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Index of Subjects --Apple-Mail-94-989360860 Content-Type: text/plain; charset=ISO-8859-1; format=flowed; delsp=yes Content-Transfer-Encoding: quoted-printable I'll take a quick stab at it! There are two other things you need to consider. The first is that the =20= Moon's orbit is elliptical, which means that it moves faster when =20 closest to Earth, and slowest when furthes away. To make it simple, if =20= you assume that the month had exactly 30 days, then you would expect =20 the Moon to move 360=B0/30 days =3D 12=B0/day and that the Earth would = have =20 to rotate an extra 12=B0 every day so that you would see the Moon each =20= night 48 minutes later. (The Earth rotates through 360=B0 in 24 hours, =20= or 15=B0/hour. The reason this is not the case is because as the moon gets closer to =20= the Earth it would move more than 12=B0 in this example (rising later =20= than expeted, and at the farthest point in its orbit it would move =20 less than 12=B0 and appear to rise earlier than expected. The other complication is that you drew your diagram on a piece of =20 paper which is flat. The Moon's orbit as tipped by 5=B0 with respect to =20= the Earth's equator. This means that while the Moon is always moving =20 "eastward" against the background sky, when it is at the maximum of 5=B0 = =20 above or below the equator, all of its orbital motion is eastward, At =20= other times, some of this motion will be "north" or "south" and this =20 component in at a maximum when it is above the Earth's equator. What may help to visualise this is to draw a short, tall sine wave and =20= then move your pencil along it at a constant speed. You will see that =20= the "horizontal" component of the speed will vary depending on how =20 much "up" and "down" it has to do. Adding these two effects together gives the variation you are seeing, =20= as they are not in step with each other. Hope that helps. Pat PS: There two effects also produce the "east-west" variation of the =20 Sun in the analemma (or Equation of time) since the Earth's orbit =20 about the Sun is elliptical, and the Sun's path is tipped by 23.5=B0 =20 with respect to the Earth's equator. This is one reason why most =20 styles of sundials need to be corrected, and is also why the earliest =20= sunset and the latest sunrise occur, respectively, before and after =20 the winter solstice. On Jan 21, 2012, at 5:23 PM, David & Alison Webster wrote: > Dear All, Jan 21, 2012 > Some years ago, while reading an Old Farmer's Almanac, I noticed =20 > that the time between successive rises of the moon varied and, in =20 > addition, was variously greater than or less than the time between =20 > successive moon sets. > > To try and rationalize this I made a sketch of sun, earth and moon =20= > as viewed from 'above'. When viewed from above all motions in this =20 > sketch (earth's orbit, earth's rotation and moon's orbit) are =20 > counterclockwise. That didn't help. > > So I tried tabulating the daily differences etc. using the period =20= > Jan 15, 2010 to Feb 12, 2010. And for example on Jan 18 the moon =20 > rises 19 minutes later than it did on Jan 17 but sets 63 minutes =20 > later. On Feb 2 the comparable differences are 76 and 24 minutes. =20 > But working with these numbers still left me baffled. > > Can someone shed light on this ? > > Yt, Dave Webster, Kentville > > > > > > > > =3D=20 =3D=20 =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D Patrick Kelly Director of Computer Facilities =3D=20 =3D=20 =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D Faculty of Architecture and Planning Dalhousie University =3D=20 =3D=20 =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D MAIL COURIER PO Box 15000 5410 Spring Garden Road Halifax, Nova Scotia B3H 4R2 Halifax, Nova Scotia Canada Canada =3D=20 =3D=20 =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D Phone:(902) 494-3294 FAX:(902) 423-6672 E-mail:patrick.kelly@dal.ca =3D=20 =3D=20 =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D --Apple-Mail-94-989360860 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable <html><body style=3D"word-wrap: break-word; -webkit-nbsp-mode: space; = -webkit-line-break: after-white-space; ">I'll take a quick stab at = it!<div><br></div><div>There are two other things you need to consider. = The first is that the Moon's orbit is elliptical, which means that it = moves faster when closest to Earth, and slowest when furthes away. To = make it simple, if you assume that the month had exactly 30 days, then = you would expect the Moon to move 360=B0/30 days =3D 12=B0/day and that = the Earth would have to rotate an extra 12=B0 every day so that you = would see the Moon each night 48 minutes later. (The Earth rotates = through 360=B0 in 24 hours, or 15=B0/hour.