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03/13/2017 – Ephemeris – More thoughts about yesterday’s time change

March 13, 2017 Comments off

Ephemeris for Monday, March 13th.  The Sun will rise at 7:58.  It’ll be up for 11 hours and 48 minutes, setting at 7:46.  The Moon, 1 day past full, will rise at 9:03 this evening.

We are now plunged back into dark mornings like we were two month’s ago thanks to the start of Daylight Saving Time.  However we are only a week from the vernal equinox, the first day of spring here in the northern hemisphere.  However some of my blog followers down under will experience the start of autumn on that day.  For us in the next three months the sunrise time will back down 2 hours, and will rise around 6 a.m.  Our sunset times will advance a bit less than that, an hour and 45 minutes.  The lopsidedness is a consequence of both the Earth’s axial tilt and its slightly elliptical orbit.  We are moving somewhat away from the Sun now and are slowing down a bit.  It’s all kind of hard to explain, but makes perfect sense… eventually.

Times are for the Traverse City/Interlochen area of Michigan. They may be different for your location.

Addendum

Well, I’m going to try to explain it now.

If one visits most observatories, there will be a clock, usually in the dome that doesn’t seem to read the correct time. We have one in Northwestern Michigan College’s Rogers Observatory’s dome. It only agrees with the time on your watch for an instant on October 16th. It’s called a sidereal clock and it measures Earth’s rotation with respect to the stars, and it gains approximately 4 minutes a day compared to our normal clocks which are geared to the Sun.

The Earth and all the planets orbit the Sun in a counterclockwise direction when seen from the north. Also the Earth and most of the planets spin also in a counterclockwise direction. The exceptions are Venus and Uranus. Most large satellites like our Moon also orbit their planets in a counterclockwise direction. From the surface of the Earth these bodies appear to generally move eastward, while the celestial sphere mirror reflects our eastward rotation by appearing to move east to west.

The Sun appears to move about one degree a day eastward. (360° / 365 days = 1° approximately). The Earth rotates through 15° an hour (360°/24 hours = 15° and 60 minutes in an hour / 15 = 4 minutes to rotate a degree). So on average and approximately after the Earth rotates back to the same point with regard to the stars, it has to rotate and extra degree to catch up to the Sun, which takes 4 more minutes, which is why the solar day is 4 minutes longer than a sidereal day. (Well, 3 minutes 55.9084 seconds if you want to get picky about it!)

Of course it’s not that simple. It never is that simple. This would all work out if the Earth orbited the Sun in a uniform circle and the Earth had no axial tilt. The Earth’s tilt is also called obliquity. The Sun would appear to move uniformly over the Earth’s equator. That Sun, called the mean Sun is what we base our solar time on, not the real Sun. However the Earth’s orbit is elliptical, with the Earth moving fastest at its perihelion or closest point to the Sun, around January 3rd, and slowest at aphelion or farthest point around July 4th. Also the Earth’s axial tilt is 23 ½ °, and is only on the equator two days a year March 20th and September 23rd.

Ever see this funny figure 8 in the Pacific Ocean on old globes?

The Analemma

Illustration 1. An Analemma graphically demonstrating the actual Sun’s relation to the mean Sun during the year.

Both eccentricity and obliquity work together to produce the analemma as seen in the diagram below. This figure 8 can actually be photographed in the sky by exposing the same frame of film at regular intervals, or stacking images of the same area of the sky over a year at the same time of day. There are plenty of examples using an Internet search engine to search for analemma images. It is one way to illustrate the equation of time, which is the correction one must make to a sundial reading to get to the correct local mean solar time. To that one must add or subtract one’s offset from the time zone’s time meridian. See Friday’s post.

Cause of the analemma

Illustration 2. How eccentricity of the Earth’s orbit and obliquity combine to affect the analemma. The effects add at the bottom near the winter solstice and subtract near the summer solstice.


The above diagram was taken from Ethan Siegel’s Starts with a Bang blog: http://scienceblogs.com/startswithabang/2010/12/17/celebrate-this-winter-solstice/ which also explains it.

