[Tom Bishop]

I see that the concept of computing offset with division of degrees and circles, and the relation of such is lost on some.

You are right. I did assume that the earth orbit around the sun was a perfect circle. But we can do this without degrees, and with a method that does not assume that the orbit of the earth around the sun is a perfect circle. With easy and simple math that will make all very clear.


Napkin Calculations # 5 & 6

--- --- --- ---

Premise:

     - A Solar Day happens every 24 hours
     - A Year happens every 365 days

365 days / 2 = 185.5 days in six months

Now, we need to fit 24 into 185.5

185.5 days divided by 24 = 7.729

Conclusion: 24 does not fit cleanly into 185.5. If it did, it would be a whole number.

Conclusion: The day does not fit neatly into half of the year. Solar Noon will not be at the same place at that point.

--- --- --- ---

Lets now define that a Solar Day happens every 23.933333 hours, and correct the year as well.

Premise:

     - A Sidrael Day/Solar Day happens every 23.933333 hours
     - A Sidrael Year happens every 365.25636 days

365.25636 / 2 = 182.62818 days in six months

182.62818 / 23.933333 = 7.730.

Conclusion: 23.93333 hours does not fit neatly into 182.62818 days. If it did it would be a whole number.*

Conclusion 2: The Sidrael Day does not fit neatly into half of the Sidrael Year. Solar Noon will not be in the same place at that point.

An aside point: When we compare the ratios we got of 7.729 and 7.730 we can see that trying to use the slightly different numbers of Sidrael Day and Sidrael Year makes hardly a difference.

* For arguments that the numbers actually do fit, and but we just aren't "accurate enough" in the measured values of Sidrael Day and Year, and there were a few more numbers after the decimal numbers, the ratio result should still be very near to a whole number. It should be 8.00001 or something of that nature. But we are way off.

[Tumeni]

I see that the concept of computing offset with division of degrees and circles, and the relation of such is lost on some.

I see that you can be exceedingly condescending to someone who has been nothing but polite toward you. What is this 'offset concept', and where has it been discussed or mentioned, prior to your post?

You are right. I did assume that the earth orbit around the sun was a perfect circle.

I never said you did that. Once again, you took a number of hours divided by the number of degrees in a circle; all this yields is the number of hours taken to cover one degree of that circle

But we can do this without degrees, and with a method that does not assume that the orbit of the earth around the sun is a perfect circle. With easy and simple math that will make all very clear.

Napkin Calculations # 5 & 6

--- --- --- ---

Premise:
     - A Solar Day happens every 24 hours
     - A Year happens every 365 days
365 days / 2 = 185.5 days in six months
Now, we need to fit 24 into 185.5
185.5 days divided by 24 = 7.729
24 does not fit cleanly into 185.5. If it did, it would be a whole number.
Conclusion: The day does not fit neatly into half of the year. Solar Noon will not be at the same place at that point.

Dividing the number of days in a half year by the number of hours in one day produces .... what? A random number.

Lets now define that a Solar Day happens every 23.933333 hours, and correct the year as well.

Premise:
     - A Sidrael Day/Solar Day happens every 23.933333 hours
     - A Sidrael Year happens every 365.25636 days
365.25636 / 2 = 182.62818 days in six months
182.62818 / 23.933333 = 7.730.
23.93333 hours does not fit neatly into 182.62818 days. If it did it would be a whole number.
Conclusion: The Sidrael Day does not fit neatly into half of the Sidrael Year. Solar Noon will not be in the same place at that point.

Again, all you're doing is deriving a random number by dividing the number of days in a half year by the number of hours in one day ....


365/24 = 15.21. Days fit equally as badly into a year as they do into a half-year. You appear to have 'proved' that our days don't fit in with our years....

[Tom Bishop]

Dividing the number of days in a half year by the number of hours in one day produces .... what? A random number.

It's not a random number. Division gives a ratio. If the number of days fit into half the year, it should be a whole number.

An example:

24 / 6 = 4.

The number 4 is whole. The number 6 fits neatly into 24 four times.

This is a very, very clear concept.

[garygreen]

This is a very, very clear concept.

indeed it is.

a sidereal day is 4 minutes shorter than a solar day.

4 minutes per solar day * 180 solar days = 720 minutes = 12 hours.

tbh i don't understand what you think the problem is.

[Tom Bishop]

This is a very, very clear concept.

indeed it is.

a sidereal day is 4 minutes shorter than a solar day.

I accounted for that in my last example. Did you not see where I stated:

Premise:
     - A Sidrael Day/Solar Day happens every 23.933333 hours

[Tumeni]

It's not a random number. If the number of days (24 hour cycles) fit into half the year, it should be a whole number

An example:
24 / 6 = 4.
The number 4 is whole. The number 6 fits neatly into 24 four times.
This is a very, very clear concept.

.... then you need to divide the number of hours in a half year by the number of hours in a day to try and get an exact fit of days into the half year ....

Not divide the number of days in a half year by the number of hours in a day.

