Time and Chart Calculation
Part 5: Chart Calculation Course
Hi Everyone,
Here is part 5 of the chart calculation series. I needed to talk more about time for my own learning purposes, so that is what this article is about. Hopefully, it provides helpful context for you and others. In the next article, we'll continue with the chart calculations.
Anticipating the next article, the final time calculation step we’ll be doing involves dividing (and possibly multiplying) with degrees, minutes, and seconds (DMS). You can use calculators for that, but if you don’t know how to do it by hand and would like to learn, I’ve posted how-to videos on my Patreon page*. They are public posts, so are freely available. There are three videos on the page, one covering how to divide with DMS, one on how to multiply, and one on how to convert DMS to decimal degrees and the other way around.
[*Update Sept 11, 2023: I have taken down my Patreon page (it just never felt like the right fit) and have uploaded everything onto my Youtube channel. I am still in the process of making videos public, but you can visit my Youtube channel and it will be visible at some point. I am sorry for the inconvenience, but thank you for understanding.]
I recommend taking the time to learn if you don’t already know how to do it, even if, in practice, you rely on calculators. I didn’t know how to do it and learning has helped to improve my sense of competence, confidence, and security, even though I currently rely on calculators for most of my work.
For more on time, see part 2 of the series, Why Do Charts Need to Be Calculated? and the video portion of part 4, Overview of the Chart Calculation Process & First Steps. I have included links to the rest of the articles in the series at the end.
Two Ways to Measure Solar Time
As talked about in part 2 of the introduction, Why Do Charts Need to Be Calculated? solar time is determined by measuring the Earth's relationship with the Sun. In relatively recent times, people have used a couple of different ways to record time based on this relationship. One way that was used in the 19th century was Local Mean Time. Another way that was used through the first half or so of the 20th century was Greenwich Mean Time, a specific variation of Local Mean Time.1
Since then, more precise ways have been found to measure mean solar time. But these other methods rely, initially, on reference points other than the Earth-Sun relationship. So, while they are technically measures of it, their starting points are different.
For the purposes of calculating charts by hand, understanding the two relatively recent but previous ways that have been used to measure time can be helpful. I’ll talk about these below and then briefly touch on four other kinds of time measurement that might be helpful to know about.
Local Mean Time (LMT)
Local Mean Time is the measurement of the Sun’s apparent passage through the sky for one day and night. To determine the duration of this passage, the Sun’s transit over a local meridian, averaged over time, is used as a reference point.2 Time is then measured by breaking up into 24 equal segments the span between one transit over the meridian to the next, with each segment broken further into 60 minute segments.3
Thus, to find the time in New York using Local Mean Time, it would be a matter of tracking the Sun's passage over New York's meridian and working out the time from there. For Tokyo, it would be a matter of working out the time based on Tokyo's meridian. And for Nairobi, it would be a matter of tracking the Sun's passage over Nairobi's meridian. And so on for other locations around the globe, big or small, near or far.
The challenge with using Local Mean Time is that there is no standard time. Each location would set their clocks independently of every other location. Thus, clock time could be different for towns not very far apart from one another. This reality became an issue in the late 19th century when people wanted to coordinate transportation between different places.4
From a chart calculation perspective, if LMT is used to record an event time and it is the only means available for measuring time, then there would be no standard time one could use to make time adjustments. To take our Virgo New Moon, if LMT had been used to record the event date and time, and it had been the only way of keeping time, then we could not have relied on a standard time measurement and corresponding offset to convert the time to Greenwich Mean Time. Thus, we would have needed to find some other way to make the conversion.
Greenwich Mean Time (GMT)
Greenwich Mean Time (GMT) is the Local Mean Time for Greenwich, England. The longitude used to calculate its time is the meridian that runs through Greenwich. To solve the time coordination issue, this meridian was designated as 0 degrees of longitude, called the Prime Meridian, and used as the basis for creating time zones.5
Starting with the Prime Meridian, longitude lines were spaced around the globe.6 Cities and towns then synced their clocks with the time for the longitude that defined their time zone. The time for this shared longitude was, in turn, set relative to Greenwich Mean Time.7
Thus, locations no longer used the meridian for their specific location to determine time. Instead, they relied on the relationship between the time for the time zone in which they resided and Greenwich Mean Time. Today, we still use this system, but different methods are used to calculate Greenwich Mean Time.
