lunar distance

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lunar distance

Irv Bromberg
Dear Kalendarists:

Please see the discussion and charts on my lunar web page, in the new section entitled "Periodic Earth-Moon Distance Variations". Here is the direct link:

http://individual.utoronto.ca/kalendis/lunar/index.htm#dist

Any comments / concerns / corrections / criticisms / suggestions / questions?

-- Irv Bromberg, University of Toronto, Canada

http://www.sym454.org/lunar/



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Re: lunar distance

Karl Palmen

Dear Irv and Calendar People

 

Irv’s graph of the lunar distance seems to show a periodic  variation of the lunar orbit eccentricity very close to half a full moon cycle, so close that no difference can be discerned within the 3 years shown.

 

May be there is no difference, which would be the case if the periodic variation were caused by solar tides, which would stretch the orbit, when the major axis line (through perigee & apogee) passes close to the sun.

 

This is confirmed by Irv’s 3rd graph of the quarterly lunar distances for years 2000 to 2100. The full & new moon distances vary as much as each other and more than the half-moon distances.

 

Another thing is that I notice that the dates on the x-axis of the first two graphs are 56 days apart. Is that a choice Irv made or is it fixed by the plotting software?

 

Karl

 

16(15(25

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Irv Bromberg
Sent: 12 November 2017 05:25
To: [hidden email]
Subject: lunar distance

 

Dear Kalendarists:

Please see the discussion and charts on my lunar web page, in the new section entitled "Periodic Earth-Moon Distance Variations". Here is the direct link:

http://individual.utoronto.ca/kalendis/lunar/index.htm#dist

Any comments / concerns / corrections / criticisms / suggestions / questions?

-- Irv Bromberg, University of Toronto, Canada

http://www.sym454.org/lunar/


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Re: lunar distance

Irv Bromberg
From: East Carolina University Calendar discussion List [[hidden email]] on behalf of Karl Palmen [[hidden email]]
Sent: Monday, November 13, 2017 08:06

Irv’s graph of the lunar distance seems to show a periodic  variation of the lunar orbit eccentricity very close to half a full moon cycle, so close that no difference can be discerned within the 3 years shown.

 

May be there is no difference, which would be the case if the periodic variation were caused by solar tides, which would stretch the orbit, when the major axis line (through perigee & apogee) passes close to the sun.


This is confirmed by Irv’s 3rd graph of the quarterly lunar distances for years 2000 to 2100. The full & new moon distances vary as much as each other and more than the half-moon distances.


[Bromberg] Right, as explained in my discussion points, lunar orbital eccentricity is maximal when its major axis is aligned with the Sun-Earth line. This makes the distance extremes of the new moon and full moon greater than at any other place in the orbit. Also, as explained in the paragraph on that page that starts with "According to SOLEX" the lunar orbital nodes regress westward but are temporarily stationery whenever the major axis is nearly aligned with the Earth-Sun line.


(This makes it approximately 3 times more likely that eclipses will occur, so they usually occur in groups of 3: solar-lunar-solar or lunar-solar-lunar.) [Both of these effects are overt relativistic space-time curvature right in our "back yard" but were accounted for empirically in the traditional algorithms for lunar motion, hence the relativistic effects are inseparable from the classical Newtonian motions.]

 

[Karl continued] Another thing is that I notice that the dates on the x-axis of the first two graphs are 56 days apart. Is that a choice Irv made or is it fixed by the plotting software?


[Bromberg] I chose 56 as a multiple of 28, which is a multiple of 7, so that the major and minor tick marks would be conveniently spaced. The minor ticks are at 14-day intervals, which is 1/4 of 56.


 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Irv Bromberg
Sent: 12 November 2017 05:25
To: [hidden email]
Subject: lunar distance

 

Dear Kalendarists:

Please see the discussion and charts on my lunar web page, in the new section entitled "Periodic Earth-Moon Distance Variations". Here is the direct link:

http://individual.utoronto.ca/kalendis/lunar/index.htm#dist

Any comments / concerns / corrections / criticisms / suggestions / questions?

-- Irv Bromberg, University of Toronto, Canada

http://www.sym454.org/lunar/


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Re: lunar distance

Karl Palmen

Dear Irv and Calendar People

 

Thank you Irv for your reply.

 

Irv replied: [Bromberg] I chose 56 as a multiple of 28, which is a multiple of 7, so that the major and minor tick marks would be conveniently spaced. The minor ticks are at 14-day intervals, which is 1/4 of 56.

 

I thought 59 days might be a good idea, because it is very near two synodic months with little more than 1 day’s drift over 3 years and also seven of these are little more 1 day in excess of a mean full moon cycle. The minor ticks would then correspond to half a lunar month.