The equation of time can be found in tabular form for easy sundial correction, or in a linear graphical form as seen below.

Equation of Time

Illustration 3. Linear representation of the equation of time

Actually the biggest effect on the equation of time, is especially near the solstices is the Earth’s obliquity (axial tilt). Below we see how the Sun’s declination affects how fast it appears time wise.

Sun crossing time lines

Illustration 4. How the Sun’s declination affects how rapidly it appears to cross time lines (meridians).

Declination of celestial objects is the same as latitude on the Earth. A star whose declination is the same value as one’s latitude will cross at the zenith once a day. In illustration 4 note that the near the solstices the time lines (meridians) are closer together, so the Sun will pass them faster than when near the equinoxes where the time lines are farther apart and the Sun is moving somewhat diagonally, taking longer to cross the time lines. In time only east-west motion counts.

Looking at Illustration 2, I’ve added arrows at the top (northern) and bottom (southern) extremities of each analemma source to give some idea of the Sun’s apparent speed at the solstices. At the bottom, near the December solstice the eccentricity speed of the Sun adds to the obliquity speed increasing the effects at that part of the analemma lobe, making it bigger. At the June solstice end of things eccentricity speed is in the opposite direction, slowing the Sun down.

So what? This affects the dates of the earliest and latest sunrises and sunsets. Here are those dates and time values for us here in northern Michigan (specifically the Interlochen/Traverse City area):

Earliest and Latest Sunrises and Sunsets

Table of Earliest and Latest Sunrises and Sunsets during the year for Interlochen/Traverse City area of Michigan.

All this may make little difference to our modern lives, governed by the atomic clocks in Paris and Fort Collins, Colorado, divorced as they are from the Earth’s actual rotation and the Sun except for the inclusion of the occasional leap second, like we had last December 31st. To folks like me who are amateur astronomers and have (or had in my case)  a day job, it would’ve been nice to have, on the summer solstice, astronomical evening twilight end before midnight.

I hope this helped rather than confused you.  What do you think?  drop me a comment.

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12/31/2016 – Ephemeris year end

December 31, 2016 Comments off

No radio program today, being the weekend, so at the end of the calendar page below are the stats for today, the 31st.  This is the form of the calendar that I have on my Ephemeris website, which I update monthly.  It was created with the same data that the first portion of my program is generated from.  I have yearly calendars for 6 communities in the Interlochen Public Radio area in northwestern lower Michigan, and 1 in the U.P.  (That’s the Upper Peninsula, if you’re not from around here.)

You will have to hold off your New Years festivities for a bit tonight.  Not long, just one second.  Today, December 31st, 2016 will be 24 hours and 1 second long.  This “leap second” will be added as the 61st second of the minute 6:59 p.m. EST (23:59 UT).  The reason is that the Earth’s rotation is slowing down ever so slightly, compared to the atomic clocks at the Bureau of Time.  There is some discussion of eliminating this leap second.  Most scientists want to use a constant time stream, and don’t give a hang about the rotation of the Earth.  The positions of the Earth, Moon and the other planets would be incorrect if we used time strictly based on the Earth’s rotation.  Atomic time which is also affected by special and general relativity is used by GPS navigation satellites.  A one second jump in time, at our latitude (45° north) is equivalent of the earth’s rotation of about two tenths of a mile.  I hope everyone’s coordinated on this.

