Saros 136 and the solar eclipse of 07/22/2009

The recent solar eclipse reminded me of another total solar eclipse
(one I saw) of 07/11/1991. With the 18-year difference, I was
wondering if they might be part of the same Saros series:

Cf.:
http://en.wikipedia.org/wiki/Saros_cycle

The answer is yes:

For the eclipse of 07/11/1991:

http://eclipse.gsfc.nasa.gov/5MCSEma...1991-07-11.gif

(Saros 136).

For the eclipse of 07/22/2009:

http://eclipse.gsfc.nasa.gov/5MCSEma...2009-07-22.gif

(Saros 136 also).

In the NASA publication:

[ I downloaded Revision 1.0 (2007 May 11) from he
http://unjobs.org/authors/jean-meeus ].

NASA/TP–2006–214141 by Fred Espenak and Jean Meeus, Ref. #2
in the Wikipedia article on "Saros cycle",

the authors relate the following on page 37:

One Saros is equal to 223 synodic months, however, 242 draconic
months and 239 anomalistic months are also equal
(within a few hours) to this same period:

223 Synodic Months = 6585.3223 days
242 Draconic Months = 6585.3575 days
239 Anomalistic Months = 6585.5375 days

A synodic month is the average of new moon to new moon,

a draconic month is from node to node [ where the moon crosses the
ecliptic plane going Northward]

An anomalistic month is from perigee to perigee.
[ Meeus and Espenak, page 37].

I have to wonder if some resonance effect might come into play
because, for example, the 223 synodic months and the
242 draconic months are only 0.035 days apart ...
I don't know the answer to that. Meeus and Espenak write:
"The Saros arises from a harmonic between three of the Moon’s
orbital cycles."

Coincidentally, the Saros cycle is illustrated in the Espenak/Meeus
publication using Saros 136 in Figure 4-1, page 38.

The three-Saros period of ~ 54 years is very close to an integer
number of days, and with a Saros being 18 years 11.32 days,
I think that explains why after three Saros cycles, eclipses occur
at roughly the same longitude.

Figure 4-1 shows the next eclipse of Saros 136 as being
on August 2, 2027: Southern Europe, Mediterranean,
Northern Africa, Egypt and Middle East.

David Bernier

David Bernier wrote:
The recent solar eclipse reminded me of another total solar eclipse
(one I saw) of 07/11/1991. With the 18-year difference, I was
wondering if they might be part of the same Saros series:

Cf.:
http://en.wikipedia.org/wiki/Saros_cycle

The answer is yes:

For the eclipse of 07/11/1991:

http://eclipse.gsfc.nasa.gov/5MCSEma...1991-07-11.gif

(Saros 136).

For the eclipse of 07/22/2009:

http://eclipse.gsfc.nasa.gov/5MCSEma...2009-07-22.gif

(Saros 136 also).

In the NASA publication:

[ I downloaded Revision 1.0 (2007 May 11) from he
http://unjobs.org/authors/jean-meeus ].

NASA/TP–2006–214141 by Fred Espenak and Jean Meeus, Ref. #2
in the Wikipedia article on "Saros cycle",

the authors relate the following on page 37:

One Saros is equal to 223 synodic months, however, 242 draconic
months and 239 anomalistic months are also equal
(within a few hours) to this same period:

223 Synodic Months = 6585.3223 days
242 Draconic Months = 6585.3575 days
239 Anomalistic Months = 6585.5375 days

A synodic month is the average of new moon to new moon,

a draconic month is from node to node [ where the moon crosses the
ecliptic plane going Northward]

An anomalistic month is from perigee to perigee.
[ Meeus and Espenak, page 37].

I have to wonder if some resonance effect might come into play
because, for example, the 223 synodic months and the



242 draconic months are only 0.035 days apart ...
I don't know the answer to that. Meeus and Espenak write:
"The Saros arises from a harmonic between three of the Moon’s
orbital cycles."

It could be a "fluke". I'm not sure.


Coincidentally, the Saros cycle is illustrated in the Espenak/Meeus
publication using Saros 136 in Figure 4-1, page 38.

The three-Saros period of ~ 54 years is very close to an integer
number of days, and with a Saros being 18 years 11.32 days,
I think that explains why after three Saros cycles, eclipses occur
at roughly the same longitude.