For chart calculation purposes, the system of timekeeping based on Greenwich Mean Time allows us to rely on time zone standards to convert event dates and times to GMT. From there, we can find the sidereal time, which is the kind of time we need in order to calculate planet and house cusp positions.
But there’s a problem. Converting the event date and time to its Greenwich sidereal time equivalent is an intermediate step, not the final step. We still need to find sidereal time for the event location, not Greenwich, and we need to find it for the specific location of the event, not the general time zone in which the location falls. If, up until now, we have relied for our calculations for the Virgo New Moon on time zone standards, we will need to figure out a way to convert the time back to Los Angeles itself, not to the time zone in which Los Angeles resides.
To make sense of the question of how to convert the Greenwich sidereal time for an event back to its original location when initially using GMT, and also get an idea of how it might be possible to calculate charts using LMT, we need to look at the correlation between time and longitude.
How Longitude and Time Are Related
One thing that LMT and GMT have in common is that they both use longitude to measure time. In the case of LMT, the local longitude is used. In the case of GMT, a universal longitude is used. Thus, the solution for the chart calculation issue relating to GMT and also the one relating to LMT can be found by looking at longitude.
As the history of using longitude to determine time shows, there is a correlation between longitude and time. I talked about this correlation in the video portion of the previous lesson, so it may help to watch that, but I’ll go into some more detail here.8
Because the Earth is a sphere, its circumference, like circumferences for all spheres, is 360 degrees. That means that when the Earth completes one full rotation through night and day, it rotates 360 degrees.9 But how do we find the point that marks the start and end?
From the vantage point of the Earth, it looks like the Sun moves around the Earth. Thus, we could say that, over the course of one night and day, the Sun travels 360 degrees. To mark the start and end points of the Sun’s daily transit cycle, we can create imaginary lines (longitudes) around the globe, and then note when the Sun passes over the line of a given location when it is highest in the sky, and then note it again the next time it passes over.
We can then assign a number to how long the Sun’s transit took from one passage to the next. The number we use is 24, and the units are hours. Thus, we say that there are 24 hours in a day. We already established that the Sun travels 360 degrees during its apparent transit around the Earth over the course of one day, or 24 hours. Thus, for the Sun to travel 360 degrees, it takes 24 hours. We can use this correlation to determine how many degrees the Sun travels in one hour by dividing 360 degrees by 24 hours. When we do that, we get:
360 arc degrees / 24 hours = 15 arc degrees per hour10
Thus, in one hour of time, the Sun appears to travel 15 degrees of longitude.11 Practically, if we tracked sunrise across the globe, we would see that every hour, the Sun rises 15 degrees away from where it rose the hour before.12
Although all of the correlations above are rough estimates because, in reality, there are so many factors involved, we can use this information to help us find time. If we were working with an event date and time recorded using LMT, we could, presumably, use this correlation to help us find the date and time in Greenwich, England, for an event.13 And when working with standard GMT time zones, we could use the correlation to help us convert the Greenwich sidereal date and time for an event back to the specific location. We’ll do that in the next article.
Next, I’ll briefly explain the current ways of tracking time that I know about. The descriptions below represent my best understanding, but the topic is complex and I may need to revise my descriptions at some point as I learn more.
Universal Time (UT)
When using astro.com’s ephemerides, you’ll find in the top right corner of each page that there is a notation that reads, “00:00 UT”. This notation indicates that their ephemerides are calculated for midnight, Universal Time (UT).
Universal Time (UT) is an indirect, but more precise way of measuring mean solar time. Instead of relying on the (apparent) path of the Sun, calculating UT relies on stars for measuring the start and end points of one rotation of the Earth. Thus, it is a form of sidereal time but is used to more accurately measure solar time.14 Neil F. Michelsen, in his book, The Koch Book of Tables, writes that UT “is the twenty-four-hour clock version of Greenwich Mean Time”.15 Thus, for practical purposes, they are interchangeable.16 Michelsen also mentions that it is a measure of the Earth’s rotation,17 thus confirming that it is a measurement of sidereal time, not of the Sun’s apparent path in relationship to the Earth, or solar time.