 

Karl

 

16(15(25

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Irv Bromberg
Sent: 13 November 2017 13:47
To: [hidden email]
Subject: Re: lunar distance

 

From: East Carolina University Calendar discussion List [[hidden email]] on behalf of Karl Palmen [[hidden email]]

Sent: Monday, November 13, 2017 08:06

Irv’s graph of the lunar distance seems to show a periodic  variation of the lunar orbit eccentricity very close to half a full moon cycle, so close that no difference can be discerned within the 3 years shown.

 

May be there is no difference, which would be the case if the periodic variation were caused by solar tides, which would stretch the orbit, when the major axis line (through perigee & apogee) passes close to the sun.

 

This is confirmed by Irv’s 3rd graph of the quarterly lunar distances for years 2000 to 2100. The full & new moon distances vary as much as each other and more than the half-moon distances.

 

[Bromberg] Right, as explained in my discussion points, lunar orbital eccentricity is maximal when its major axis is aligned with the Sun-Earth line. This makes the distance extremes of the new moon and full moon greater than at any other place in the orbit. Also, as explained in the paragraph on that page that starts with "According to SOLEX" the lunar orbital nodes regress westward but are temporarily stationery whenever the major axis is nearly aligned with the Earth-Sun line.

 

(This makes it approximately 3 times more likely that eclipses will occur, so they usually occur in groups of 3: solar-lunar-solar or lunar-solar-lunar.) [Both of these effects are overt relativistic space-time curvature right in our "back yard" but were accounted for empirically in the traditional algorithms for lunar motion, hence the relativistic effects are inseparable from the classical Newtonian motions.]

 

[Karl continued] Another thing is that I notice that the dates on the x-axis of the first two graphs are 56 days apart. Is that a choice Irv made or is it fixed by the plotting software?

 

[Bromberg] I chose 56 as a multiple of 28, which is a multiple of 7, so that the major and minor tick marks would be conveniently spaced. The minor ticks are at 14-day intervals, which is 1/4 of 56.

 

 

From: East Carolina University Calendar discussion List [[hidden email]] On Behalf Of Irv Bromberg
Sent: 12 November 2017 05:25
To: [hidden email]
Subject: lunar distance

 

Dear Kalendarists:

Please see the discussion and charts on my lunar web page, in the new section entitled "Periodic Earth-Moon Distance Variations". Here is the direct link:

http://individual.utoronto.ca/kalendis/lunar/index.htm#dist

Any comments / concerns / corrections / criticisms / suggestions / questions?

-- Irv Bromberg, University of Toronto, Canada

http://www.sym454.org/lunar/

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Re: lunar distance

Irv Bromberg
Good idea, thank you for the suggestion.
I tried 59 as the major tick mark interval, and 14.75 as the minor tick interval.

The tick marks do line up nicely with the syzygy events, although without vertical grid lines that isn't very obvious, and with grid lines the chart is too cluttered.

I didn't change my web page yet.


From: East Carolina University Calendar discussion List [[hidden email]] on behalf of Karl Palmen [[hidden email]]
Sent: Monday, November 13, 2017 11:10

Irv replied: [Bromberg] I chose 56 as a multiple of 28, which is a multiple of 7, so that the major and minor tick marks would be conveniently spaced. The minor ticks are at 14-day intervals, which is 1/4 of 56.

 

I thought 59 days might be a good idea, because it is very near two synodic months with little more than 1 day’s drift over 3 years and also seven of these are little more 1 day in excess of a mean full moon cycle. The minor ticks would then correspond to half a lunar month.

 

Karl

 

16(15(25

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Irv Bromberg
Sent: 13 November 2017 13:47
To: [hidden email]
Subject: Re: lunar distance

 

From: East Carolina University Calendar discussion List [[hidden email]] on behalf of Karl Palmen [[hidden email]]

Sent: Monday, November 13, 2017 08:06

Irv’s graph of the lunar distance seems to show a periodic  variation of the lunar orbit eccentricity very close to half a full moon cycle, so close that no difference can be discerned within the 3 years shown.

 

May be there is no difference, which would be the case if the periodic variation were caused by solar tides, which would stretch the orbit, when the major axis line (through perigee & apogee) passes close to the sun.

 

This is confirmed by Irv’s 3rd graph of the quarterly lunar distances for years 2000 to 2100. The full & new moon distances vary as much as each other and more than the half-moon distances.

 

[Bromberg] Right, as explained in my discussion points, lunar orbital eccentricity is maximal when its major axis is aligned with the Sun-Earth line. This makes the distance extremes of the new moon and full moon greater than at any other place in the orbit. Also, as explained in the paragraph on that page that starts with "According to SOLEX" the lunar orbital nodes regress westward but are temporarily stationery whenever the major axis is nearly aligned with the Earth-Sun line.

