Question about variations of the Sun's path over long periods of time

[evanbpeters]

TL;DR Summary

Do shadows remain the same throughout time over hundreds of years?

Hello. I am a filmmaker writing a screenplay and I am in need of technical support to validate a method being used in the film.

I am going to post this in the Earth Science forum but I'll copy it here, in case anyone reading this might know.

Thank you all!

"I am wondering if shadows cast from the sun in 1880 would be the same in 2020? For example, would the shadow of a mountain be in the same spot on May 1, 1880, 12:00 p.m. as it would be on May 1, 2020, 12:00 p.m. (given that the mountain's shape has not changed)?"

 

[sysprog]

Well, it depends partly on the weather and on the atmospheric detrita (e.g. pollen or pollution), but otherwise yes, pretty much exactly.

 

[evanbpeters]

Hello. I am wondering if shadows cast from the sun in 1880 would be the same in 2020? For example, would the shadow of a mountain be in the same spot on May 1, 1880, 12:00 p.m. as it would be on May 1, 2020, 12:00 p.m. (given that the mountain's shape has not changed)?"

Any help would be appreciated. I would love links to info/studies on this too, if anyone has them.

Thank you,

Evan

 

[evanbpeters]

Thank you. This is very helpful and good news.

Do you have any links to more info on this? Or could you tell me what the field I'm in here is technically called? Someone on reddit suggested contacting their Aerospace Engineering forum.

 

[sysprog]

Thank you. This is very helpful and good news.

Do you have any links to more info on this? Or could you tell me what the field I'm in here is technically called? Someone on reddit suggested contacting their Aerospace Engineering forum.

Thanks for the effort to check plausibility when contemplating making a film. I would say that the primary disciplines associated with your question are Earth Science, Astronomy, and Opticks. Please consider how precisely an eclipse casts a shadow -- at a very precise time -- is either of your dates an eclipse date? (i don't know; I haven't checked, but most dates aren't, so I guess probably not).

 

[evanbpeters]

No it was just a random date for speculation. The actual event in the script doesn't take place during an eclipse. It just relies on the use of shadows for the purpose of location.

I will check out the sources there. I've got the question posted in the astronomy, astrophysics and aerospace engineering forums in reddit right now. Getting a little feedback as well.

Thank you again for your help!

 

[BvU]

Hello @evanbpeters , !

It would not be in the same spot, but very close .
"How close ?" Is the harder question . Happy calculating !

Google terms like
precession and nutation of Earth axis
Polar motion
True polar wander

This one has a ton of math !

[edit after threads were merged] My first reply to a then new thread looks a bit silly now. Film makers are not interested in calculations. And IMHO viewers couldn't care less about shadows. They are used to candles projecting a shadow of themselves on the wall.

 

[anorlunda]

[Moderator: Duplicate threads merged.]

 

[DrClaude]

Clocks didn't change for summer time in 1880, so the shadow in 2020 would be the same at 13:00 if it is in a time zone that uses summer time.

 

[Dr_Nate]

From my reading on antiquity and their cosmological views, I learned that in approximately 70 years the zodiacs shift about 1 degree.

Well I just looked it up. It's actually 71.39 years for one degree of precession.

 

[anorlunda]

@DrClaude raises an interesting point about local time. Have you heard of railway time? By 1880 the railroads imposed defined times zones in most places but not every place. Also, without the telegraph, a locality would have difficulty synchronizing their clocks with the rest of the country. Clocks and watches of the time might drift 1-2 minutes per day, and there is no way to tell how often a particular citizen synchronized his clocks with the "standard."

Finally, remember that there is approximately one hour difference beteween sun time and clock time on the eastern border of a time zone compared with the western border of the time zone. And some time zone boundaries follow political borders, not lines of longitude.

I'm reminded of a real life incident. I traveled once from New York to a town in Indiana. It was the day of switch from daylight savings to standard time. To get there, I flew from New York (Eastern time) to Chicago (Central time), then I flew to Indianappolis (Eastern time), and drove to the meeting site through several counties where it was county option which time zone to observe. When I arrived at the meeting, I found the locals made a betting pool on when I would get there. The guesses ranged over 3 hours.

Even in modern times, you can get confusion if you drive with your cell phone near a time zone boundary and it tries to show local time.

All those things should give a movie maker considerable freedom to hypothesize just how inaccurate estimates of local time might be. I think those uncertainties are much bigger than astronomical or geological variations.

 

[evanbpeters]

@sysprog @BvU @DrClaude @Dr_Nate @anorlunda Thank you, everyone. I am super appreciative of your input.

Based on all of the feedback it looks like I can go ahead with the plot mechanism and not worry about experts scoffing at the absurdity of it.

