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/ |
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 3^{rd} 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 Dear Kalendarists: |
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 3^{rd} 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
Dear Kalendarists: |
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 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 3^{rd} 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 Dear Kalendarists: |
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
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 3^{rd} 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
Dear Kalendarists: |
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:
(You may need to refresh your web browser to be able to see these changes.)
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? |
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:
(You may need to refresh your web browser to be able to see these changes.)
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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