7 (days) divided by 24 (hours) = 0.29 - if the number of days fit into the week, it should be a whole number, shouldn't it?
24 (hours) divided by 60 (minutes) = 0.4 - if the number of hours fit into the day, it should be a whole number, shouldn't it?
1 (hour) divided by 60 (seconds) = 0.01667 - if the number of minutes fits into the hour, it should be a whole number, shouldn't it?

Are you any kin to Mr Thrive and Survive, or The Potter's Clay, both of whom are active on YouTube?

[garygreen]

I accounted for that in my last example. Did you not see where I stated:

Premise:
     - A Sidrael Day/Solar Day happens every 23.933333 hours

then i don't see what the issue is.  it's a very simple calculation.  i even stuck to integers to make it clearer to see.

4 minutes per solar day * 180 solar days = 720 minutes = 12 hours.

over the course of 6 months, sidereal noon will be ~12 hours behind solar noon.  what's the problem?

[Tom Bishop]

It's not a random number. If the number of days (24 hour cycles) fit into half the year, it should be a whole number

An example:
24 / 6 = 4.
The number 4 is whole. The number 6 fits neatly into 24 four times.
This is a very, very clear concept.

.... then you need to divide the number of hours in a half year by the number of hours in a day to try and get an exact fit of days into the half year ....

We don't know the number of hours in half a year in this problem. That is an number or ratio we are trying to compute based on the length of day and the length of year, to see if the Solar Time cycle matches up.

If you assume that half of the year is composed of full 24/23.933.. hour cycles, then you just assumed your result. You need to do the math without that assumption.

And even if you do use that assumption for half of the year, that assumption will not fit into the full year if you do the calculations.

This last example I gave should have been very clear.

[Tumeni]

This last example I gave should have been very clear.

And my examples make it very clear that your method generates other random numbers when applied to other periods.

[Stagiri]

It's not a random number. If the number of days (24 hour cycles) fit into half the year, it should be a whole number

An example:
24 / 6 = 4.
The number 4 is whole. The number 6 fits neatly into 24 four times.
This is a very, very clear concept.

.... then you need to divide the number of hours in a half year by the number of hours in a day to try and get an exact fit of days into the half year ....

We don't know the number of hours in half a year in this problem. (...)

Since [hour], [day] and [year] are all simply time units which we can quite easily convert to each other if we know the time in [days] (or [years]) we automatically know it in [hours] too.
We don't need to assume anything.

[Tumeni]

We don't know the number of hours in half a year in this problem.

.. but your premise to start with was

Premise:
     - A Solar Day happens every 24 hours
     - A Year happens every 365 days
365 days / 2 = 185.5 days in six months

So ....185.5 * 24 = 4452 hours.

[Tom Bishop]

I accounted for that in my last example. Did you not see where I stated:

Premise:
     - A Sidrael Day/Solar Day happens every 23.933333 hours

then i don't see what the issue is.  it's a very simple calculation.  i even stuck to integers to make it clearer to see.

4 minutes per solar day * 180 solar days = 720 minutes = 12 hours.

over the course of 6 months, sidereal noon will be ~12 hours behind solar noon.  what's the problem?

I think the definitions we are using for these terms may be slightly mixed up.

Lets look at this:

https://community.dur.ac.uk/john.lucey/users/e2_solsid.html

Solar time is time measured with respect to the Sun's apparent motion in the sky. The clocks we use for civil timekeeping are based on this motion. Of course, the apparent motion of the Sun across the sky is actually caused by the rotation of the Earth. So, our clocks measure the length of time required for the Earth to rotate once with respect to the Sun. From our perspective, the Sun revolves around the Earth every 24 hours. This period is known as a solar day.

Sidereal time is time measured with respect to the apparent motion of the 'fixed' stars in the sky due to the Earth's rotation. While the Earth is rotating on its axis it is also moving along its orbit around the Sun. Over the course of a day the Earth moves about one degree along its orbit (360 degrees in a full orbit divided by 365.25 days in a year is about one degree). Therefore, from our perspective, the Sun moves about one degree from west to east with respect to the 'fixed' stars.

And this one:

http://astronomy.swin.edu.au/cosmos/S/Sidereal+Day

A solar day is the time it takes for the Earth to rotate about its axis so that the Sun appears in the same position in the sky. The sidereal day is ~4 minutes shorter than the solar day. The sidereal day is the time it takes for the Earth to complete one rotation about its axis with respect to the 'fixed' stars.

It says that Solar time is measured with respect to the Sun's apparent motion in the sky, and is 24 hours.
 
Sidrael time is measured with respect to the Stars, and is the 23.933333 hours per rotation value. Why would you use the time the stars rotate around the earth in this when we are concerned with the Sun?

Those links say that Solar Time has a 24 hour cycle. Lets use the value according to this link.

Lets now define that a Solar Day happens every 24 hours, and the year every 365.25636 days.

