Can we predict the Sun's path accurately?

[Trainee Engineering]

I've seen several online sun path calculator like this one:
http://keisan.casio.com/exec/system/1224682277

I'm wondering just how accurate are these tools? the tool above can even produce results for year 2099. is this possible? I mean, is there no possibility that these might change in the future, like perhaps caused by Earth's axis tilting a bit (would that be a bad thing), or some adjustment on Earth's orbital trajectory? just thinking out loud here. some can even produce results as granular as minute of hour.
Thanks

 

[D H]

Almost all of those online tools are based on Jean Meeus's book Astronomical Algorithms, or his earlier book, Astronomical Formulae for Calculators. The earlier book is based on techniques developed in the late 19th / early 20th century. The latter one (Astronomical Algorithms) takes advantage of the huge improvements in solar system ephemerides thanks to space age developments.

Meeus's models are quite accurate over about a 150 year interval centered on the late 1980s. Anything outside of that is extrapolation using a model that is not well suited to such extrapolation. To make computations efficient, Meeus used third order polynomials in time, with time expressed in Julian centuries (365.25*86400 seconds) from noon universal time on 1 January 2000. (This is a standard time reference in astronomy.) He developed these third order polynomials as a best fit to higher precision models. Ignoring leap seconds, the errors in sunrise / sunset time should be small, less than a minute, for the next several decades. However, polynomials are not a good model for long term behavior of something that is bounded. Using those models to represent centuries is problematic, and anything beyond centuries is highly problematic.

Leap seconds are also an issue. The Earth's rotation rate is gradually slowing down. Predicting the time of sunrise and sunset is a bit problematic even over the course of multiple decades due to leap seconds. The predicted sunrise and sunset times form year 2099 are probably off by about a minute just because of accumulated leap seconds from the early 1980s to 2099.

 

[Trainee Engineering]

Almost all of those online tools are based on Jean Meeus's book Astronomical Algorithms, or his earlier book, Astronomical Formulae for Calculators. The earlier book is based on techniques developed in the late 19th / early 20th century. The latter one (Astronomical Algorithms) takes advantage of the huge improvements in solar system ephemerides thanks to space age developments.

Meeus's models are quite accurate over about a 150 year interval centered on the late 1980s. Anything outside of that is extrapolation using a model that is not well suited to such extrapolation. To make computations efficient, Meeus used third order polynomials in time, with time expressed in Julian centuries (365.25*86400 seconds) from noon universal time on 1 January 2000. (This is a standard time reference in astronomy.) He developed these third order polynomials as a best fit to higher precision models. Ignoring leap seconds, the errors in sunrise / sunset time should be small, less than a minute, for the next several decades. However, polynomials are not a good model for long term behavior of something that is bounded. Using those models to represent centuries is problematic, and anything beyond centuries is highly problematic.

Leap seconds are also an issue. The Earth's rotation rate is gradually slowing down. Predicting the time of sunrise and sunset is a bit problematic even over the course of multiple decades due to leap seconds. The predicted sunrise and sunset times form year 2099 are probably off by about a minute just because of accumulated leap seconds from the early 1980s to 2099.

I see. in that case, do you have any recommendations of the more modern online sun path calculator? the one that takes leap seconds into account. Thanks

 

[D H]

I see. in that case, do you have any recommendations of the more modern online sun path calculator? the one that takes leap seconds into account. Thanks

There is no way to account for future leap seconds. Regarding better models that those in Meeus's Astronomical Algorithms, something that is based on a long term ephemeris is needed. For example, the JPL Horizons System, http://ssd.jpl.nasa.gov/horizons.cgi, can be used to calculate sunrise and sunset times. However, even those results need to be taken with a grain of salt when used far into the past or future.

 

[jim mcnamara]

Define calculator. A phone app, software?

The JPL DE404 long ephemeris is used to find the position of astronomical features in the past. As @D H explained the Earth does not cooperate in terms of a fixed number of seconds in a day. Generally it is slowing almost imperceptably. Which is a dirty rotten trick So, you cannot project sunrise and sunset accurately in the future or back in time before historical accurate observations.

Short answer: No software can guess when the Earth will play more tricks on us. Leap seconds can be either positive or negative.

The current score is heavily in favor of the Earth over astronomers, note that really accurate timekeeping is complex:

BEFORE THE 2015 LEAP SECOND: GPS-UTC WAS 16 (GPS AHEAD OF UTC BY 16 SECONDS)
AFTER THE 2015 LEAP SECOND: GPS-UTC BECAME 17 (GPS AHEAD OF UTC BY 17 SECONDS)

As of 1 July 2012, and until the leap second of June 30 2015
TAI is ahead of UTC by 35 seconds.
TAI is ahead of GPS by 19 seconds.
GPS is ahead of UTC by 16 seconds.
After June 2015,
TAI is ahead of UTC by 36 seconds.
TAI is ahead of GPS by 19 seconds.
GPS is ahead of UTC by 17 seconds.

TAI is "atomic clock time", a statistical atomic time scale based on a large number of clocks operating at standards laboratories around the world
UTC is Universal Coordinated Time, which is used to regulate clocks (like on a computer),
GPS time is the time of the global positioning system, based on Jan 1, 1980.

http://tycho.usno.navy.mil/leapsec.html

 

[Chronos]

The ancient Greeks and Chinese were able to predict solar eclipses before the common era. You need to be able to fairly accurately predict the apparent path of the sun and moon across the sky with little more than the naked eye to pull that off. Chinese astrologers were known to be beheaded for getting it wrong. Astronomy was a difficult career path even in ancient times.

 

[Trainee Engineering]

sorry, was occupied with something else.
a follow up question, in this case, is it possible to determine sun's position (azimuth and elevation) on certain Earth GPS coordinate for like 10 years from now?
so, azimuth and elevation of the sun on said GPS coordinate in 5-min interval starting from now to 10 years in the future. how big a miss do we anticipate?
thanks

 

[rootone]

I would think on the scale of ten years this can be predicted to very high accuracy, although it would nevertheless be an estimate.
Nothing dramatic is likely to alter in the dynamics of the solar system and in particular the Earth's rotation rate in such a short time.
Just a guess, but I doubt you would start seeing errors on the scale of whole seconds until attempting to predict several hundred years

 

[russ_watters]

sorry, was occupied with something else.
a follow up question, in this case, is it possible to determine sun's position (azimuth and elevation) on certain Earth GPS coordinate for like 10 years from now?
so, azimuth and elevation of the sun on said GPS coordinate in 5-min interval starting from now to 10 years in the future. how big a miss do we anticipate?
thanks

Well, in the Navy I used decades-old tables to predict positions of stars and the sun to small fractions of a degree (or, rather, to use that to calculate the ship's position and heading/calibrate the ship's compass). So I would think you should be able to get closer than a minute of arc over 10 years.

 

[Trainee Engineering]

I see.
right now, I'm using http://keisan.casio.com/exec/system/1224682277
any other good source to get elevation / azimuth for the next 10 years, or maybe more? I definitely can tolerate 1 minute arc per decade miss.
thanks

 

[davenn]

any other good source to get elevation / azimuth for the next 10 years, or maybe more? I definitely can tolerate 1 minute arc per decade miss.

there's a dozen and one astronomy programs out there
a very popular one many of us use is Stellarium you can pick any year month or day ... it just doesn't give a list
if lists are what you want, not sure what to suggest