Figure 4-1 shows the next eclipse of Saros 136 as being
on August 2, 2027: Southern Europe, Mediterranean,
Northern Africa, Egypt and Middle East.

By expanding 29.530589/27.212221 as a continued fraction,
one finds other close rational approximations to
29.530589/27.212221 . For eclipse geometry, I think
new moon to new moon (synodic month) and
ascending node to ascending node (the draconic month)
being "synchronized" matters most. The earth-moon
distance repeats (approximately) at perigee to perigee
month intervals (the anomalistic month). Also, the earth is farthest
from the sun in early summer (Northern hemisphere), so
early summer should be the time for the longest solar
eclipses, I believe.


4519*29.530589 = 133448.731691 days and
4904*27.212221 = 133448.731784 days,

for a difference of 0.000093 days or about 8 seconds.

133448.731691 days = 365 years 135.22 days.

07/22/2009 was a Wednesday ...


07/22/2009 + 365 years 135.22 days:
12/04/2374 (December 4, 2374, Wednesday):

http://eclipse.gsfc.nasa.gov/5MCSEma...2374-12-04.gif

Total eclipse, 2374 Dec 04, duration 3min 42 sec .



+ 365 years 135.22 days once mo

2740 April 18 : [a Thursday]

http://eclipse.gsfc.nasa.gov/5MCSEma...2740-04-18.gif

Total, dur. = 2min 43 sec

David Bernier

In article ,
David Bernier wrote:
David Bernier wrote:
The recent solar eclipse reminded me of another total solar eclipse
(one I saw) of 07/11/1991. With the 18-year difference, I was
wondering if they might be part of the same Saros series:

Cf.:
http://en.wikipedia.org/wiki/Saros_cycle

The answer is yes:

For the eclipse of 07/11/1991:

http://eclipse.gsfc.nasa.gov/5MCSEma...1991-07-11.gif

(Saros 136).

For the eclipse of 07/22/2009:

http://eclipse.gsfc.nasa.gov/5MCSEma...2009-07-22.gif

(Saros 136 also).

In the NASA publication:

[ I downloaded Revision 1.0 (2007 May 11) from he
http://unjobs.org/authors/jean-meeus ].

NASA/TPÐ2006Ð214141 by Fred Espenak and Jean Meeus, Ref. #2
in the Wikipedia article on "Saros cycle",

the authors relate the following on page 37:

One Saros is equal to 223 synodic months, however, 242 draconic
months and 239 anomalistic months are also equal
(within a few hours) to this same period:

223 Synodic Months = 6585.3223 days
242 Draconic Months = 6585.3575 days
239 Anomalistic Months = 6585.5375 days

A synodic month is the average of new moon to new moon,

a draconic month is from node to node [ where the moon crosses the
ecliptic plane going Northward]

An anomalistic month is from perigee to perigee.
[ Meeus and Espenak, page 37].

I have to wonder if some resonance effect might come into play
because, for example, the 223 synodic months and the



242 draconic months are only 0.035 days apart ...
I don't know the answer to that. Meeus and Espenak write:
"The Saros arises from a harmonic between three of the MoonÕs
orbital cycles."

It could be a "fluke". I'm not sure.

Using continued fractions, we can find a point where two periods line
up closely. The Inex uses the next step in the continued fraction
for the ratio between the synodic and draconic months to get a ratio
of 777/716; however, the Inex is defined as 358 synodic months which
is approximately 388.5 draconic months, so eclipses alternate the
hemisphere in which they occur. Note that

358 synodic months = 10571.95122 days
388.5 draconic months = 10571.94747 days

These are approximately 1/10 as far apart as 223 synodic months and
242 draconic months. However, 10571.95 days is 383.67348 anomalistic
months, so the eclipses will not be the same magnitude. Furthermore,
since the orbit of the moon is fairly eccentric, the moon may be a
bit slow or fast, so the pattern is not as pronounced as it is with
the Saros Cycle and eclipses at the beginning and end of a series.

However, it is quite lucky (is this what you mean by "fluke"?) that
the synodic, draconic, and anomalistic months allow small integer
multiples to agree so closely and create the Saros Cycle.

For more on the Inex Cycle, see http://en.wikipedia.org/wiki/Inex.

Coincidentally, the Saros cycle is illustrated in the Espenak/Meeus
publication using Saros 136 in Figure 4-1, page 38.