Would Kepler's laws of planetary motion be applicable for referencing why the sun stays on course? I am planning on using dialogue about the function of a sundial to inspire the character to later use shadows to mark a location. I'm trying to come up with a snappy little monologue that references real world people/facts to sell it to the audience. (I am going to look into @BvU 's recommendations as well)

Thank you all again!

 

[Dr_Nate]

What do you mean by why the sun stays on course?

Two more helpful things to look at are the tropical year and the apparent solar time (regarding a sundial).

 

[Baluncore]

I am wondering if shadows cast from the sun in 1880 would be the same in 2020? For example, would the shadow of a mountain be in the same spot on May 1, 1880, 12:00 p.m. as it would be on May 1, 2020, 12:00 p.m. (given that the mountain's shape has not changed)

The height of the sun in the sky varies during the day and during the year. For that reason, at the same time on the same day of the year, a shadow will fall in the same place.

The Sun is not a point source but is a circular source of light. Therefor the edge of a shadow is not sharp, it is a gradation that changes over about half a degree, over at least two minutes of time. The thing that is sharp is the point or the instant when the first edge of the Sun is seen above the mountain profile or horizon.

The relative position of the Moon will change over a month and is not synchronised with the solar year. So the phase of the Moon is unlikely to be the same between two different years. Likewise the ocean tide will probably be different also. Keep the age of the Moon out of the discussion to avoid contradictions.

 

[256bits]

@sysprog @BvU @DrClaude @Dr_Nate @anorlunda Thank you, everyone. I am super appreciative of your input.

Based on all of the feedback it looks like I can go ahead with the plot mechanism and not worry about experts scoffing at the absurdity of it.

Would Kepler's laws of planetary motion be applicable for referencing why the sun stays on course? I am planning on using dialogue about the function of a sundial to inspire the character to later use shadows to mark a location. I'm trying to come up with a snappy little monologue that references real world people/facts to sell it to the audience. (I am going to look into @BvU 's recommendations as well)

Thank you all again!

Kepler's laws - they do describe planetary orbits.

Anyways, the shadow cast from one year to the next, same day, same time, will be off somewhat.
At the present epoch, the Earth takes 365 AND 1/4 days to complete a solar year, so a shadow lining up to the same "location" will be off by that quarter day.
See, from another thread about the equinoxes,
http://www.astropixels.com/ephemeris/soleq2001.html
2001 Mar 20 13:31 Jun 21 07:38 Sep 22 23:05 Dec 21 19:22
2002 Mar 20 19:16 Jun 21 13:25 Sep 23 04:56 Dec 22 01:15
2003 Mar 21 01:00 Jun 21 19:11 Sep 23 10:47 Dec 22 07:04
2004 Mar 20 06:49 Jun 21 00:57 Sep 22 16:30 Dec 21 12:42
2005 Mar 20 12:34 Jun 21 06:46 Sep 22 22:23 Dec 21 18:35
2006 Mar 20 18:25 Jun 21 12:26 Sep 23 04:04 Dec 22 00:22
2007 Mar 21 00:07 Jun 21 18:06 Sep 23 09:51 Dec 22 06:08
2008 Mar 20 05:49 Jun 21 00:00 Sep 22 15:45 Dec 21 12:04
2009 Mar 20 11:44 Jun 21 05:45 Sep 22 21:18 Dec 21 17:47
2010 Mar 20 17:32 Jun 21 11:28 Sep 23 03:09 Dec 21 23:38
You can see that there is about 6 hours difference between one vernal equinox to the next. After 4 years ( we have a leap year to keep the calendars and the sun in sinc ), the times just about line up but not quite. Same 6 hour difference for consecutive autumn equinox and the solstices.

The equinox is the time when the sun makes no shadow at some point along the equator.
So if you pick say the 2001 vernal equinox, Mar 20 at 13:31 , when there is no shadow. On Mar 20, 2002 at 13:31 at the same location there will be slight shadow of the sundial, since the 2002 year has not yet reached an equinox. Note that the locations on the Earth where the equinoxes occur are about 6 hours apart ( time zone distance ) from year to year.

Note also, the same location on Earth that had the sun casting no shadow at vernal equinox in 2001, is now on the opposite side of the earth, out of sunlight, and in darkness when the vernal equinox occurs in 2003.
Your not really interested in that, but rather how much the shadow differs from one year to the next at the same location, same time. The sun will have moved about a quarter of a degree in "its orbit around the earth", or 1 / 1440 of its total path in the sky. What that translates into shadow difference is not all that much, but definitely not zero.

 

[Baluncore]

Anyways, the shadow cast from one year to the next, same day, same time, will be off somewhat.
At the present epoch, the Earth takes 365 AND 1/4 days to complete a solar year, so a shadow lining up to the same "location" will be off by that quarter day.

You seem to be saying that sundials slip 6 hours per year.

