Well, Shipmates, it took a bit of time but a brilliant and forward thinking PHD student at Cornell University answered my question about keeping local time... enthusiastically I might add.
Below is the entire email exchange; I have taken out the addresses and names for privacy. My initial email is at the bottom.
Read it carefully and give it a go. Approach the astronomy and Ham radio clubs etc in your area to get the ideas flowing.
Although it's a wonderful thing that governments have, for the last few centuries, provided accurate time for the masses, it may be time to relearn the art and technique of time keeping for ourselves and practice disseminating same.
Email exchange:
Excellent question.
I apologize for taking so long to get back to you.
>we desire to decentralize time keeping<
I have the utmost respect for this goal. In the event of a catastrophe, people like you who are prepared will be important for preserving knowledge and information and disseminating it back out to the world at large.
I was surprised that I couldn't find any guides to this by searching on the internet. When you get a working set up, please post it somewhere.
All that you'll need for this project is the location of your observatory, the RA and DEC of a few reference stars (at least one, but more is better), and a way to measure the altitude of one of the reference stars.
Quick caveat, I'll tell you how to get UTC instead of GMT, since UTC is essentially GMT without DST, and I hope that DST does not survive whatever catastrophe we are preparing for in this thought experiment.
1) Measure the altitude of the reference star, the distance from the horizon in degrees.
2) Calculate the Local Sidereal Time (the RA angle currently passing through the local meridian): LST = (90degrees - ALTreferencestar)/(cos(DECreferencestar)cos(latitudeofobservatory))
3) Convert to Greenwich Mean Sidereal Time (GMST, the RA angle currently passing through the prime meridian) using the longitude of the observatory converted into hour angles (15 degrees in an hour, the longitude is the offset of LST from GMST).
4) Convert from GMST to UTC (this is the trickiest part of the calculation, and why it took me so long to get back to you because I had to dig up an old homework from a class I took a while back and re-solve it and double check that my math matched the plots my code produced and I turned in, and I'm pretty sure this is all correct)
To do this properly, we need to calculate the ecliptic longitude (position angle) of the Earth along its orbit, including the eccentricity and argument of periapse of the Earth's orbit, which can influence the result by up to a half-hour.
Going from UTC to GMST is rather straightforward, but the reverse is a transcendental equation that we will have to approximate.
Because I have it on hand (the homework assignment was calculating/plotting an analemma), we'll do this for the Sun instead, which is 180 degrees from the position of the Earth.
From Kepler's 2nd law, to first order in eccentricity, we have:
lambda = lambda_perihelion + n(t-t_perihelion) + 2esin(n(t-t_perihelion))
Where:
n is the average angular rate of the Earth's orbit (~ 0.985647 degrees per day),
e is the Earth's eccentricity (~0.017),
lambda_perihelion is the ecliptic longitude of the Sun at the time of the last perihelion, along the ecliptic (283.59 degrees in 2015),
t_perihelion is the date of the last perihelion (~07:00 UTC on January 4th in 2015)
t is the current date
and lambda is the ecliptic longitude of the sun at the current date
You can also calculate the slight changes of t_perihelion and lambda_perihelion from the precession of the earth's orbit, but that's not going to have a significant impact on your answer for the next few hundred years, so we'll ignore that for now.
Now, to get from lambda to RA and DEC of the sun, we use the following three equations to rotate the sphere of our coordinate system:
sin(DEC) = sin(Epsilon)sin(lambda)
sin(RA) = cos(Epsilon)sin(lambda)/cos(DEC)
cos(RA) = cos(lambda)/cos(DEC)
where Epsilon is the obliquity of the Earth (23.5 degrees)
We need two equations to determine RA because inverse trig functions are multi-valued on a domain that spans multiple quadrants, such as for RA.
Now subtract 180 degrees from the RA of the Sun to get that of the Earth (think: the direction away from the Sun is what's overhead at midnight, which is 0:00 UTC)
Now divide by 15 to go from degrees to hours (15 degrees in an hour)
This is the time, in hours between GMST and UTC, so add it to your GMST value from the previous step to get the time in UTC!
Please let me know if you have any questions, confusion, or think I made a mistake and want me to run back through the math.
And please keep me updated on your progress for implementing this! I'm honestly very interested.
