even motion of the sun in the heavens, and if we set up a camera to take a picture of the sun at noon daily for a year, we would expect to see a vertical line of suns in the south. The upward and downward motion of the sun being due to the tilt of the earth, the sun being high south in the summer, and low south in the winter. But that is not what we actually get if we were to snap a picture. Because a day is not exactly 24 hours but changes from day-to-day, this makes the sun speed up and slow down at various times, and we'd actually get a southern picture with the sun also moving left and right of the southern meridian like this:

View attachment 2519

This "figure 8" pattern is called an analemma as we gnomonists (sundial guys) would say, and the time difference between the sun and clock is called the equation of time. You add or subtract those minutes to sundial time to get your local (not time-zone) mean time. So the sundial is not really wrong, as a sundial is nothing more than a meridian marker but since the sun does not move at a constant rate, the sundial tells apparent solar time. Before the days of precise clocks, this was good enough given that the human mind cannot detect the slight variation in the length of the day. The sundial was the main time-keeping device. But with the advent of clocks, it was discovered that they did not agree, and at first people thought their clocks were wrong and had to be corrected!

And that's a mini-lesson on the length of the solar day, clocks and sundials. I'm fascinated with time.

 

[lordkalvan]

Cool. Very interesting. If the board had a rep function, consider yourself repped.

 

[Pizzaguy]

I'm fascinated with time.

You must know that Marty McFly guy.

 

[evenifigoalone]

Interesting. We learn something new every day, I guess.

 

[Sinthesis]

Pretty cool.:

 

[Barbarian]

This one (which has not been photoshopped) is particularly interesting:

Have you been to this site?
http://www.perseus.gr/Astro-Solar-Analemma.htm

 

[tim-from-pa]

This one (which has not been photoshopped) is particularly interesting:

Have you been to this site?
http://www.perseus.gr/Astro-Solar-Analemma.htm

Yes, now that you mentioned it, I do remember visiting this site months ago. This is a better picture than the images I searched. Thanks.

I have never tried to photograph the analemma. As the article states, it is very, very difficult to have the camera mounted that precise and steady for a whole year! The first photograph of an analemma I ever saw was in one of my astronomy books and it was this one:

View attachment 2523

The photographer picked another meridian (i.e. time) which is just as valid albeit tilted. But I wanted to get a picture where the figure 8 was vertical as one would see it in the south to avoid confusion. Yours is better. One interesting thing to take note in this picture. Notice that one can see the sun "through the tree" at the bottom. This is not photoshopped. Rather, he was taking this picture toward the east and the sun is at the base of the figure 8 in the winter. The tree had no leaves when those pictures were taken!

 

[Barbarian]

That shot was published in the (80s?) by Eastman Kodak, in Scientific American, promoting their lab supplies and special imaging products.

The title: "Very Pretty - And all natural."

 

[Pizzaguy]

Now, of course, the sun does not change speed - it's the earth that changes speed.

Now, care to explain why/how this can be and how it can be so predicable and cyclic?

(Asking because I THINK I know, but I'm unsure.)

 

[Pizzaguy]

"Very Pretty - And all natural."

I have a smart remark to make... but I will show self-control.

(Very unlike me, I know.) :toofunny

 

[Pizzaguy]

View attachment 3081

I HATE that I must ask, but what are the three "comet-tails"?
(Got a feeling the answer is gonna embarass me.)

Sundial EoT ~ -9.9sin(60m+18)-7.7sin(30m-3)
My very simplified equation derived using Kepler's Law and Spherical trig
​

What is "EoT" and "m"? (Probably gonna embarrass myself again, but not gonna let that stop my from learning.)
My guess: "EoT" is "error of time" or IOW, the error in the sundial's indication of time due to the "wandering" sun, measured in minutes?

But what the heck is "m"????

 

[Barbarian]

Now, of course, the sun does not change speed - it's the earth that changes speed.

Now, care to explain why/how this can be and how it can be so predicable and cyclic?

Newton's theory of gravitation. When the planet is at the aphelion, the pull of gravity is less on the Earth, and it moves slower. As it gets closer to the sun, the pull increases and it speeds up. As it moves farther away from the sun, it slows down due to gravity. So it's fastest at the perihelion, and slowest at the aphelion.

Newton explained why, but of course Kepler discovered the motion first.

http://www.drennon.org/science/kepler.htm

 

[Pizzaguy]

I thought that Tycho Brahe noticed the varying speeds of the planets and wondered how they could be doing this, since he "knew" the planets orbited in circles. THEN, Kepler came along, verified the varying speeds but ALSO discovered the eliptical orbits and that the sun was not at the center, but at a focus of the ellipse.