 

[256bits]

You seem to be saying that sundials slip 6 hours per year.

Take the vernal equinox example, with a sundial at the equator.
That happens only at one location at one time.
Suppose at this vernal equinox, the location is along the Greenwich meridian, and suppose the time is exactly 1200 noon.
At the equator along the Greenwich meridian, a sundial would cast no shadow
While the Earth rotates to bring the next time zone to 1200 local for that time zone, the Earth has moved on its orbit,
A sundial at the equator on the longitude for each successive zone would cast a shadow at the local 1200 noon.
24 hours later, the Greenwich equator location sundial casts a shadow.
The shadows becomes more evident as the days progress reaching a maximum at the summer solstice, where they begin decreasing as we approach the fall equinox. The same happens from fall equinox, through winter solstice just shy from the vernal equinox, ie 365 days where the Greenwich location will record 1200 noon, but still cast a small shadow.
The Earth has to revolve in ts orbit, and subsequently rotate one more quarter day for the vernal equinox, where on Earth at the equator a different sundial at another longitude ( not a whole number ) will be the one to not cast a shadow.

 

[Baluncore]

Maybe you are trying to explain the Equation of Time or the Analemma.
https://en.wikipedia.org/wiki/Equation_of_time#Graphical_representation

 

[russ_watters]

Clocks didn't change for summer time in 1880, so the shadow in 2020 would be the same at 13:00 if it is in a time zone that uses summer time.

Yes, we've read your book Riley.

Spoiler

"National Treasure" reference

 

[256bits]

Maybe you are trying to explain the Equation of Time or the Analemma.
https://en.wikipedia.org/wiki/Equation_of_time#Graphical_representation

Don't know from where you get that thought.
1200 noon is 12 noon for a time zone meridian sundial ( baring secondary effects )
The length of the shadow will vary somewhat about a mean value for a particular day and time from one year to the next.

 

[BvU]

Originally we were worrying over a period of 140 years "exactly":

Summary:: Do shadows remain the same throughout time over hundreds of years?
...
in the same spot on May 1, 1880, 12:00 p.m. as it would be on May 1, 2020, 12:00 p.m.

 

[Baluncore]

The length of the shadow will vary somewhat about a mean value for a particular day and time from one year to the next.

The gnomon of a sundial is aligned to be parallel with the Earth's axis, it is the axial line of the gnomon that casts the time shadow, not the tip of the sundial. The length of the shadow will vary with the season.

The horizontal axis of the analemma shows how the time of the Sun crossing the meridian varies against a regular clock.
The vertical axis of the analemma gives the height of the Sun and so, the length of a shadow.
The figure '8' line of the analemma is followed each year, but the date along that line varies slightly over the four year leap day cycle. In the years either side of a leap day, there is a partial day variation in the progress of the Sun along the analemma.
@256bits Is that the variation you are concerned about?
That variation will be a blend of declination and time, the blend depending on the day of the year and the slope of the analemma curve for that date.
Notice how at the solstices, the time of sunrise and sunset are changing rapidly in the same direction, but the length of shadows is most stable.

1200 noon is 12 noon for a time zone meridian sundial ( baring secondary effects )

That may be now, but in the time of sundials, (the middle ages), "Noon" was the “ninth hour”, we now call that 3PM.
"Solar noon" or "high noon" was mid-day, when the Sun crossed the meridian.
AM and PM refer to before and after the meridian passage of the Sun at "solar noon".

 

[256bits]

That may be now, but in the time of sundials, (the middle ages), "Noon" was the “ninth hour”, we now call that 3PM.
"Solar noon" or "high noon" was mid-day, when the Sun crossed the meridian.
AM and PM refer to before and after the meridian passage of the Sun at "solar noon".

Actually a good tidbit of historical information.

Even now, since time zone demarcation does not follow exact meridians, one cannot generally say a blanket statement at what time of day the sun is at its highest point at your location.

 

[klimatos]

Time zones were not used before 1883. Before that, every community set its own local noon bases on its longitude. Precise times of day (to the minute) had almost no value before the coming of the railroad. Many people used local church bells to signify the rough time of day.

 

[anorlunda]

Precise times of day (to the minute) had almost no value before the coming of the railroad.

Many places had telegraphs earlier than railroads. Wouldn't that give them a simple way to get precision time signals? "At the time of the next dash, the time will be exactly 12:00:00" Even after arrival of railroads, I expect that the RR's telegraph would be the primary tool of minute-scale synchronization.

The RR's big contribution was imposition of time zones for hour-scale synchronization, plus a big clock at the RR station visible by all in the town which was corrected daily to a remote time reference. People who did not travel daily to a central place to see the RR clock, would have difficulty keeping their home clocks and watches accurate on the minute-scale.

