Summer Solstice Calculation Questions

I was playing around with Starry Night Pro 5, and I thought I'd see if
I could determine the exact time of the summer solstice by watching
the solar coordinates. With SNP, you can select the sun, bring up an
info panel, and then watch the RA and Dec change as you run through
the clock time at the speed of your choice. I saw some things that I
can't explain, and I hope somebody here can help me.

First, in case my problem is with fundamental knowledge, tell me if
I'm wrong about any of these assumptions:

1) The solstice occurs when the sun reaches its maximum declination of
the year, which should be around 23.5 degrees N. The declination
never decreases between the vernal equinox and the summer solstice,
and never increases between the summer solstice and the autumnal
equinox.

2) The sun's RA at the solstice should be very close to 6 hours, but
since the RA is defined by the vernal equinox rather than the
solstice, the solstice may not occur at exactly 6 hours.

3) The sun's RA and Dec do not depend on my location, so if I read in
an almanac that the solstice occurred on June 21 at 8:26 AM EDT, I
need only correct for my time zone, rather than fractions of a time
zone (as I would if I were trying to calculate my local sunrise, for
example).

4) SNP has two sets of RA/Dec coordinates in its info panel, one
labeled J2000, and one labeled JNow. I assume that JNow will be more
accurate for current observations.

OK, assuming all that is correct, here is what I found. All times are
EDT.

1) On June 21, the maximum RA reached was 23 degrees and 26.386
minutes. This was maintained from 2:00 PM to 3:16 PM EDT. The
almanac says the solstice should have been at 8:26 AM EDT.

2) When I ran the time backward from there, the declination slowly
decreased, but it hit a minimum (when it was 23deg 26.314') that
lasted from 2:03 AM to 3:39 AM of June 21, then it began to increase
as I went farther back. It peaked at 23deg 26.332' from about 7:37 PM
to 8:20 PM of June 20, and steadily decreased as I went earlier than
that..

So if SNP is correct, there were three solstices, i.e. a max on both
the 20th and 21st, and a local min between them. I could understand
if round-off errors produced fluctuations right around the true
solstice, but I can't understand
a) the absolute max being nearly six hours off the published time,
and
b) apparently smooth progressions between two maximums nearly a day
apart.

Any explanations, or pointers to URLs, appreciated.

The oldest European monument standing is an astronomical clock which
registers the mid-point between the Sept/Mar Equinoxes.

http://www.iol.ie/~geniet/eng/newgrang.htm

The builders constructed the roofbox to register the midpoint
(solstice) at exactly the same time each year at roughly 9:11 AM each
and every year.

Now,the Ra/Dec system is based on 3 years of 365 days and 1 year of 366
days hence it is impossible to construct a monument like the solstice
marker of Newgrange based on the calendar system.

Astronomy and timekeeping,being a Universal heritage of humanity,has
descended so far from the careful reasoning of those people of
Newgrange,Stonehenge,the pyramid builders,the Ptolemaic astronomers and
the heliocentric astronomers.The great intutive insights which balance
the intutive with the observational faculties are now almost lost .

In short,if you believe a computer program (an observational
convenience) can substitute for astronomy and its insights,it ain't
astronomy you are doing.


wrote:
I was playing around with Starry Night Pro 5, and I thought I'd see if
I could determine the exact time of the summer solstice by watching
the solar coordinates. With SNP, you can select the sun, bring up an
info panel, and then watch the RA and Dec change as you run through
the clock time at the speed of your choice. I saw some things that I
can't explain, and I hope somebody here can help me.

First, in case my problem is with fundamental knowledge, tell me if
I'm wrong about any of these assumptions:

1) The solstice occurs when the sun reaches its maximum declination of
the year, which should be around 23.5 degrees N. The declination
never decreases between the vernal equinox and the summer solstice,
and never increases between the summer solstice and the autumnal
equinox.

2) The sun's RA at the solstice should be very close to 6 hours, but
since the RA is defined by the vernal equinox rather than the
solstice, the solstice may not occur at exactly 6 hours.

3) The sun's RA and Dec do not depend on my location, so if I read in
an almanac that the solstice occurred on June 21 at 8:26 AM EDT, I
need only correct for my time zone, rather than fractions of a time
zone (as I would if I were trying to calculate my local sunrise, for
example).