Premise:
     - A Solar Day happens every 24 hours
     - A year happens every 365.25636 days

365.25636 / 2 = 182.62818 days in six months
182.62818 / 24 = 7.609

A 24 hour cycle does not fit neatly into 182.62818 days.

Sidrael Time is star time, not the day and night time, and if that is the definition then I don't see why we should use it in this at all.

[Stagiri]

(...)
365.25636 / 2 = 182.62818 days in six months
(...)

Which six months? The year isn't divided evenly... (and there's reason for it)

[garygreen]

Sidrael Time is star time, not the day and night time, and if that is the definition then I don't see why we should use it in this at all.

it's clear you simply don't fully understand the model you're criticizing.



i added a star to show you how these are related.  at the top, solar noon and "sidereal noon" are the same.  at the bottom, solar noon and sidereal noon are 12 hours apart.

[Tom Bishop]

(...)
365.25636 / 2 = 182.62818 days in six months
(...)

Which six months? The year isn't divided evenly... (and there's reason for it)

But it doesn't matter if the movement of the earth around the sun is not a perfect circle. We are concerned solely with with ratios. The illustration is of Vernal and Autumnal Equinox.

Sidrael Time is star time, not the day and night time, and if that is the definition then I don't see why we should use it in this at all.

it's clear you simply don't fully understand the model you're criticizing.



i added a star to show you how these are related.  at the top, solar noon and "sidereal noon" are the same.  at the bottom, solar noon and sidereal noon are 12 hours apart.

Sideral Noon is the fixed star's position. Yes, both images are facing us (the star). Congratulations. Sideral Noon (star time) changed.

But look at the picture! Solar Noon for NYC is different between both positions. NYC is in midnight in the bottom illustration. Uh oh.

It appears that Star Time is not what we want to talk about here, and the rate the stars move in respect to the sun are not directly relevant. Why should we be concerned with the movement of the stars when we are talking about Solar Noon?

[Tumeni]

At which point, I refer you back to reply #13 and the wikipedia link.

[Tom Bishop]

We don't know the number of hours in half a year in this problem.

.. but your premise to start with was

Premise:
     - A Solar Day happens every 24 hours
     - A Year happens every 365 days
365 days / 2 = 185.5 days in six months

So ....185.5 * 24 = 4452 hours.

The length of the earth's day doesn't fit into the year, whether whether we use 24 hours or 23.933333 hours (which is just star time, as we have read).

It doesn't work if we assume that the year is 365 days long or 365.25636 days long.

Please show how the number of days fits perfectly into the year.

This is very easy math.

We know that Solar Time has a 24 hour cycle. We know that the year is 365.25636 days long. How does it work?

[garygreen]

Sideral Noon is the fixed star's position. Yes, both images are facing us (the star). Congratulations. Sideral Noon changed.

But look at the picture! Solar Noon for NYC is different between both positions. NYC is in midnight in the bottom illustration. Uh oh. Solar Noon needs to be on the opposite side.

you're still not getting this.  just look at the image.  for the top bit, solar noon and sidereal noon are the same.  the star and the sun cross the local meridian at the same time.

for the bottom bit, sidereal noon happens at "solar midnight."  they're out of phase by twelve hours.  i genuinely do not understand what's troubling you about this geometry.

i think the problem is that you're assuming that over the course of an orbital period, a sidereal day and a solar day must have an integer ratio.  why must that be the case?

[Tom Bishop]

Sideral Noon is the fixed star's position. Yes, both images are facing us (the star). Congratulations. Sideral Noon changed.

But look at the picture! Solar Noon for NYC is different between both positions. NYC is in midnight in the bottom illustration. Uh oh. Solar Noon needs to be on the opposite side.

you're still not getting this.  just look at the image.  for the top bit, solar noon and sidereal noon are the same.  the star and the sun cross the local meridian at the same time.

for the bottom bit, sidereal noon happens at "solar midnight."  they're out of phase by twelve hours.  i genuinely do not understand what's troubling you about this geometry.

i think the problem is that you're assuming that over the course of an orbital period, a sidereal day and a solar day must have an integer ratio.  why must that be the case?

This is very easy to understand, Gary. I don't know why you are talking about the movement of the stars in relation to the sun. We are not talking about Star Time.

Lets break it down even simpler. Let not talk about half of the year. Lets talk about the full year. Very basic.

The Solar Time has a 24 hour cycle. That cycle does not fit into the length of the year of 365.25636 days.

Easy one, right? Just divide and we will get a whole number. But that is not what happens. The days don't fit.

[Tumeni]

The length of the earth's day doesn't fit into the year, whether whether we use 24 hours or 23.933333 hours.

Why not?

Please show how the number of days fits perfectly into the year.

1 year = 365 days for three years.
1 year = 366 days for one year. Leap year
Repeat ad infinitum

What's the difficulty?

How does it work?

Have you considered consulting some wikipedia pages, or decent astronomical textbooks?

https://en.wikipedia.org/wiki/Day#Apparent_and_mean_solar_day
https://en.wikipedia.org/wiki/Leap_year