Atomic Time (TAI)
Atomic Time, or International Atomic Time, measures the frequency of energy transfer in an atom of cesium that results when flooded with microwaves. This frequency is precise and stable over long periods of time. By counting the number of energy transfers, or oscillations, in a second, it is possible to measure the duration of a second to a fine degree, thus making Atomic Time extremely accurate.18
Universal Coordinated Time (UTC)
Universal Coordinated Time (UTC) is a way of measuring time that relies on input from numerous atomic clocks around the globe. This input is then reconciled to provide one time output. Currently, clocks around the world are set according to UTC. However, because atomic time does not account for irregularities in the Earth’s movement, UTC has to be adjusted every so often to align it with mean solar time.19
Ephemeris Time (ET)
According to Michelsen in his book, The Koch Book of Tables, Ephemeris Time (ET) measures the rotation of the Earth as if there were no variations in its motion. Thus, it is an idealized version of Universal Time. He also notes that newer ephemerides use Ephemeris Time because it is more appropriate than Universal Time for the kinds of calculations needed to determine planet positions.20 In his book, The American Ephemeris for the 21st Century, he informs that Ephemeris Time was used to calculate planet positions in that version of the ephemeris but that Universal Time was used for the 20th century version, The American Ephemeris for the 20th Century.21
Conclusion
That’s it for time. My hope and intention in talking about this subject has been to provide context for what we’re doing when we calculate charts so we’re not just crunching numbers without some understanding. Also, I wanted to introduce some of the types of time you might encounter to head off some unnecessary confusion. I remember many years back when first looking at the astro.com ephemerides having no clue what UT was. It helped to have a little understanding.
Ways You Can Support Me
I am, happily, starting to take myself more seriously and, with that, am introducing ways that people can support me in this work. Below are some of the ways currently possible, both free and paid. I appreciate your support immensely, in whatever ways that feel right for you.
Free ways to support me
Subscribe to this newsletter if you haven’t already (there is a free tier). It is wonderful to know people are interested in my articles and other posts.
Recommend and share my newsletters with others you think would appreciate and benefit from it. I enjoy sharing what I learn so it is wonderful to know that their are people who value what I share.
Click the like button and/or leave a comment, if you appreciate a post. I love knowing that my posts are appreciated and beneficial in some way.
More ways to come!
Paid ways to support me
[Update September 17, 2023: I have decided not to go down the affiliate route so I have closed my bookshop and am no longer an affiliate of Notion. I still highly recommend bookshop.org as a place to buy books and Notion as a fantastic online workspace. I will likely be creating videos on how to use Notion in the future.]
Consider becoming a paid subscriber if you appreciate what I share. Your support means the world.
Purchase books via my Astrology Journal Bookshop. My bookshop is an affiliate of Bookshop.org, so when you use the link I’ve provided and purchase a book from my shop, you support both me and independent booksellers. I am deeply thankful for your patronage.
Use the Notion badge below or this link if you would like to open a Notion account at one of their paid levels. Notion is a powerful and versatile online creative space for capturing ideas, managing projects, creating tools, and generally organizing your life if you’d like to use it that way. I use Notion to organize my projects, keep track of ideas, and create tools to help me do my work. I am now an affiliate so your purchase supports me in doing this work!
More ways to come!
Related Posts
Below are links to the previous posts in the chart calculation series:
Part 1
Part 2
Part 3
Part 4
Updates
August 22, 2023: I changed the image thumb for the article from a blue vector globe to a map of the US showing latitude and longitude lines.
References
Barss, K. (2020, August 24). Time Zone Origins. Infoplease.com. https://www.infoplease.com/calendars/history/time-zone-origins
Bikos, K. (n.d.). What Is Local Mean Time? timeanddate.com https://www.timeanddate.com/time/local-mean-time.html#:~:text=Local%20Mean%20Time%20(LMT)%20is,Sundials%20show%20true%20solar%20time.&text=A%20sundial%20shows%20the%20true%20or%20apparent%20solar%20time.