Ephemeris of Sky Events for Interlochen/TC

December, 2016 – Local time zone: EST
Date Sun Twilight* Moon Illum
Rise Set Hours End Start Phase R/S** Time Fractn
Thu 1 08:00a 05:03p 09:03 06:48p 06:15a Set 07:10p 6%
Fri 2 08:01a 05:03p 09:01 06:47p 06:16a Set 08:02p 11%
Sat 3 08:02a 05:02p 09:00 06:47p 06:17a Set 08:59p 18%
Sun 4 08:03a 05:02p 08:58 06:47p 06:18a Set 09:59p 26%
Mon 5 08:04a 05:02p 08:57 06:47p 06:19a Set 11:02p 36%
Tue 6 08:05a 05:02p 08:56 06:47p 06:20a Set 12:08a 46%
Wed 7 08:06a 05:02p 08:55 06:47p 06:21a F Qtr Set 01:16a 57%
Thu 8 08:07a 05:02p 08:54 06:47p 06:22a Set 02:26a 68%
Fri 9 08:08a 05:02p 08:53 06:47p 06:22a Set 03:39a 78%
Sat 10 08:09a 05:02p 08:52 06:47p 06:23a Set 04:53a 87%
Sun 11 08:10a 05:02p 08:51 06:48p 06:24a Set 06:08a 94%
Mon 12 08:11a 05:02p 08:51 06:48p 06:25a Set 07:21a 98%
Tue 13 08:12a 05:02p 08:50 06:48p 06:26a Full Rise 05:18p 100%
Wed 14 08:12a 05:02p 08:49 06:48p 06:26a Rise 06:17p 98%
Thu 15 08:13a 05:02p 08:49 06:49p 06:27a Rise 07:21p 94%
Fri 16 08:14a 05:03p 08:48 06:49p 06:28a Rise 08:28p 88%
Sat 17 08:14a 05:03p 08:48 06:49p 06:28a Rise 09:35p 80%
Sun 18 08:15a 05:03p 08:48 06:50p 06:29a Rise 10:41p 70%
Mon 19 08:16a 05:04p 08:48 06:50p 06:29a Rise 11:44p 61%
Tue 20 08:16a 05:04p 08:48 06:51p 06:30a L Qtr Rise 12:46a 51%
Wed 21 08:17a 05:05p 08:48 06:51p 06:30a Rise 01:46a 41%
Thu 22 08:17a 05:05p 08:48 06:52p 06:31a Rise 02:45a 32%
Fri 23 08:18a 05:06p 08:48 06:52p 06:31a Rise 03:43a 24%
Sat 24 08:18a 05:07p 08:48 06:53p 06:32a Rise 04:40a 16%
Sun 25 08:18a 05:07p 08:48 06:53p 06:32a Rise 05:37a 10%
Mon 26 08:19a 05:08p 08:49 06:54p 06:32a Rise 06:33a 5%
Tue 27 08:19a 05:09p 08:49 06:55p 06:33a Rise 07:26a 2%
Wed 28 08:19a 05:09p 08:50 06:55p 06:33a Rise 08:16a 0%
Thu 29 08:19a 05:10p 08:50 06:56p 06:33a New Set 05:57p 1%
Fri 30 08:19a 05:11p 08:51 06:57p 06:34a Set 06:53p 3%
Sat 31 08:20a 05:12p 08:52 06:58p 06:34a Set 07:52p 7%
* Astronomical Twilight
** Moonrise or moonset, whichever occurs between sunset and sunrise

The far right column of the table, the Moon’s illuminated fraction, may or may not appear in the calendar above depending on you browser or screen size.  It is correct on the Ephemeris website.

12/30/2016 – Ephemeris – Looking ahead at the eclipses of 2017

December 30, 2016 2 comments

Ephemeris for Friday, December 30th.  The Sun will rise at 8:19.  It’ll be up for 8 hours and 51 minutes, setting at 5:11.  The Moon, 1 day past new, will set at 6:53 this evening.

Looking ahead at astronomical events of the 2017.  There is one big one that all of us astronomers, both amateur and professional are looking forward to.  That is the total eclipse of the Sun on August 21st, where the center of the Moon’s shadow will sweep across the continental United States from Oregon to South Carolina.  The closest this path of totality will get to our area is around Carbondale, Illinois.  For the Grand Traverse area the Sun will be some 75% covered by the Moon.  As kind of a warm up event, we’ll have a slight eclipse of the Moon February 10th, where the Moon will enter the Earth’s outer partial shadow, nearly grazing the Earth’s inner shadow in the early evening.  It’s called a penumbral lunar eclipse.