4) SNP has two sets of RA/Dec coordinates in its info panel, one
labeled J2000, and one labeled JNow. I assume that JNow will be more
accurate for current observations.

OK, assuming all that is correct, here is what I found. All times are
EDT.

1) On June 21, the maximum RA reached was 23 degrees and 26.386
minutes. This was maintained from 2:00 PM to 3:16 PM EDT. The
almanac says the solstice should have been at 8:26 AM EDT.

2) When I ran the time backward from there, the declination slowly
decreased, but it hit a minimum (when it was 23deg 26.314') that
lasted from 2:03 AM to 3:39 AM of June 21, then it began to increase
as I went farther back. It peaked at 23deg 26.332' from about 7:37 PM
to 8:20 PM of June 20, and steadily decreased as I went earlier than
that..

So if SNP is correct, there were three solstices, i.e. a max on both
the 20th and 21st, and a local min between them. I could understand
if round-off errors produced fluctuations right around the true
solstice, but I can't understand
a) the absolute max being nearly six hours off the published time,
and
b) apparently smooth progressions between two maximums nearly a day
apart.

Any explanations, or pointers to URLs, appreciated.

On Fri, 28 Jul 2006 10:22:21 -0700, wrote:
1) The solstice occurs when the sun reaches its maximum declination of
the year, which should be around 23.5 degrees N. The declination
never decreases between the vernal equinox and the summer solstice,
and never increases between the summer solstice and the autumnal
equinox.

Correct, for half the year. You can include the whoile year by going
solstice-to-solstice: the Sun increases in dec from winter solstice to
summer solstice, decreases from summer solstice to winter solstice.
The appropriate equinoxes occur in between.

2) The sun's RA at the solstice should be very close to 6 hours, but
since the RA is defined by the vernal equinox rather than the
solstice, the solstice may not occur at exactly 6 hours.

True for times off a chart's given epoch. By definition though, 0h is
the intersection of the equator and the ecliptic, and the
intersections of the ecliptic with the 6, 18, and 12 hour circles mark
the equioxes and solstices.

3) The sun's RA and Dec do not depend on my location, so if I read in
an almanac that the solstice occurred on June 21 at 8:26 AM EDT, I
need only correct for my time zone, rather than fractions of a time
zone (as I would if I were trying to calculate my local sunrise, for
example).

The RA and dec do depend on your location. However, given the diameter
of the Earth, it's really, really, miniscule. The solsitces and
equinoxes take the alignments of the centers of the bodies. Your
parallax off of that will vary.

4) SNP has two sets of RA/Dec coordinates in its info panel, one
labeled J2000, and one labeled JNow. I assume that JNow will be more
accurate for current observations.

Those are the epochs. The great circle equator rotates around the sky
as the earth's axis wobbles over 25,600 years. That's enough to cause
errors when using large magnifications in telescopes. Typically,
standard epocjs are given every 50 years. 1950 was a common epoch
until halfway to 2000 (1975), when it became less accurate, but more
available because of already-preinted charts. Software can now display
wahtever epoch you like, down to real-time (now).

OK, assuming all that is correct, here is what I found. All times are
EDT.

1) On June 21, the maximum RA reached was 23 degrees and 26.386
minutes. This was maintained from 2:00 PM to 3:16 PM EDT. The
almanac says the solstice should have been at 8:26 AM EDT.

2) When I ran the time backward from there, the declination slowly
decreased, but it hit a minimum (when it was 23deg 26.314') that
lasted from 2:03 AM to 3:39 AM of June 21, then it began to increase
as I went farther back. It peaked at 23deg 26.332' from about 7:37 PM
to 8:20 PM of June 20, and steadily decreased as I went earlier than
that..

So if SNP is correct, there were three solstices, i.e. a max on both
the 20th and 21st, and a local min between them. I could understand
if round-off errors produced fluctuations right around the true
solstice, but I can't understand
a) the absolute max being nearly six hours off the published time,
and
b) apparently smooth progressions between two maximums nearly a day
apart.

Any explanations, or pointers to URLs, appreciated.

Dunno offhand. Difference in epochs?