Bikos, K., & Buckle, A. (n.d.). International Atomic Time. timeanddate.com. https://www.timeanddate.com/time/international-atomic-time.html
Bikos, K., Buckle, A., & Hocken, V. (n.d.). How Many Time Zones Are There? timeanddate.com. https://www.timeanddate.com/time/current-number-time-zones.html
Bikos, K., & Jones, G. (n.d.). What Is Universal Time (UT)? timeanddate.com. https://www.timeanddate.com/time/universal-time.html
Devlin, K. (1999, December). About Time. Devlin’s Angle, Mathematical Association of America. https://www.maa.org/external_archive/devlin/devlin_12_99.html
Michelsen, N. F. (2005). The American Ephemeris for the 21st Century: 2000 to 2050 at Midnight (Revised 2nd ed.). ACS Publications.
Michelsen, N. F. (1984). The Koch Book of Tables. ACS Publications, Inc.
NASA. Time Zones and Universal Time. (n.d.). NASA Eclipse Website. https://eclipse.gsfc.nasa.gov/SEhelp/TimeZone.html
Royal Museums Greenwich. (n.d.) What is Greenwich Mean Time (GMT) - and Why Does It Matter? (n.d.). https://www.rmg.co.uk/stories/topics/greenwich-mean-time-gmt
Ward, K. (n.d.). Astrology: Calculating the Chart - UT or GMT. Ken Ward’s Astrology Pages, Trans4mind.com. https://trans4mind.com/personal_development/astrology/Calculations/calcGMT.htm
Notes
According to the Royal Museums Greenwich article, What is Greenwich Mean Time?, mean time is solar time averaged out over time. Because solar time varies, mean time is used to make time predictable.
See Bikos’ article, What Is Time?
In his article, About Time, Devlin talks about the relationship between time and distance, but does so as it relates to the rotation of the Earth. I am applying this understanding to the apparent transit of the Sun.
See Barss’ article, Time Zone Origins. Also see the Royal Museums Greenwich article, Bikos’ solo-authored article, and Devlin’s article.
See the Royal Museums Greenwich article. Also see Barss’ article and Devlin’s article.
In the video portion of the previous lesson, Overview of the Chart Calculation Process and First Steps, I said that there were 24 times zones. Devlin says the same in his article. Ideally, this would be the case, each spaced 15 degrees apart. But, according to the article by Bikos, Buckle & Hocken, How Many Time Zones Are There?, to accommodate borders and boundaries, the lines are not equidistant and there are more than 24. Barss also addresses this issue.
See the articles by Barss, Devlin, and the Royal Museums Greenwich.
See footnote 6 for a correction regarding the video portion for the previous lesson.
See Devlin. Also see Barss.
The formula for the relationship between time and longitude, as I have written it, represents my effort to work out the equation for myself and make it as clear as possible for others.
See Devlin for a discussion on the mathematical relationship between time and longitude. Also see footnote 3 above. Barss also briefly goes over the math.
I had in mind the diagram and accompanying explanation in Ward’s article, Astrology: Calculating the Chart - UT or GMT, when thinking about the idea of tracking sunrise across the globe.
I first learned about using Local Mean Time to calculate charts from Ward’s article, although he was not using a chart for an event recorded when LMT was being used. Instead, he was showing a way to convert the standard time for an event to GMT by using the local longitude. Thus, it is not clear to me if there would be additional factors to consider than those covered by Ward when making time adjustments when no standard time was in effect. But since, according to Devlin, going back centuries, sailors used local time to figure out their longitude at sea, I assume it would also be possible to convert time for events recorded when LMT was in effect.
See Bikos’ & Jones’ article, What Is Universal Time?. Also see NASA’s article, Time Zones and Universal Time.
Michelsen, The Koch Book of Houses, p. 4.
Michelsen, The Koch Book of Houses, p.4. NASA, in its article, Time Zones and Universal Time, also indicates that measurement results using UT and GMT track closely with one another and can be regarded as interchangeable.
Michelsen, The Koch Book of Houses, p. 5.
See Devlin for a helpful explanation of Atomic Time. Also see Bikos’ & Buckle’s article, What Is International Atomic Time (TAI)?
See Bikos’ & Buckle’s article. Also see NASA’s article.
See Michelsen’s book, The Koch Book of Houses, p.5.
See Michelsen’s book, The American Ephemeris for the 21st Century: 2000 to 2050 at Midnight, Revised 2nd ed. See the section towards the front of the book titled Introduction.