11 August 2006

Yesterday National Public Radio (NPR) reported some advance intelligence on the meeting of the International Astronomical Union (IAU) to be held in Prague next week where the astronomers are scheduled to vote on the definition of a planet.

The story says it isn't certain that the proposed definition will be accepted but that it is likely that Pluto will still be a planet although a lesser one. The proposed definition apparently breaks the planets up into three categories and results in a few object being promoted to planetdom:

• Terrestrial Planets
  • Mercury
  • Venus
  • Earth
  • Mars
• Giant Planets
  • Jupiter
  • Saturn
  • Uranus
  • Neptune
• {Dwarf Planets} - actual name is uncertain
  • Pluto
  • Planet X - UB313 ??
  • (1) Ceres ??
  • ??
  • ??
  • ???

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Peter and I have been chasing crescent Moons, trying to get the minimum time between opposing crescents (oldest last crescent and youngest first crescent). So far we have only seen opposing crescents once and although we cought the last old crescent we had to settle for the second young crescent of the following lunation. We always discuss the science involved in this so I decided to do some reading to get myself better versed on the topic. Below are my notes.

The bottom line is that there are a lot of variables that go into determining when a crescent moon is visible and they rarely conspire for a perfect event so you just have to go out there on every opportunity and hope you get lucky.

Ottewell: Astronomical Calendar 2005

At any age under 24 hours the Moon is breathtakingly thin and barely brighter than the low density sky around it! At 18 hours it is quite difficult to see even with binoculars, and in near-perfect conditions. How much more difficult with the naked eye!

• Minimum limits of detectability are 7° from the sun and 3° above the horizon.

  Angular distances like these, rather than age, are what really determine visibility. They do not correlate exactly with age because of the differing speeds and heights at which the Moon passes the Sun. When it passes widely north of the Sun, as in June, July and August, or widely south, as in January, February and December, the exact values of "New Moon" and age loose their importance.

  Comparing the tracks on the different passages, you can see how several factors affect the Moon's visibility:

  --The angle of the Moon's path to the horizon: steep in spring evenings and autumn mornings; as much as 50° lower in spring mornings and autumn evenings, Why is this? Because in northern spring the Sun and Moon are moving from day to day up the steepest northward part of the ecliptic; in autumn, down the steepest southward part.

  --Whether the part of the Moon's path in which it passes the Sun lies north or south of the Sun, until it rises to cross in front of it at the eclipse of April 8 [2005]. At each New Moon after that it passes north of the Sun--highest on July 6--until it recrosses the Sun at the eclipse of Oct. 3.

  --Finally, the moment in the Earth's rotation when New Moon happens; this will favor a certain longitude-zone of the Earth.

Peter and I discussed the effect of the slope of the ecliptic on the setting Moon. When the ecliptic is steep the moon is farther away from the horizon at sunrise/sunset which would make it easier to locate and provide a longer observation period. But looking at the charts on Ottewell I find that when the ecliptic is steep at Moonrise/Sunrise it is shallow at Sunset/Moonset. So while a steep ecliptic at sunrise would favor sighting an old crescent Moon the corresponding shallow ecliptic would hinder sighting the young crescent Moon a few days later. I feel that a factor in determining the best time to sight opposing crescents would be a neutral (~45°) ecliptic at both sunrise and sunset and the only time that occurs, at least in 2005 (the only Ottewell I have right now), appears to be around the time of the Summer Equinox.

For the table below I measured the slope of each setting Moon on Ottewell's charts on pages 34 and 35 of the Astronomical Calendar 2005. Moons with a slope of 40-50° are shown in yellow.

I thought I read it in Ottewell but I don't find it there now so don't know where I found this tidbit, or if it is my own observation. Opposing crescents are easiest achieved when the New Moon occurs close to midnight, so I have looked up the New Moon time in Planetarium and included it. New Moons between 2300 and 0100 are shown in yellow.