The three-Saros period of ~ 54 years is very close to an integer
number of days, and with a Saros being 18 years 11.32 days,
I think that explains why after three Saros cycles, eclipses occur
at roughly the same longitude.

Figure 4-1 shows the next eclipse of Saros 136 as being
on August 2, 2027: Southern Europe, Mediterranean,
Northern Africa, Egypt and Middle East.

By expanding 29.530589/27.212221 as a continued fraction,
one finds other close rational approximations to
29.530589/27.212221 . For eclipse geometry, I think
new moon to new moon (synodic month) and
ascending node to ascending node (the draconic month)
being "synchronized" matters most. The earth-moon
distance repeats (approximately) at perigee to perigee
month intervals (the anomalistic month). Also, the earth is farthest
from the sun in early summer (Northern hemisphere), so
early summer should be the time for the longest solar
eclipses, I believe.


4519*29.530589 = 133448.731691 days and
4904*27.212221 = 133448.731784 days,

for a difference of 0.000093 days or about 8 seconds.

Since the precision of the periods is 5e-7 days, the error in 4519
periods should be over 3 minutes, so a difference of 8 seconds is a
little ambitious.

133448.731691 days = 365 years 135.22 days.

07/22/2009 was a Wednesday ...


07/22/2009 + 365 years 135.22 days:

It would probably be better to measure the time in days. If you use
years, you should specify what kind of year (sidereal, tropical,
Julian, Gregorian, etc). Something is definitely left unsaid when a
difference of 133448.731691 days is converted to 365 years 135.22
days. The Earth should rotate 263.4 degrees (.731691 day) but
365 years 135.22 days would indicate a rotation of 79.2 degrees.

Furthermore, note that over a period of 365 years, the synodic month
increases by about .0000008 days, the draconic month by about .0000014
days, and the anomalistic month decreases by .0000038 days. Since
the continued fraction computation to get 4904/4519 needs a precision
of .0000015 days, 365 years looks to be the maximum time frame we can
use 4904/4519.

12/04/2374 (December 4, 2374, Wednesday):

http://eclipse.gsfc.nasa.gov/5MCSEma...2374-12-04.gif

Total eclipse, 2374 Dec 04, duration 3min 42 sec .



+ 365 years 135.22 days once mo

2740 April 18 : [a Thursday]

http://eclipse.gsfc.nasa.gov/5MCSEma...2740-04-18.gif

Total, dur. = 2min 43 sec

Rob Johnson
take out the trash before replying
to view any ASCII art, display article in a monospaced font

Rob Johnson wrote:
In article ,
David Bernier wrote:
David Bernier wrote:
The recent solar eclipse reminded me of another total solar eclipse
(one I saw) of 07/11/1991. With the 18-year difference, I was
wondering if they might be part of the same Saros series:

Cf.:
http://en.wikipedia.org/wiki/Saros_cycle

The answer is yes:

For the eclipse of 07/11/1991:

http://eclipse.gsfc.nasa.gov/5MCSEma...1991-07-11.gif

(Saros 136).

For the eclipse of 07/22/2009:

http://eclipse.gsfc.nasa.gov/5MCSEma...2009-07-22.gif

(Saros 136 also).

In the NASA publication:

[ I downloaded Revision 1.0 (2007 May 11) from he
http://unjobs.org/authors/jean-meeus ].

NASA/TPÐ2006Ð214141 by Fred Espenak and Jean Meeus, Ref. #2
in the Wikipedia article on "Saros cycle",

the authors relate the following on page 37:

One Saros is equal to 223 synodic months, however, 242 draconic
months and 239 anomalistic months are also equal
(within a few hours) to this same period:

223 Synodic Months = 6585.3223 days
242 Draconic Months = 6585.3575 days
239 Anomalistic Months = 6585.5375 days

A synodic month is the average of new moon to new moon,

a draconic month is from node to node [ where the moon crosses the
ecliptic plane going Northward]

An anomalistic month is from perigee to perigee.
[ Meeus and Espenak, page 37].

I have to wonder if some resonance effect might come into play
because, for example, the 223 synodic months and the


242 draconic months are only 0.035 days apart ...
I don't know the answer to that. Meeus and Espenak write:
"The Saros arises from a harmonic between three of the MoonÕs
orbital cycles."
It could be a "fluke". I'm not sure.

