The Moon - 24hrs 49 mins????

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ethan5
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The Moon - 24hrs 49 mins????

Post by ethan5 »

Hi,
Could someone explain to me, or direct me to a good website, how the Moon appears to travel east to west across the sky in 24hrs 49mins. I just can't get my head round it and I'm helping my son with his GCSE Physics.
Thanks for your time,

Bill.
David Frydman
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Post by David Frydman »

Dear Bill,
The Moon would hardly change its position night to night if it did not rotate around the Earth once a month.
The Moon travels once around the Earth in about 29 1/2 days.
24 hours is 1,440 minutes.
Divide 1,440 minutes by 29.5 and you get according to my Tesco 83p calculator 48.8 minutes. It isn't exactly 29.5 days, and the Moon has an elliptical path around the Earth, and there are many other smaller effects, but you get the idea.
24 hours plus 48.8 or 49 minutes equals 24 hours 49 minutes.

Simples (well maybe not).

Regards, David
David Frydman
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Post by David Frydman »

You can do this in your head, simple arithmetic.
1,440 minutes divided by 30 equals 48 minutes
But the Moon goes around the Earth every 29.5 days about, so the correction for 29.5 days instead of 30 is 30/29.5 or 60/59, so correct by 1/59, say 1/60 to the first approximation.
48 minutes divided by 60 equals 0.8 minutes.
so 48.8 minutes approximately.

I was brought up on £.s.d.
Everybody then was better at mental arithmetic as you had to add things up in your head.
This new fangled decimal system dulls everybody's brains.

Bring back fathoms, bushels, pints, lbs., tons etc. I suppose the Navy might still use fathoms.

Regards, David
David Frydman
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Post by David Frydman »

The Babylonian Calendar, which is still used in modified forms consisted of 12 months of about 29.5 days giving 354 day years.
It had 7 leap years of 13 months of about 29.5 days every 19 years.
This corrected the average year to near the correct value for a year, which is 365 days, 5 hours 48 minutes 46 seconds. I think this is 31,556,926 seconds from memory, which is our present year corrected by leap seconds occasionally by reference to atomic clocks or even maybe nowadays more accurate measures.
Previously the year was taken as 31,556,926.08 seconds but they rounded it down and added the leap seconds.
The calendar we use has leap years every four years by making February 29 days, with further corrections.
None of these calendars are totally accurate and days, months, years etc, change slightly with time.

Not part of the original question I know, but anyway I mention it.

David
stella
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Post by stella »

The Moon goes round the Earth in 27.3 days.
It goes through its phases in 29.5 days.
David Frydman
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Post by David Frydman »

Thank you for that correction.
Am I correct otherwise in respect of the 24 hours 49 minutes explanation?
If I am not correct, please explain better.
There is a good description if you look up Wikipedia on the rotation of the Moon.
I relied purely on memory so I should have at least looked at an old BAA Handbook.
Thanks.

Regards, David

Looking at an old BAA Handbook it gives Synodic length of month as 29.53059 say 29.53.
This is New Moon to New Moon.
1440 divided by this gives 48.76 minutes.
There are several other Month lengths depending on definition.
David Frydman
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Post by David Frydman »

Should I be dividing 1440 minutes by 29.53 giving 48.76 minutes or the 23h 56m i.e. 1436 divided by 29.53 giving 48.62 minutes?
Or indeed 24hrs 04 minutes i.e. 1444 divided by 29.53 giving 48.9 minutes?

I don't think it is the last one?
But I am interested in which one is correct to get the answer of 24 hours 49 minutes in the original question.

Regards, David
David Frydman
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Post by David Frydman »

Unfortunately the current and recent BAA Handbooks omit all the valuable information that I relied on.
Everything was in one handy small reference year by year but now you have to look it up or go back to old BAA Handbooks of ten or so years ago.
I think this was not a good change.

Luckily I do have these older Handbooks and I should consult them more often.

Regards, David
David Frydman
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Post by David Frydman »

Dear Bill,
Although I may have made a mistake in the terminology of the month I think unless someone tells us differently that what I initially said is correct.
The Moon is moving around the Earth and gives the extra 49 minutes in your question.

If you look up Astronomical and Physical constants in say an old BAA Handbook there are so many and given to great accuracies, that only an expert in the field knows what all of them mean.

To keep it simple I would go more or less with what I said, but the Synodic month, New Moon to New Moon is 29.53 days.

Incidentally in the BAA Handbook for 2001 it gives the Tropical year (1900) as 31,556,925.9747 seconds, close to what I said above.
But again there are different measures of the year so I don't know which one I remember.

Regards, David
David Frydman
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Post by David Frydman »

Dear Bill,
I Googled 'moon's period of 24 hours 49 minutes' and got an expert's explanation by cseligman 'The Motion of the Moon'.
He explains it takes an extra 53 minutes on average in addition to the 23 hours and 56 minutes of the sidereal day.
And he goes into detail.

However, I think I probably get the same result doing it my simple way.
Again, if someone wishes to explain more fully, please do so.

I am not sure how detailed an explanation a GCSE Physics exam requires.

Regards, David
ethan5
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Post by ethan5 »

Thank you David and Stella. With everything else my son is studying this issue had me. Haven't used my bins much as it's been so cloudy!
Thanks,
Bill.
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