=============
- Dale Gombert (SkySea at aol.com)
122.38W, 47.58N, W. Seattle, WA
http://flavorj.com/~skysea

SkySea wrote:
2) The sun's RA at the solstice should be very close to 6 hours, but
since the RA is defined by the vernal equinox rather than the
solstice, the solstice may not occur at exactly 6 hours.

True for times off a chart's given epoch. By definition though, 0h is
the intersection of the equator and the ecliptic, and the
intersections of the ecliptic with the 6, 18, and 12 hour circles mark
the equioxes and solstices.

No, I think the original poster was right: The vernal equinox is at 0h,
but the autumnal equinox and the solstices are all based on properties
of the ecliptic and the celestial equator. So the autumnal equinox is
when the ecliptic crosses the equator going southward, and the solstices
are the two points where the Sun's declination is at one of its two
extremes.

I have no explanation for the bizarre behavior of SNP, though.

--
Brian Tung
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.html

wrote:
I was playing around with Starry Night Pro 5, and I thought I'd see if
I could determine the exact time of the summer solstice by watching
the solar coordinates. With SNP, you can select the sun, bring up an
info panel, and then watch the RA and Dec change as you run through
the clock time at the speed of your choice. I saw some things that I
can't explain, and I hope somebody here can help me.

First, in case my problem is with fundamental knowledge, tell me if
I'm wrong about any of these assumptions:

1) The solstice occurs when the sun reaches its maximum declination of
the year, which should be around 23.5 degrees N. The declination
never decreases between the vernal equinox and the summer solstice,
and never increases between the summer solstice and the autumnal
equinox.

The standard definition of the equinoxes and the solstices are actually
in terms of the apparent geocentric *longitude* of the sun, not in terms
of declination. Summer solstice happens when the sun's geocentric
longitude is exactly 90 degrees. (This happens to be equivalent to
RA = 6h.)

2) The sun's RA at the solstice should be very close to 6 hours, but
since the RA is defined by the vernal equinox rather than the
solstice, the solstice may not occur at exactly 6 hours.

No; see above.

3) The sun's RA and Dec do not depend on my location, so if I read in
an almanac that the solstice occurred on June 21 at 8:26 AM EDT, I
need only correct for my time zone, rather than fractions of a time
zone (as I would if I were trying to calculate my local sunrise, for
example).

Actually the apparent RA and Dec *do* depend on your location, because
of both topocentric parallax and topocentric aberration. The latter
doesn't affect the declination though.

4) SNP has two sets of RA/Dec coordinates in its info panel, one
labeled J2000, and one labeled JNow. I assume that JNow will be more
accurate for current observations.

JNow is presumably true-of-date coordinates.

OK, assuming all that is correct, here is what I found. All times are
EDT.

1) On June 21, the maximum RA reached was 23 degrees and 26.386
minutes. This was maintained from 2:00 PM to 3:16 PM EDT. The
almanac says the solstice should have been at 8:26 AM EDT.

2) When I ran the time backward from there, the declination slowly
decreased, but it hit a minimum (when it was 23deg 26.314') that
lasted from 2:03 AM to 3:39 AM of June 21, then it began to increase
as I went farther back. It peaked at 23deg 26.332' from about 7:37 PM
to 8:20 PM of June 20, and steadily decreased as I went earlier than
that..

So if SNP is correct, there were three solstices, i.e. a max on both
the 20th and 21st, and a local min between them. I could understand
if round-off errors produced fluctuations right around the true
solstice, but I can't understand
a) the absolute max being nearly six hours off the published time,
and
b) apparently smooth progressions between two maximums nearly a day
apart.

The two local maxima in declination are probably caused by topocentric
effects. The difference between the declination at those maxima is
0.018' by your reckoning, just over 1". The earth subtends an angle of
about 17" as seen from the sun; the difference between geocentric and
topocentric coordinates can amount to over 8".

Can you set your coordinates to the center of the earth and see what
happens?

Any explanations, or pointers to URLs, appreciated.



One last thing: As the ecliptic is defined as the mean orbit of the
earth-moon barycenter, and as the moon's orbit is inclined 5 deg to the
ecliptic, the earth bobs up and down each month, and the sun's ecliptic
latitude can reach about 1 arcsec north or south. Add this effect on
top of the earth's orbital motion, and you'll see that the sun's maximum
declination won't necessarily happen at ecliptic longitude 90 deg (or
RA 6h). Likewise, the sun's declination won't be exactly zero at the
equinoxes, when the longitude is 0 or 180.