THEN... Newton came along and put it all together mathematically as well as gravitationally.


I have more to say, but lets start there!

THIS is a FUN thread!

 

[Barbarian]

I thought that Tycho Brahe noticed the varying speeds of the planets and wondered how they could be doing this, since he "knew" the planets orbited in circles. THEN, Kepler came along, verified the varying speeds but ALSO discovered the eliptical orbits and that the sun was not at the center, but at a focus of the ellipse.

Actually Tycho thought the Sun orbited the Earth. He had his own system that combined elements of the Copernican and Ptolemaic systems. Kepler was initially held back by his philosophical belief that the orbits of planets must be circular. Only after he was willing to let go of that idea, did he finally understand.

THEN... Newton came along and put it all together mathematically as well as gravitationally.

Right. We call them "Kepler's Laws" because they predict the movement of the planets. We call it "Newton's Theory of Gravitation" because it predicted and explained the motion.

Edit:

I HATE that I must ask, but what are the three "comet-tails"?

It looks as though the shutter was left open on three different mornings, although that bgrings up some technical issues about exposure.

 

[Pizzaguy]

Actually Tycho thought the Sun orbited the Earth. He had his own system that combined elements of the Copernican and Ptolemaic systems. Kepler was initially held back by his philosophical belief that the orbits of planets must be circular. Only after he was willing to let go of that idea, did he finally understand.

I knew that, I remember that Brahe went off to Prague "not understanding" those "wobbling orbits". (James Burke quotes)

Yea, it was Kepler - he made some kind of conceptual leap of imagination, and arrived at elliptical orbits. (Not sure how.)

Kepler was more a mathematician than Brahe, I think he thought logically, or MORE logically (which math will make you do).

It looks as though the shutter was left open on three different mornings....

I knew I'd be embarrassed. Kinda obvious now that you say it. :bigfrown

 

[tim-from-pa]

The equation of time is caused by two primary motions.

1) The earth moves in an elliptical orbit, not circular, so when the earth is closest to the sun it speeds up. This means that in a given "day" the earth has to turn a tad more to catch up with the sun, thus the day is longer. At it's furthest point, the opposite happens. This moves the sun "ahead and behind" in a cyclical fashion in a sine-like wave with a period being one year. The amplitude of this amounts to about 7 minutes error (behind or ahead of the point in a circular orbit). This is the green wave on my picture.

2) The earth is tilted 23.5 degrees so the sun moves along the ecliptic instead of the equator so that a certain degree motion along the ecliptic does not equate to the same degree motion along the equator, which is the circle that the longitude lines divide the hours. This is because there is some vertical motion in the sun, not just "horizontal" along the equator. This error produces a sine-like wave up to about 10 minutes of error. If the earth had a perfectly circular orbit, the equation of time would be a plus and minus 10 minute sine-like wave agreeing at the solstices and equinoxes, and therefore this wave has a period of only half a year. This is the red wave on my picture.
3) Adding the effects together we get the familiar equation of time curve: (click on picture to enlarge)

View attachment 2526

Now if you "fold the black equation of time curve back on itself" you get the figure 8, because this is merely a graph with the x-axis time going forward, whereas in the sky the sun goes up and then backtracks causing the figure 8.

Now, look at the formula in my signature I had up for a few months now. You can perhaps discern each component. But this is an approximation. I tend to calculate directly (I use a spreadsheet program I created) in that the green curve is calculated by Kepler's Law and the red curve by spherical trigonometry.

I have to watch myself. I may slip into scientific sun-god worship (this stuff is so interesting to me). :toofunny

 

[Barbarian]

Hmmm... so you didn't adjust for axial precession? Your calculations will be seriously affected in a few thousand years.

 

[tim-from-pa]

Hmmm... so you didn't adjust for axial precession? Your calculations will be seriously affected in a few thousand years.

No, I did not adjust for axial precession. I calculate only to a few seconds and the ET changes year-to-year slightly anyway. That's 'cus these sundials of mine can't really read better than to the nearest minute, if that, so it's close enough for me.

When the tropical year becomes such that perihelion is no longer in the winter centuries from now, you know what that means..... phase shift my equations. :toofunny

 

[Barbarian]

Er, excuse me Mate, but the perihelion is in the summer months. At least it is, in the Southern Hemisphere.

 

[tim-from-pa]

Er, excuse me Mate, but the perihelion is in the summer months. At least it is, in the Southern Hemisphere.

:toofunny Yeah, that's right. I have to go back to those sensitivity training classes. Us Northerners aren't the only ones!