I love doomsday prepping and figuring out how to decentralize our information heap instead of relying on centralized sources.
Let me know how things go,
A***** S* F****
PhD Student
Cornell University
Department of Astronomy and Space Sciences
On Sat, Oct 20, 2018 at 4:17 PM C****** R****> wrote:
Name
j****
Email
Your Background
Curious Person
Subject
Others
Message
John Harrison used the stars and his neighbors chimney to keep track of sidereal time - or so the story goes... What simple and effective astronomy procedure might one use these days to track time locally within a few seconds of GMT in the event access to WWV or other standard clock references are interrupted? I assume it would have something to do with knowing the exact location of the observatory and which best stars and their sidereal hour angles to use throughout the year. The plan for our celestial navigation group is to provide accurate time to the local community in the event of catastrophe; which would no doubt come in handy for marine navigation and other common purposes.. It seems to us that the keeping of time is taken for granted... we desire to decentralize time keeping.
Latest reply to the time-keeping instructions:
A****,
Thank you, and Mr R*****, for providing a wonderfully concise reply to my question about local time keeping. I feel honored.
I have posted your information on the Celestial Navigation forum site where I hope the idea of time keeping will germinate and take root. Here is the address of the thread in question:
https://thenauticalalmanac.com/Forum/sho...666#pid666
Being a Ham Radio enthusiast as well, I plan to approach our local club about disseminating time hacks. And I plan to contact local astronomy clubs to challenge them with your time keeping process. I think the boy-scouts might be interested in providing badges for timekeeping; at least I will address the issue with them.
You and your peers are welcome to contribute to the forum, as your expertise is not common among us.
I will study hard your time keeping instructions and endeavor to create an easy to digest proforma which might render the process accessible to lay persons such as myself. Time is everything.
Thank you again and please feel welcomed at the forum... I am but a contributor; the forum site is run by an individual who seeks to educate and provide pertinent almanacs and publications common to solving Celestial Navigation observations (reductions).
Respectfully
J**
PS Please spread your time keeping process to contacts and websites of which you have interest... I think the concept of democratizing time-keeping is more important than me or any single individual... Most importantly, have fun spreading the word.
Below is the entire email exchange; I have taken out the addresses and names for privacy. My initial email is at the bottom.
Read it carefully and give it a go. Approach the astronomy and Ham radio clubs etc in your area to get the ideas flowing.
Although it's a wonderful thing that governments have, for the last few centuries, provided accurate time for the masses, it may be time to relearn the art and technique of time keeping for ourselves and practice disseminating same.
Email exchange:
Excellent question.
I apologize for taking so long to get back to you.
>we desire to decentralize time keeping<
I have the utmost respect for this goal. In the event of a catastrophe, people like you who are prepared will be important for preserving knowledge and information and disseminating it back out to the world at large.
I was surprised that I couldn't find any guides to this by searching on the internet. When you get a working set up, please post it somewhere.
All that you'll need for this project is the location of your observatory, the RA and DEC of a few reference stars (at least one, but more is better), and a way to measure the altitude of one of the reference stars.
Quick caveat, I'll tell you how to get UTC instead of GMT, since UTC is essentially GMT without DST, and I hope that DST does not survive whatever catastrophe we are preparing for in this thought experiment.
1) Measure the altitude of the reference star, the distance from the horizon in degrees.
2) Calculate the Local Sidereal Time (the RA angle currently passing through the local meridian): LST = (90degrees - ALTreferencestar)/(cos(DECreferencestar)cos(latitudeofobservatory))
3) Convert to Greenwich Mean Sidereal Time (GMST, the RA angle currently passing through the prime meridian) using the longitude of the observatory converted into hour angles (15 degrees in an hour, the longitude is the offset of LST from GMST).
4) Convert from GMST to UTC (this is the trickiest part of the calculation, and why it took me so long to get back to you because I had to dig up an old homework from a class I took a while back and re-solve it and double check that my math matched the plots my code produced and I turned in, and I'm pretty sure this is all correct)
To do this properly, we need to calculate the ecliptic longitude (position angle) of the Earth along its orbit, including the eccentricity and argument of periapse of the Earth's orbit, which can influence the result by up to a half-hour.