I imagine that was the state of the art for home timekeeping until the advent of home telephones and AC electricity.

I haven't actually researched this topic, I'm just trying to apply common sense. My father was a clockmaker and collector. I grew up in a house with maybe 2000 ticking clocks and watches. It was absolute hell in that house to know what time it was. We used TV/radio and the dial up telephone service, "The time is now ..."

In Sweden, the phone/TV time service was called "Fröken ur" (Miss clock). We came to be completely familiar with her lovely voice. Years later, I was eating in a restaurant in San Francisco. I heard a voice behind me. I immediately pivoted and said "Fröken ur?" The woman smiled and said, "Yes. I recorded those things many years ago."

Forgive the rambling post. Self-isolation cabin fever.

 

[Vanadium 50]

Wouldn't that give them a simple way to get precision time signals?

Sure. But why would you need that?

I can tell the computer I am typing this on has a time good to about 25 microseconds. That's better than I need it. I can get it to a few nanoseconds if I chose. But what would be the point?

 

[anorlunda]

Sure. But why would you need that?

To set their clocks and watches to the correct time-of-day. One minute per day fast/slow was a reasonable number for the drift of windup clocks and watches. So if you want one-minute accuracy, you needed to reset your clock once per day.

Remember, the OP is talking about 1880.

 

[Vanadium 50]

Right, but apart from railroads, when was time needed at the one minute resolution in 1180? And, maybe more to the point, why would it be needed to sync up across towns?

 

[anorlunda]

Right, but apart from railroads, when was time needed at the one minute resolution in 1180? And, maybe more to the point, why would it be needed to sync up across towns?

Are you questioning why people in 1880 bothered with clocks at all?
It is not a question of resolution, it is a question of accuracy.

• I presume there were things such as appointments.
• I presume there would be legal implications, "Your honor, I heard the shot at 6:15." "Your honor, I did pay the fine before the noon deadline."
• There were employers and schools that expected employees and students to show up on time.

Unless people synchronized their clocks regularly, their independent estimates of time of day could easily have had a standard deviation of 3 hours.

But you remind me of my time living on a sailboat. Unless doing celestial navigation, I needed no clocks, no calendars. Sunrise, sunset, seasons had meaning. Otherwise, I didn't care. When someone said, "I'll meet you in Miami on the 8th of May," that caused real stress among sailors, who would prefer to say, "I'll meet you in the spring."

 

[Vanadium 50]

Are you questioning why people in 1880 bothered with clocks at all?

I think I wrote 1180, but that was before the invention of the railroad. Or the minute. But I meant 1880.

It's not the clock so much, it's the need to synchronize clocks in distant cities. The fact that high noon comes at different times in Dodge City as Tombstone didn't matter as far as I can tell pre-railroad. One clock in the town square and you're pretty much done.

 

[hutchphd]

And I believe the placing of clocks in church towers was not simply a nod to visibility. The more puritanical denominations (in the USA, at least) took a vested interest in people organizing their labors throughout the day to better serve divine purpose. No idle hands you know...
Incidentally until about a decade ago Indianapolis and its environs simply eschewed Daylight Savings Time altogether. Made for interesting phone conference scheduling with folks.
But actually I think the moving the clock back and forth is silly.

 

[anorlunda]

It's not the clock so much, it's the need to synchronize clocks in distant cities. The fact that high noon comes at different times in Dodge City as Tombstone didn't matter as far as I can tell pre-railroad. One clock in the town square and you're pretty much done.

OK, I can see that. It was true to certain extent. But it's also true that the telegraph changed everything. By Civil War time, the telegraph was nearly ubiquitous, and the owner of the town steeple clock used the telegraph to set the clock's minute hand. The choice for the hour hand was a local custom. With no synchronization, the town clock might drift 6 or more hours per year, and the telegraph was much easier than a sextant or a sundial to synch it.

The stories from young Thomas Edison are rich with anecdotes about use of the telegraphs in the 1860s. The big application was not the railroads, or timekeeping, but rather the ability to get news from remote places on the same day as it happened. Edison's first commercial success came when he telegraphed out the headline "20,000 Dead Shiloh" and then sold newspapers providing the details. Consider it the 1860s version of TV or Twitter.

 

[Baluncore]

Time was only critical where ships headed off on long voyages. They needed to calibrate their navigational chronometers to handle the problem of determining longitude. That is why the national sea ports had an astronomical observatory watching the Sun and the stars in meridian transit. At the observatory, a ball was slowly raised up a mast in the minutes before midday, held there, then dropped at midday, when a gun was also fired.

A sundial is accurate to a couple of minutes and served for many years to set the time of church bells and services. That is why there is often a sundial in a churchyard. The bell rung from the local church was sufficient to synchronise clocks and get the townsfolk to work on time. Later the church put a clock in the bell tower.