-- Bill Owen

Brian Tung wrote:
SkySea wrote:

2) The sun's RA at the solstice should be very close to 6 hours, but
since the RA is defined by the vernal equinox rather than the
solstice, the solstice may not occur at exactly 6 hours.

True for times off a chart's given epoch. By definition though, 0h is
the intersection of the equator and the ecliptic, and the
intersections of the ecliptic with the 6, 18, and 12 hour circles mark
the equioxes and solstices.


No, I think the original poster was right: The vernal equinox is at 0h,
but the autumnal equinox and the solstices are all based on properties
of the ecliptic and the celestial equator. So the autumnal equinox is
when the ecliptic crosses the equator going southward, and the solstices
are the two points where the Sun's declination is at one of its two
extremes.

I have no explanation for the bizarre behavior of SNP, though.

Sorry I didn't see this post before I finished replying to the original
one.

The vernal equinox point on the celestial sphere is indeed exactly at
RA 0h, Dec 0 deg in equatorial coordinates; latitude 0 deg, longitude
0 deg in ecliptic coordinates.

The center of the sun will NOT go through this point in general, because
its geocentric latitude is zero only at the instant when the moon is at
one of the nodes of its orbit. If the sun's latitude happens to be
positive around March 20, it will cross the celestial equator before it
hits longitude 0.

If the moon's "argument of latitude" is between 90 and 270 deg, it is
moving southward in ecliptic coordinates, the earth is moving
northward, and the sun's apparent latitude is decreasing. If this
situation holds around June 21, the sun's declination will max out
before the solstice. Remember, the solstice is defined by ecliptic
longitude, not by RA, not by maximum Dec.

-- Bill Owen

wrote:
I was playing around with Starry Night Pro 5, and I thought I'd see if
I could determine the exact time of the summer solstice by watching
the solar coordinates. With SNP, you can select the sun, bring up an
info panel, and then watch the RA and Dec change as you run through
the clock time at the speed of your choice. I saw some things that I
can't explain, and I hope somebody here can help me.

First, in case my problem is with fundamental knowledge, tell me if
I'm wrong about any of these assumptions:

1) The solstice occurs when the sun reaches its maximum declination of
the year, which should be around 23.5 degrees N. The declination
never decreases between the vernal equinox and the summer solstice,
and never increases between the summer solstice and the autumnal
equinox.



Good thing I looked this up, as I would have been totally wrong!

Explanatory Supplement - Astronomical Almanac

9.211 Equinoxes and Solstices (pg 477)

The times of the equinoxes and solstices are *defined* when the Sun's
*apparent ecliptic longitude* lambda_s is a multiple of 90°; i.e.,
it is calculated from f(t) = 0, where f(t) = lambda_s -0°, 90°, 180°,
or 270°. Thus in the northern hemisphere, for the spring equinox
f(t) = lambda_s, for the summer solstice, f(t) = lambda_s - 90°, for
the autumn equinox f(t) = lambda_s - 180° and for the winter solstice
f(t) = lambda_s - 270°. At the equinoxes the Sun crosses the equator
when the length of the day exceeds the length of the night due to
refraction, semidiameter, and parallax of the Sun. At that time the
lengths of the day and night are approximately equal everywhere.

Sam Wormley wrote:
wrote:

I was playing around with Starry Night Pro 5, and I thought I'd see if
I could determine the exact time of the summer solstice by watching
the solar coordinates. With SNP, you can select the sun, bring up an
info panel, and then watch the RA and Dec change as you run through
the clock time at the speed of your choice. I saw some things that I
can't explain, and I hope somebody here can help me.
First, in case my problem is with fundamental knowledge, tell me if
I'm wrong about any of these assumptions:

1) The solstice occurs when the sun reaches its maximum declination of
the year, which should be around 23.5 degrees N. The declination
never decreases between the vernal equinox and the summer solstice,
and never increases between the summer solstice and the autumnal
equinox.



Good thing I looked this up, as I would have been totally wrong!