Using continued fractions, we can find a point where two periods line
up closely. The Inex uses the next step in the continued fraction
for the ratio between the synodic and draconic months to get a ratio
of 777/716; however, the Inex is defined as 358 synodic months which
is approximately 388.5 draconic months, so eclipses alternate the
hemisphere in which they occur. Note that

358 synodic months = 10571.95122 days
388.5 draconic months = 10571.94747 days

These are approximately 1/10 as far apart as 223 synodic months and
242 draconic months. However, 10571.95 days is 383.67348 anomalistic
months, so the eclipses will not be the same magnitude. Furthermore,
since the orbit of the moon is fairly eccentric, the moon may be a
bit slow or fast, so the pattern is not as pronounced as it is with
the Saros Cycle and eclipses at the beginning and end of a series.

However, it is quite lucky (is this what you mean by "fluke"?) that
the synodic, draconic, and anomalistic months allow small integer
multiples to agree so closely and create the Saros Cycle.

When I mentioned "resonance effect" above, I meant ratios that
are very close to small integer ratios, and based
on celestial mechanics, e.g. as with some of the
satellites of Jupiter:
http://en.wikipedia.org/wiki/Orbital...s_of_resonance

I think the Saros Cycle is really quite remarkable.
But it may well be a lucky coincidence.





For more on the Inex Cycle, see http://en.wikipedia.org/wiki/Inex.

Coincidentally, the Saros cycle is illustrated in the Espenak/Meeus
publication using Saros 136 in Figure 4-1, page 38.

The three-Saros period of ~ 54 years is very close to an integer
number of days, and with a Saros being 18 years 11.32 days,
I think that explains why after three Saros cycles, eclipses occur
at roughly the same longitude.

Figure 4-1 shows the next eclipse of Saros 136 as being
on August 2, 2027: Southern Europe, Mediterranean,
Northern Africa, Egypt and Middle East.
By expanding 29.530589/27.212221 as a continued fraction,
one finds other close rational approximations to
29.530589/27.212221 . For eclipse geometry, I think
new moon to new moon (synodic month) and
ascending node to ascending node (the draconic month)
being "synchronized" matters most. The earth-moon
distance repeats (approximately) at perigee to perigee
month intervals (the anomalistic month). Also, the earth is farthest
from the sun in early summer (Northern hemisphere), so
early summer should be the time for the longest solar
eclipses, I believe.


4519*29.530589 = 133448.731691 days and
4904*27.212221 = 133448.731784 days,

for a difference of 0.000093 days or about 8 seconds.

Since the precision of the periods is 5e-7 days, the error in 4519
periods should be over 3 minutes, so a difference of 8 seconds is a
little ambitious.

Right. There's not enough digits to put in 8 seconds. oops ...


133448.731691 days = 365 years 135.22 days.

07/22/2009 was a Wednesday ...


07/22/2009 + 365 years 135.22 days:

It would probably be better to measure the time in days. If you use
years, you should specify what kind of year (sidereal, tropical,
Julian, Gregorian, etc). Something is definitely left unsaid when a
difference of 133448.731691 days is converted to 365 years 135.22
days. The Earth should rotate 263.4 degrees (.731691 day) but
365 years 135.22 days would indicate a rotation of 79.2 degrees.

Yes, measuring the time in days is a better idea. So
I suppose 2*133448.731691 days being 7n days + 1.46 day
approximately (n is an integer) is in good accord
with the eclipse of 2740 April 18 being on a Thursday.

Furthermore, note that over a period of 365 years, the synodic month
increases by about .0000008 days, the draconic month by about .0000014
days, and the anomalistic month decreases by .0000038 days. Since
the continued fraction computation to get 4904/4519 needs a precision
of .0000015 days, 365 years looks to be the maximum time frame we can
use 4904/4519.

I understand.


12/04/2374 (December 4, 2374, Wednesday):

http://eclipse.gsfc.nasa.gov/5MCSEma...2374-12-04.gif

Total eclipse, 2374 Dec 04, duration 3min 42 sec .



+ 365 years 135.22 days once mo

2740 April 18 : [a Thursday]

http://eclipse.gsfc.nasa.gov/5MCSEma...2740-04-18.gif

Total, dur. = 2min 43 sec


David Bernier