Times are for the Traverse City/Interlochen area of Michigan. They may be different for your location.

Addendum

 

February 10, 2017 Penumbral Eclipse of the Moon

This is the maximum of the February 10th penumbral lunar eclipse. The Moon will appear to move diagonally down to the left. It is shown at maximum eclipse at 7:45 p.m. (0:45 UT February 11). Created using Cartes du Ciel.

Shadows are, of course, invisible unless they are cast on an object, so the Moon would appear alone, though the upper left part of it would be noticeably dimmer than the opposite side.

August 21, 2017 Total Solar Eclipse Path of Totality

A screen cap of the map showing the path of totality of the August 21, 2017 total solar eclipse from NASA’s eclipse page. Credit: NASA and Google Maps.  Click on image to enlarge.

Click here to go to the page where this interactive map is located.  The magenta marker with GD is the point with the greatest duration of totality of 2 minutes 40.2 seconds.  The green marker with GE denotes where the Moon’s umbral shadow is the widest.  Clicking on any point on the map will pop a balloon shows all the eclipse information for viewing it from that place.  The partial eclipse can be seen from all fifty states, though in Hawai’i the Sun rises with the eclipse in progress.

Here in the Grand Traverse Region, the Moon will encroach on about 8/10ths of the Sun’s diameter, covering 75% of the Sun’s face.

Maximum eclipse in Traverse City

What the maximum eclipse would look like with proper filtering at Traverse City, MI. Created using Stellarium.

Eclipse Times for Traverse City

Eclipse Starts 12:58:03 p.m.
Maximum Eclipse 2:20:15 p.m.
Eclipse Ends 3:40:51 p.m.
Magnitude of the eclipse 0.798
Obscuration of the Sun 75.1%

Solar Corona

This is an inkling of what a totally eclipsed Sun looks like. No photograph can do it justice. Ya gotta be there! The solar corona displayed during the July 10, 1972* total solar eclipse from Prince Edward Island. Credit Bob Moler.

* Update:  Thanks for the heads up on the typo: NationalEclipse.com.

Program Note:

I’ve developed a PowerPoint slide presentation highlighting my four total eclipses and a look at future eclipses.  I will be happy to give this presentation to school groups and organizations free of charge except for mileage reimbursement over 50 miles.  Contact me at bob@bjmoler.org.

December 31st – the longest day, really.

December 31st will be 24 hours and 1 second long.  This “leap second” will be added as the 61st second of the minute 6:59 p.m. EST (23:59 UT).  The reason is that the Earth’s rotation is slowing down ever so slightly, compared to the atomic clocks at the Bureau of Time.  There is some discussion of eliminating this leap second.  Most scientists want to use a constant time stream, and don’t give a hang about the rotation of the Earth.  The exact time which is also affected by special and general relativity is used by GPS navigation satellites.  A one second jump in time, at our latitude (45° north) is equivalent of the earth’s rotation of about two tenths of a mile.  I hope everyone’s coordinated on this.

02/06/2012 – Ephemeris – It’s about Time

February 6, 2012 Comments off

Ephemeris for Monday, February 6th.  The sun will rise at 7:55.  It’ll be up for 10 hours and 1 minute, setting at 5:57.   The moon, 1 day before full, will set at 7:21 tomorrow morning.

What time is it?  Don’t bother to check.  This time It’s a rhetorical question.  The basis of time keeping has always been astronomical.  Astronomers almost lost it last month.  There are now two time scales.  Universal Time, that’s roughly in sync with the earth’s rotation and Atomic Time, which uses the vibrations of cesium atoms which are set to count seconds of the length they were in 1900.  Thanks mostly to the moon and the drag of the tides the earth is slowing its rotation.  The difference between the two time scales is over a minute, accumulated over that past 112 years.  Universal Time has been tied to  the earth’s rotation by the occasional addition of a leap second every year or two.  The next leap second will be added on June 30th.

* Times are for the Traverse City/Interlochen area of Michigan.  They may be different for your location.