Explanatory Supplement - Astronomical Almanac

9.211 Equinoxes and Solstices (pg 477)

The times of the equinoxes and solstices are *defined* when the Sun's
*apparent ecliptic longitude* lambda_s is a multiple of 90°; i.e.,
it is calculated from f(t) = 0, where f(t) = lambda_s -0°, 90°, 180°,
or 270°. Thus in the northern hemisphere, for the spring equinox
f(t) = lambda_s, for the summer solstice, f(t) = lambda_s - 90°, for
the autumn equinox f(t) = lambda_s - 180° and for the winter solstice
f(t) = lambda_s - 270°. At the equinoxes the Sun crosses the equator
when the length of the day exceeds the length of the night due to
refraction, semidiameter, and parallax of the Sun. At that time the
lengths of the day and night are approximately equal everywhere.





Yes, as Bill Owen points out, geocentric as opposed to topocentric.

S. Caro wrote:
Sam Wormley wrote:



Good thing I looked this up, as I would have been totally wrong!

Explanatory Supplement - Astronomical Almanac

9.211 Equinoxes and Solstices (pg 477)

The times of the equinoxes and solstices are *defined* when the Sun's
*apparent ecliptic longitude* lambda_s is a multiple of 90°; i.e.,
it is calculated from f(t) = 0, where f(t) = lambda_s -0°, 90°, 180°,
or 270°. Thus in the northern hemisphere, for the spring equinox
f(t) = lambda_s, for the summer solstice, f(t) = lambda_s - 90°, for
the autumn equinox f(t) = lambda_s - 180° and for the winter solstice
f(t) = lambda_s - 270°. At the equinoxes the Sun crosses the equator
when the length of the day exceeds the length of the night due to
refraction, semidiameter, and parallax of the Sun. At that time the
lengths of the day and night are approximately equal everywhere.


Does the analemma effect not factor into this ? (Perhaps the math
above explains it :-)



The analema is a figure 8-shaped plot of the apparent Sun relative to
the mean Sun. This curve is sometimes seen on globes, maps and the
photography of Dennis di Cicco and most notably, Anthony Ayiomamitis!
And it does change slightly over the millennia.

On Fri, 28 Jul 2006 13:54:10 -0700, Bill Owen
wrote:

The standard definition of the equinoxes and the solstices are actually
in terms of the apparent geocentric *longitude* of the sun, not in terms
of declination. Summer solstice happens when the sun's geocentric
longitude is exactly 90 degrees. (This happens to be equivalent to
RA = 6h.)

OK, when I looked at that, it happened at 8:15 for my location (w
Oregon) and 8:17 for the center of the earth. So that's just nine
minutes off the almanac prediction; much better than six hours.


Actually the apparent RA and Dec *do* depend on your location, because
of both topocentric parallax and topocentric aberration. The latter
doesn't affect the declination though.

4) SNP has two sets of RA/Dec coordinates in its info panel, one
labeled J2000, and one labeled JNow. I assume that JNow will be more
accurate for current observations.

JNow is presumably true-of-date coordinates.

Yes. The JNow RA was exactly 6 when the Long was exactly 90. The
J2000 lagged a bit.


The two local maxima in declination are probably caused by topocentric
effects. The difference between the declination at those maxima is
0.018' by your reckoning, just over 1". The earth subtends an angle of
about 17" as seen from the sun; the difference between geocentric and
topocentric coordinates can amount to over 8".

Can you set your coordinates to the center of the earth and see what
happens?

Yes. The max dec was 23deg 26.455', and it happened from 7:39 AM to
8:55 AM EDT, so the 90deg longitude was within that window. I don't
see any deviation from an increase before, and a decrease after, the
max. So I guess the puzzle is solved.


One last thing: As the ecliptic is defined as the mean orbit of the
earth-moon barycenter, and as the moon's orbit is inclined 5 deg to the
ecliptic, the earth bobs up and down each month, and the sun's ecliptic
latitude can reach about 1 arcsec north or south. Add this effect on
top of the earth's orbital motion, and you'll see that the sun's maximum
declination won't necessarily happen at ecliptic longitude 90 deg (or
RA 6h). Likewise, the sun's declination won't be exactly zero at the
equinoxes, when the longitude is 0 or 180.

-- Bill Owen

Thanks for the help.