2005
Old Crescent	New Moon	Young Crescent
Moonrise Angle	Date Time	Moonset Angle
35°	10Jan05 0704 EST	64°
31°	8Feb05 1729 EST	70°
21°	10Mar05 0411 EST	66°
21°	8Apr05 1633 EDT	77°
15°	8May05 0446 EDT	67°
34°	6Jun05 1756 EDT	63°
49°	6Jul05 0803 EDT	56°
66°	4Aug05 2305 EDT	27°
76°	3Sep05 1446 EDT	22°
73°	eOct05 1501 EDT	19°
73°	1Nov05 2025 EST	20°
59°	1Dec05 1001 EST	36°

S&T Apr89

• Lunar dateline - the location where the first crescent moon is first seen 40-50 degrees wide

S&T Jul88

Sightings of the Moon within 20 hours of conjunction are extremely rare. Of the reliable reports, the record for naked-eye visibility, 15.4 hours, was set by Julius Schmidt on September 14, 1871, from Athens, Greece. For observations with optical aid, the record belongs to R. Morgan, who made a sighting at 14.9 hours on March 15, 1972, from California. Since the ability to make a sighting depends atmospheric clarity, sky brightness, and the sensitivity of the eye during twilight, this exercise is a matter of scientific as well as sporting interest.

...the average phase cycle is about 29.53 days, and any particular cycle can be as much as 6 hours longer or shorter.

The earliest records containing predictions of first visibility come from the Babylonians. Methods for making such forecasts were further developed by Indian and Muslim astronomers, including Omar Khayyam. One method of prediction is based on the time lag between sunset and moonset. That is, the Mon will bee visible if it sets at least 48 minutes after sunset. According to another procedure, visibility is predicted if the Moon and Sun are separated by a specific number of degrees.

…

As Earth rotates, the line marking local sunset sweeps westward around the globe. After conjunction the Moon recedes from the Sun, so that at some locations our satellite becomes visible after sunset. Thus a “lunar dateline” is formed. For observers west of such a line, the Moon will be observable on the first night; viewers to the east must wait one more day. All predictions have a “zone of uncertainty” bracketing the lunar dateline. Within this region the sighting is difficult to predict because of the effects of slight variations in observing conditions.

S&T Feb72

• An experienced Mercury observer made both of his young crescent moon sightings, 16 years apart, when the moon was near perigee. S&T says they wrote about this being a favorable circumstance in the previous astronomical scrapbook (Vol 42-43 @ SIBL)

Danjon's Limit of Visibility

...

Observations of the crescent 24 hours before or after new are fairly common, but sightings less than 20 hours from conjunction are very rare.

...

When the moon is a slender crescent, the shadowed sides of lunar mountains are turned toward us, and furthermore they tend to mask the sunlit areas beyond them. That is, the illuminated crescent looks narrower and shorter than if our satellite were a perfect sphere.

...

...when the moon is seven degrees from the sun...there is no longer any sunlit crescent visible. For an elongation of seven degrees or less, the entire crescent is contained in the shadowed region and disappears from terrestrial view.

Thus, the limit of visibility of a young moon is set by its angular distance from the sun, not by its age. For a particular age, the angular distance can have quite a wide range of values, depending on the moon’s latitude and whether it is near perigee or apogee.

The last time we were chasing the crescents I asked if the length of all lunations is constant. Neither of us was sure. To answer the question I compared the length of three recent lunations which I reported on in my 2Aug06 post. The bottom line is that they are not. Further reading indicated that the length of a lunation is 29.53 days with an error bar of +/-6 hours.. I extended my analysis to include all lunations during 2006.

While thinking about this I wondered of chasing the oldest old crescent and the youngest young crescent was the right challenge. Elongation, the distance of the Moon from the Sun relates to how much of the moon is illuminated,

So I wondered if the variable length of the lunation might result in a thinner old Moon occurring earlier or a thinner young Moon later. So I compared Moon age and % illumination and found that that is indeed the case.

For all of these charts I looked up the time of New Moon in Planetarium and backed off 1 minute.