 

(This makes it approximately 3 times more likely that eclipses will occur, so they usually occur in groups of 3: solar-lunar-solar or lunar-solar-lunar.) [Both of these effects are overt relativistic space-time curvature right in our "back yard" but were accounted for empirically in the traditional algorithms for lunar motion, hence the relativistic effects are inseparable from the classical Newtonian motions.]

 

[Karl continued] Another thing is that I notice that the dates on the x-axis of the first two graphs are 56 days apart. Is that a choice Irv made or is it fixed by the plotting software?

 

[Bromberg] I chose 56 as a multiple of 28, which is a multiple of 7, so that the major and minor tick marks would be conveniently spaced. The minor ticks are at 14-day intervals, which is 1/4 of 56.

 

 

From: East Carolina University Calendar discussion List [[hidden email]] On Behalf Of Irv Bromberg
Sent: 12 November 2017 05:25
To: [hidden email]
Subject: lunar distance

 

Dear Kalendarists:

Please see the discussion and charts on my lunar web page, in the new section entitled "Periodic Earth-Moon Distance Variations". Here is the direct link:

http://individual.utoronto.ca/kalendis/lunar/index.htm#dist

Any comments / concerns / corrections / criticisms / suggestions / questions?

-- Irv Bromberg, University of Toronto, Canada

http://www.sym454.org/lunar/

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Re: lunar distance

Irv Bromberg
In reply to this post by Irv Bromberg
Further to my message quoted below, I've now posted updated lunar distance charts with the following changes:
  • As suggested by Karl Palmen, the first two charts now have major tick-mark interval of 59 days (about 2 lunar cycles) [instead of 56 days] and minor tick-mark interval of 14.75 days (about one half lunar cycle) [instead of 14 days], and there are now faint green vertical grid lines at the major tick-mark intervals. Every second conjunction lines up with the new vertical grid lines.
  • The cumulative centiles chart is modestly larger, and I added two first-derivative curves to confirm that the extreme lunar distances have the highest frequencies.
  • Edited the discussions in that section to explain the new features of the charts.

(You may need to refresh your web browser to be able to see these changes.)


-- Irv Bromberg, University of Toronto, Canada

http://www.sym454.org/lunar/


From: East Carolina University Calendar discussion List [[hidden email]] on behalf of Irv Bromberg [[hidden email]]
Sent: Sunday, November 12, 2017 00:25

Dear Kalendarists:

Please see the discussion and charts on my lunar web page, in the new section entitled "Periodic Earth-Moon Distance Variations". Here is the direct link:

http://individual.utoronto.ca/kalendis/lunar/index.htm#dist

Any comments / concerns / corrections / criticisms / suggestions / questions?
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Re: lunar distance

Irv Bromberg
Further to the thread quoted below, today I added 3 more charts depicting the distance variations when Moon is actually at perigee or apogee, added sources used for the calculations, and made minor revisions of the discussions in that section.

http://individual.utoronto.ca/kalendis/lunar/index.htm#dist

-- Irv Bromberg, University of Toronto, Canada


From: East Carolina University Calendar discussion List [[hidden email]] on behalf of Irv Bromberg [[hidden email]]
Sent: Wednesday, November 15, 2017 00:08
To: [hidden email]
Subject: Re: lunar distance

Further to my message quoted below, I've now posted updated lunar distance charts with the following changes:
  • As suggested by Karl Palmen, the first two charts now have major tick-mark interval of 59 days (about 2 lunar cycles) [instead of 56 days] and minor tick-mark interval of 14.75 days (about one half lunar cycle) [instead of 14 days], and there are now faint green vertical grid lines at the major tick-mark intervals. Every second conjunction lines up with the new vertical grid lines.
  • The cumulative centiles chart is modestly larger, and I added two first-derivative curves to confirm that the extreme lunar distances have the highest frequencies.
  • Edited the discussions in that section to explain the new features of the charts.

(You may need to refresh your web browser to be able to see these changes.)


-- Irv Bromberg, University of Toronto, Canada

http://www.sym454.org/lunar/


From: East Carolina University Calendar discussion List [[hidden email]] on behalf of Irv Bromberg [[hidden email]]
Sent: Sunday, November 12, 2017 00:25

Dear Kalendarists:

Please see the discussion and charts on my lunar web page, in the new section entitled "Periodic Earth-Moon Distance Variations". Here is the direct link:

http://individual.utoronto.ca/kalendis/lunar/index.htm#dist

Any comments / concerns / corrections / criticisms / suggestions / questions?