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It is known that theoretically we see the same moon phase everywhere on the earth, but practically I see that people are unable to observe the 0.8% waxing crescent at different places on earth. This has some grave consequences as in some cultures like Jewish,Muslim and hindu moon sighting can mark beginnings of festive months. This link claims that different countries have different eid beginnings:

In India, Muslims will celebrate the festival on Monday or Tuesday, depending on the moon's sighting. In Pakistan, Eid will be celebrated on Tuesday as there are no chances of moon to be sighted on 27 July, The News Tribe reported. In the United Kingdom, Eid al-Fitr is likely to be celebrated on 29 July, according to timeanddate.com. In the United States, Muslims will mark the beginning of Shawwal on 28 July, the Fiqh Council of North America, an association of Muslims which is affiliated with the Islamic Society of North America (ISNA), stated in a press release. Muslims in Philippines will celebrate Eid on Tuesday as the official date of the end of Ramadan has been set as 29 July. The Philippine Government in their proclamation had declared 29 July as holiday throughout the country in observance of Eid al-Fitr.

So the question is , is it really possible for people living in different part of the world to see or not see the new moon (0.8% waxing crescent) to mark their festive seasons at different dates?

In other words do Automated calculations \ Lunar calendars give an exact picture of the moon sighting as viewed by a person on earth.

Note : These cultures put personal observation of the new moon a pre requisite to mark the months hence the motivation of this question.

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If you actually subject these empirical lunar calendar systems to the standards of modern data analysis, typical measurement resolutions for the date of new moons are +/- a couple of days. Now note that July 28+/-1 day includes the 29th, and vice versa. Intuitively, 29-28=1 and the dates differ by one day, but if your margin of error one day then 29-28=0 is also acceptable here. This is the main reason why "declaring the day of the New Moon" is even a thing in the first place. –  David H Aug 8 at 23:33

2 Answers 2

+taupunkt basically answered this: the thin lunar crescent after New Moon is only visible for a short while after sunset. While the sun is up, the moon is invisible and it becomes visible when, after sunset, the sky turns dark enough. However, the moon will set typically 1-2 hours after sunset, and will become invisible some time before that due to atmospheric extinction. Whether or not, and if so for how long, you can actually see the moon's crescent depends on the local cirumstances: the distance between the sun and moon (which correlates with the lunar phase and depends on your geographical longitude), the angle between the ecliptic and the horizon (depends on your latitude), whether you're in a mountainous area (and if so, whether you're on a mountain top or in a valley), atmospheric humidity, the weather (a few clouds at the western horizon is all it takes), whether you use your naked eye, binoculars or a telescope, your eyesight and experience, etc.

Because of this, it is difficult to predict when you can see the first/last moon crescent. I use this paper to do that for the Netherlands (Google translation, should be ok since it's a table) and for the naked eye. One thing that strikes me is that of the 25 cases of a first/last crescent sighting this year, the lunar phase ranges from 1.2-9.2%, with a mean of 4.0%, so 0.8% seems to be rather optimistic. You may allow the use a telescope though.

The table doesn't list how long the moon is visible for (the prediction of whether the moon is visible or not is sufficiently uncertain by itself), but it will definitely not be more than the time difference between the rise/set times of the sun and moon (~1-2h). If we use half of the average of those numbers, we get 45 minutes, which may well be optimistic but is not too unrealistic either (for a ~4% crescent). The other ingredient is how long the lunar phase is at 0.8%. Assuming that this means between 0.75% (below which it would be rounded down to 0.7%) and 0.85% (above which it would be 0.9%) this was the case for ~97 minutes for the last time this happened (July 27). Together with the 45-minute observation window, this gives a ~142-minute window of opportunity, or about 10% of a day, indicating that the crescent would be visible from ~10% of the earth.

Remember that we assumed a 4% crescent here, not 0.8%, so this 10% is an overestimation. My guess is that it is a huge overestimation, since in most places you will not be able to see the moon with the unaided eye at all. Even if the moon were somehow visible for an instant everywhere, the fraction of the earth the 0.8% crescent is visible from would drop to ~6.7%. If you want a more precise definition of 0.8%, e.g. 0.80%, or between 0.795% and 0.805%, the moon spends about 10 minutes at the desired phase and this would be visible from 0.7% of the earth.

Then again, you may allow the use of a telecope, so that you can see the moon even during day time. If you also don't worry about the weather, the window of observation would be 12 hours (since the moon is up for observers at about 50% of the earth's surface) and with the 97-minute time window for which the crescent is between 0.75% and 0.85%, the 0.8% crescent would be visible from about 57% of our planet's surface. For 0.795%-0.805%, this would be 51% of the earth.

The conclusion is that a 0.8% crescent of the moon is visible from beteen 0% and 60% of the surface of the earth, depending on your exact definitions and your choice of accuracy and optical aid.

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You can imagine that if you hopped into a rocket and blasted off in a lateral direction, you would be able to view the moon from a different perspective and see more and more of the side illuminated by the sun.

But the earth is only about 12,700 km across whereas the earth-moon distance averages about 385,000 km. That means that the angle you are viewing the moon from the (nearly) opposite sides of the earth is a less than two degrees.

(drawings not to scale)

enter image description here

Moreover, those 2 degree would vary over the edge of the moon (where you are viewing the crescent), so you would see significantly, significantly less difference in the crescent size over those two degrees.

enter image description here

So while it is mathematically possible that two observers of a perfectly spherical illuminated body might see just the tiniest bit more and less than than a 0.8% crescent due to parallax… in reality, the precision by which we make these observations is far, far less than what can be reasonably determined by the human eye or the margin of error due to the irregular surface of the moon, deciding what's "illuminated" in the twilight regions, etc, etc.

The discrepancy in dates is typically due to differing decrees of when the criteria have actually been met rather than any observational differences due to their position on the earth.

[I'm certain I saw a religious authority dispelling such differences in a Q&A interview; but I cannot find the link, so perhaps someone can find a reference.]

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With new moon observations it's a bit more complicated. It's visible only close to and shortly after sunset. So people on different parts of the world observe at different times. The moon moved inbetween, so indeed late observers see 'more' of it. The question seems to be whether the moon moves fast enough to give a rational explanation for the mentioned 'cultural' differences. –  taupunkt Aug 9 at 8:43

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