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Re: Lunar distance this Sunday
From: Brad Morris
Date: 2017 Apr 14, 17:24 -0400

Strict attention to the definition of Easter will determine the answer.

Easter is the first Sunday AFTER the first full Moon AFTER the vernal equinox. They cannot simultaneously occur on any given day, each must occur on a separate day (cross over midnight).

MAXIMUM ELONGATION

The Vernal equinox occurs during day 0. The full moon can occur at 23:59:59 on day 1, as it comes the day AFTER the vernal equinox. Sunday occurs 1 second later, at 00:00:00, on day 2, the day AFTER the full moon.

Elongation = 180 - 1 second / 330 hours × 180°

= 180 - 0.545 arc seconds

= 179°59'59.455"

MINIMUM ELONGATION

I can arrange the sequence of days and lunar orbital period such that the first Sunday AFTER the full moon AFTER the vernal equinox precisely aligns with 1/2 the orbit of the moon.

Elongation = 0°

All other arrangements are equally possible after a sufficiently long period, from the minimum to the maximum elongation.

AVERAGE ELONGATION

(Max-Min)/2 = 89°59'59.72" if we restrict ourselves to whole seconds as a unit of time measure.

Of course, if we wish to permit fractional seconds, then the period between the full moon on day 1 to the Sunday on day 2 is infinitely small (23:59:59.99999999 to 00:00:00) Therefore, the average elongation is 90°

Brad

On Apr 14, 2017 3:00 PM, "Brad Morris" <NoReply_Morris@fer3.com> wrote:

Frank, you wrote: (and is it always waning?)

Easter: First Sunday after the first full moon after the vernal equinox.

Since it is after the full moon, by definition, it must always be waning.

Brad

On Apr 14, 2017 1:05 PM, "Frank Reed" <NoReply_FrankReed@fer3.com> wrote:
Alex Eremenko, you wrote:
"When you say "average" you have to specify over what is this average taken. Over the day of the Easter Sunday after tomorrow (lunar distance certainly changes during the day), or over all Easter Sundays from the very first one until the present time ?"
Yes, indeed. I left that open intentionally to make the puzzle more puzzling (?). Also there are different ways of defining Easter. This year eastern and western Easter both fall on April 16. They have done so every three years or so in the 21st century so far but skipped a whole decade before that and will go eight years without a match after this year. But if you want a specific, what is the average true lunar distance of the Moon from the Sun (and is it always waning?) at noon GMT on Easter as defined by western churches for the 20th and 21st centuries (or some subset at least a decade in length)?
Speaking of averages, here's a good trick question for fans of things astronomical and celestial: what is the average distance of the Earth from the Sun? Or to make the question, more extreme: what is the average distance of Halley's comet from the Sun? Most astronomy texts are quite casual with the concept of "average distance".
Frank Reed

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