</div><div><br></div><div>The = reason this is not the case is because as the moon gets closer to the = Earth it would move more than 12=B0 in this example (rising later than = expeted, and at the farthest point in its orbit it would move less than = 12=B0 and appear to rise earlier than = expected.</div><div><br></div><div>The other complication is that you = drew your diagram on a piece of paper which is flat. The Moon's orbit as = tipped by 5=B0 with respect to the Earth's equator. This means that = while the Moon is always moving "eastward" against the background sky, = when it is at the maximum of 5=B0 above or below the equator, all of its = orbital motion is eastward, At other times, some of this motion will be = "north" or "south" and this component in at a maximum when it is above = the Earth's equator. </div><div><br></div><div>What may help to = visualise this is to draw a short, tall sine wave and then move your = pencil along it at a constant speed. You will see that the "horizontal" = component of the speed will vary depending on how much "up" and "down" = it has to do.</div><div><br></div><div>Adding these two effects together = gives the variation you are seeing, as they are not in step with each = other.</div><div><br></div><div>Hope that = helps. </div><div><br></div><div>Pat</div><div><br></div><div>PS: = There two effects also produce the "east-west" variation of the Sun in = the analemma (or Equation of time) since the Earth's orbit about the Sun = is elliptical, and the Sun's path is tipped by 23.5=B0 with respect to = the Earth's equator. This is one reason why most styles of sundials need = to be corrected, and is also why the earliest sunset and the latest = sunrise occur, respectively, before and after the winter = solstice.</div><div><br></div><div><br></div><div><br></div><div><br><div>= <div>On Jan 21, 2012, at 5:23 PM, David & Alison Webster = wrote:</div><br class=3D"Apple-interchange-newline"><blockquote = type=3D"cite"><div>Dear All, = &n= bsp; Jan 21, 2012<br> = Some years ago, while reading an Old Farmer's Almanac, I = noticed that the time between successive rises of the moon varied and, = in addition, was variously greater than or less than the time between = successive moon sets.<br><br> To try and rationalize this I = made a sketch of sun, earth and moon as viewed from 'above'. When viewed = from above all motions in this sketch (earth's orbit, earth's rotation = and moon's orbit) are counterclockwise. That didn't help.<br><br> = So I tried tabulating the daily differences etc. using the = period Jan 15, 2010 to Feb 12, 2010. And for example on Jan 18 the moon = rises 19 minutes later than it did on Jan 17 but sets 63 minutes later. = On Feb 2 the comparable differences are 76 and 24 minutes. But working = with these numbers still left me baffled.<br><br> Can = someone shed light on this ?<br><br>Yt, Dave Webster, = Kentville<br><br><br><br><br><br><br><br><br></div></blockquote></div><br>= <div apple-content-edited=3D"true"> <span class=3D"Apple-style-span" = style=3D"border-collapse: separate; color: rgb(0, 0, 0); font-family: = Helvetica; font-style: normal; font-variant: normal; font-weight: = normal; letter-spacing: normal; line-height: normal; orphans: 2; = text-align: auto; text-indent: 0px; text-transform: none; white-space: = normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: = 0px; -webkit-border-vertical-spacing: 0px; = -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: = auto; -webkit-text-stroke-width: 0px; font-size: medium; "><div = style=3D"word-wrap: break-word; -webkit-nbsp-mode: space; = -webkit-line-break: after-white-space; "><span class=3D"Apple-style-span" = style=3D"border-collapse: separate; color: rgb(0, 0, 0); font-family: = Helvetica; font-style: normal; font-variant: normal; font-weight: = normal; letter-spacing: normal; line-height: normal; orphans: 2; = text-indent: 0px; text-transform: none; white-space: normal; widows: 2; = word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; = -webkit-border-vertical-spacing: 0px; = -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: = auto; -webkit-text-stroke-width: 0px; font-size: medium; "><div = style=3D"word-wrap: break-word; -webkit-nbsp-mode: space; = -webkit-line-break: after-white-space; "><span class=3D"Apple-style-span" = style=3D"border-collapse: separate; color: rgb(0, 0, 0); font-family: = Helvetica; font-style: normal; font-variant: normal; font-weight: = normal; letter-spacing: normal; line-height: normal; orphans: 2; = text-indent: 0px; text-transform: none; white-space: normal; widows: 2; = word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; = -webkit-border-vertical-spacing: 0px; = -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: = auto; -webkit-text-stroke-width: 0px; font-size: medium; "><p = style=3D"margin-top: 0px; margin-right: 0px; margin-bottom: 0px; = margin-left: 0px; "><font face=3D"Courier" size=3D"3" style=3D"font: = normal normal normal 12px/normal Courier; "><br = class=3D"Apple-interchange-newline">=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D</font></p><p style=3D"margin-top: 0px; = margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><font = face=3D"Courier" size=3D"3" style=3D"font: normal normal normal = 12px/normal Courier; ">Patrick Kelly</font></p><p style=3D"margin-top: = 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><font = face=3D"Courier" size=3D"3" style=3D"font: normal normal normal = 12px/normal Courier; ">Director of Computer Facilities</font></p><p = style=3D"margin-top: 0px; margin-right: 0px; margin-bottom: 0px; = margin-left: 0px; "><font face=3D"Courier" size=3D"3" style=3D"font: = normal normal normal 12px/normal Courier; = ">=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= </font></p><p style=3D"margin-top: 0px; margin-right: 0px; = margin-bottom: 0px; margin-left: 0px; "><font face=3D"Courier" size=3D"3" = style=3D"font: normal normal normal 12px/normal Courier; ">Faculty of = Architecture and Planning</font></p><p style=3D"margin-top: 0px; = margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><font = face=3D"Courier" size=3D"3" style=3D"font: normal normal normal = 12px/normal Courier; ">Dalhousie University</font></p><p = style=3D"margin-top: 0px; margin-right: 0px; margin-bottom: 0px; = margin-left: 0px; "><font face=3D"Courier" size=3D"3" style=3D"font: = normal normal normal 12px/normal Courier; = ">=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= </font></p><p style=3D"margin-top: 0px; margin-right: 0px; = margin-bottom: 0px; margin-left: 0px; "><font face=3D"Courier" size=3D"3" = style=3D"font: normal normal normal 12px/normal Courier; ">MAIL = = COURIER</font></p><p = style=3D"margin-top: 0px; margin-right: 0px; margin-bottom: 0px; = margin-left: 0px; "><font face=3D"Courier" size=3D"3" style=3D"font: = normal normal normal 12px/normal Courier; ">PO Box 15000 = <span class=3D"Apple-converted-space"> = <span = class=3D"Apple-converted-space"> </span></span>5410 Spring Garden = Road</font></p><p style=3D"margin-top: 0px; margin-right: 0px; = margin-bottom: 0px; margin-left: 0px; "><font face=3D"Courier" size=3D"3" = style=3D"font: normal normal normal 12px/normal Courier; ">Halifax, Nova = Scotia B3H 4R2<span class=3D"Apple-converted-space"> </span><span = class=3D"Apple-converted-space"> <span = class=3D"Apple-converted-space"> </span></span>Halifax, Nova = Scotia</font></p><p style=3D"margin-top: 0px; margin-right: 0px; = margin-bottom: 0px; margin-left: 0px; "><font face=3D"Courier" size=3D"3" = style=3D"font: normal normal normal 12px/normal Courier; ">Canada<span = class=3D"Apple-converted-space"> </span><span = class=3D"Apple-converted-space"> = = <span = class=3D"Apple-converted-space"> </span></span>Canada</font></p><p = style=3D"margin-top: 0px; margin-right: 0px; margin-bottom: 0px; = margin-left: 0px; "><font face=3D"Courier" size=3D"3" style=3D"font: = normal normal normal 12px/normal Courier; = ">=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= </font></p><p style=3D"margin-top: 0px; margin-right: 0px; = margin-bottom: 0px; margin-left: 0px; "><font face=3D"Courier" size=3D"3" = style=3D"font: normal normal normal 12px/normal Courier; ">Phone:(902) = 494-3294<span class=3D"Apple-converted-space"> <span = class=3D"Apple-converted-space"> </span></span>FAX:(902) = 423-6672<span class=3D"Apple-converted-space"> </span><span = class=3D"Apple-converted-space"> <span = class=3D"Apple-converted-space"> </span></span>E-mail:<a = href=3D"mailto:patrick.kelly@dal.ca">patrick.kelly@dal.ca</a></font></p><p= style=3D"margin-top: 0px; margin-right: 0px; margin-bottom: 0px; = margin-left: 0px; "><font face=3D"Courier" size=3D"3" style=3D"font: = normal normal normal 12px/normal Courier; = ">=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= </font></p></span></div></span></div></span> = </div><br></div></body></html>= --Apple-Mail-94-989360860--
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