Going from UTC to GMST is rather straightforward, but the reverse is a transcendental equation that we will have to approximate.
Because I have it on hand (the homework assignment was calculating/plotting an analemma), we'll do this for the Sun instead, which is 180 degrees from the position of the Earth.
From Kepler's 2nd law, to first order in eccentricity, we have:
lambda = lambda_perihelion + n(t-t_perihelion) + 2esin(n(t-t_perihelion))
Where:
n is the average angular rate of the Earth's orbit (~ 0.985647 degrees per day),
e is the Earth's eccentricity (~0.017),
lambda_perihelion is the ecliptic longitude of the Sun at the time of the last perihelion, along the ecliptic (283.59 degrees in 2015),
t_perihelion is the date of the last perihelion (~07:00 UTC on January 4th in 2015)
t is the current date
and lambda is the ecliptic longitude of the sun at the current date
You can also calculate the slight changes of t_perihelion and lambda_perihelion from the precession of the earth's orbit, but that's not going to have a significant impact on your answer for the next few hundred years, so we'll ignore that for now.
Now, to get from lambda to RA and DEC of the sun, we use the following three equations to rotate the sphere of our coordinate system:
sin(DEC) = sin(Epsilon)sin(lambda)
sin(RA) = cos(Epsilon)sin(lambda)/cos(DEC)
cos(RA) = cos(lambda)/cos(DEC)
where Epsilon is the obliquity of the Earth (23.5 degrees)
We need two equations to determine RA because inverse trig functions are multi-valued on a domain that spans multiple quadrants, such as for RA.
Now subtract 180 degrees from the RA of the Sun to get that of the Earth (think: the direction away from the Sun is what's overhead at midnight, which is 0:00 UTC)
Now divide by 15 to go from degrees to hours (15 degrees in an hour)
This is the time, in hours between GMST and UTC, so add it to your GMST value from the previous step to get the time in UTC!
Please let me know if you have any questions, confusion, or think I made a mistake and want me to run back through the math.
And please keep me updated on your progress for implementing this! I'm honestly very interested.
I love doomsday prepping and figuring out how to decentralize our information heap instead of relying on centralized sources.
Let me know how things go,
A***** S* F****
PhD Student
Cornell University
Department of Astronomy and Space Sciences
On Sat, Oct 20, 2018 at 4:17 PM C****** R****> wrote:
Name
j****
Your Background
Curious Person
Subject
Others
Message
John Harrison used the stars and his neighbors chimney to keep track of sidereal time - or so the story goes... What simple and effective astronomy procedure might one use these days to track time locally within a few seconds of GMT in the event access to WWV or other standard clock references are interrupted? I assume it would have something to do with knowing the exact location of the observatory and which best stars and their sidereal hour angles to use throughout the year. The plan for our celestial navigation group is to provide accurate time to the local community in the event of catastrophe; which would no doubt come in handy for marine navigation and other common purposes.. It seems to us that the keeping of time is taken for granted... we desire to decentralize time keeping.
Latest reply to the time-keeping instructions:
A****,
Thank you, and Mr R*****, for providing a wonderfully concise reply to my question about local time keeping. I feel honored.
I have posted your information on the Celestial Navigation forum site where I hope the idea of time keeping will germinate and take root. Here is the address of the thread in question:
https://thenauticalalmanac.com/Forum/sho...666#pid666
Being a Ham Radio enthusiast as well, I plan to approach our local club about disseminating time hacks. And I plan to contact local astronomy clubs to challenge them with your time keeping process. I think the boy-scouts might be interested in providing badges for timekeeping; at least I will address the issue with them.
You and your peers are welcome to contribute to the forum, as your expertise is not common among us.
I will study hard your time keeping instructions and endeavor to create an easy to digest proforma which might render the process accessible to lay persons such as myself. Time is everything.
Thank you again and please feel welcomed at the forum... I am but a contributor; the forum site is run by an individual who seeks to educate and provide pertinent almanacs and publications common to solving Celestial Navigation observations (reductions).
Respectfully
J**
PS Please spread your time keeping process to contacts and websites of which you have interest... I think the concept of democratizing time-keeping is more important than me or any single individual... Most importantly, have fun spreading the word.