[Tom Bishop]

Sidrael Day is Star Time, and has nothing to do with this. What does it matter how fast the stars are moving in this?

Nobody is saying that it does matter. You seem to be manufacturing something to argue against.

Again, see https://en.wikipedia.org/wiki/Solar_time

References to a 'distant star' are merely as a reference point, a presumed stationary reference point ...

The stars move in the sky slightly slower than the sun. But this has nothing to do with the stars. Whatever you want to interpret about the stars and how the earth moves and where it is assumed to be fixed doesn't matter. In Solar Time the earth rotation is tied to the sun. If the stars disappeared from existence, Solar Time is still wrong.

Lets compare the smallest value to the largest value.

365.24162603 / 24.0000006 = 15.218400704

365.24274049 / 24.0000006 = 15.218447139

The difference isn't anywhere close to a whole number. This is way off.

Once again, you're a dividing an arbitrary number OF days by the number of hours WITHIN a day and expecting some correlation, when none is expected by anyone. ever.


As an aside;

The currency system in the UK used to be pounds, shillings and pence

1 pound = 20 shillings
1 shilling = 12 pence

You're doing the equivalent of

1 (pound) divided by 12 (pence) = 0.08333 .... oh, no, the currency system doesn't work (unless you divide 12 pounds by 12 pence, and get 1; or 24 pounds by 12 pence to get 2, 36 by 12 = 3, 48 by 12 = 4 ......) !

...

What are you talking about? Both of the values I am using involves days. 365.24 days in a Solar Year. 24 hours in a Solar Day. Each of those days in a Solar Year should have 24 hours in it.

We can see just by looking at the numbers that the 24 hour Solar Day won't fit into a 365.24 day year. The year has a decimal point at the end of it! But it's more than that. The closest kind of year a 24 hour Solar Day could fit into is if the earth had a 360 day year, or a 384 day year. A 365.24 day year does not make any sense.

From https://en.wikipedia.org/wiki/Tropical_year --

A tropical year (also known as a solar year) is the time that the Sun takes to return to the same position in the cycle of seasons, as seen from Earth; for example, the time from vernal equinox to vernal equinox, or from summer solstice to summer solstice.

The sun needs to return to the same position in the sky after one Solar Year.

This means that if Solar Noon starts over New York City at the beginning of the circuit, it needs to end with Solar Noon over New York City at the end of the circuit. As one example in the above quote shows, the Solar Time on Vernal Equinox needs to be the same as Vernal Equinox 1 and Vernal Equinox 2.

If a Solar Day can't fit into a Solar Year, that is a huge problem. Where are those extra hours coming from?

[AATW]

If a Solar Day can't fit into a Solar Year, that is a huge problem. Where are those extra hours coming from?

If a Solar Day is how long it takes the earth to rotate on its axis.
And a Solar Year is how long it takes the earth to orbit the sun.

Why must the ratio of those be an integer? That implies that for every orbit the earth makes of the sun it rotates exactly 'x' times, and x is an integer.
Why should it be? The rotation speed (which, by the way, does change over time, very slowly) and orbit speed are determined by all kinds of things, there is no reason the ratio should be an integer.

[Macarios]

From Mar 1 to Feb 28 Earth turns towards Sun 365 times and in that time travels 359.7612885 degrees around the orbit.
After whole number of 365 turns (not on that date) we reset days/months counter and increase number of years by 1.
After another 365 turns towards Sun it travels another 359.7612885 degrees.
Third time again, fourht time again.
After four sets of 365 days (turns towards Sun) Earth travelled 4 * 359.7612885 = 1439.045154 degrees.
Almost one degree is missing to 1440 (4 * 360 = 1440) and that's where Julian calendar adds Feb 29 to adjust number of own counted years with number of orbits.
So, during full set of four Julian years (one is leap) Earth travels 1440.045154 degrees.
Closer to full set of orbital events than the calendar would be without the Feb 29.
That almost (those 0.045154 degrees) makes Julian calendar still miss for 1 day every 127 years, leading to Gregorian calendar.

People couldn't speed up or slow down the Eaerth in orbit.
They also couldn't speed up or slow down the Earth's rotation to adjust length of solar day to fit in length of tropical year.
All they could do is to adjust the way of counting days in years.

[Stagiri]

(...)
If a Solar Day can't fit into a Solar Year, that is a huge problem. (...)

Maybe for you but not for the GET.

[Tumeni]

What are you talking about? Both of the values I am using involves days. 365.24 days in a Solar Year. 24 hours in a Solar Day. Each of those days in a Solar Year should have 24 hours in it.

Yes, 365 * 24 = 8760 hours, plus 0.24 of a day (6 hours approx).

Every four years, those 0.24s are rolled into (4 * 0.24, or 4 * 6 hours) = 1 extra day of 24 hours in a leap year.

You agree that humankind as a whole does this every four years, don't you?

We can see just by looking at the numbers that the 24 hour Solar Day won't fit into a 365.24 day year. The year has a decimal point at the end of it! But it's more than that. The closest kind of year a 24 hour Solar Day could fit into is if the earth had a 360 day year, or a 384 day year. A 365.24 day year does not make any sense.

Dividing 365.24 (days) BY 24 (hours) yields a meaningless figure which nobody except you expects to be an integer. The mixture of units makes it a nonsense.

Again, see my currency example and hours/seconds examples above. What am I talking about? I'm drawing an analogy intended to help you understand why expecting an integer from this calculation makes no sense....

[Tumeni]

The stars move in the sky slightly slower than the sun. But this has nothing to do with the stars. Whatever you want to interpret about the stars and how the earth moves and where it is assumed to be fixed doesn't matter.

Nobody is saying it has anything to do with the stars, other than them being a reference point outwith the Earth/Sun system. It's nothing to do with any interpretation.

[Edgar Alan Hoe]

There is something that seems wrong with the way the earth rotates around the Sun. Consider the following image that we are taught in school:




Assume that New York City is in its Solar Noon (look at where New York City is in the top and bottom September and March figures in the above illustration). After 6 months the motions suggests that New York City will be in darkness during its noontime.

Some Rough Calculations

Napkin Calculation 1

Day = 24 hours
Year = 365 days

365 days / 2 = 182.5 days in 6 months
24 hours x 182.5 days = 4380 hours in 6 months
4380 hours / 360 (since the sun rotates around the earth 360 degrees in one day) = 12.16666 hour offset

Earth should be offset by 12.16666 hours (similar to the above image)? NYC should be in night?

--- --- ---

Napkin Calculation 2

According to RET particulars, the earth doesn't rotate at exactly 24 hours a day, and the earth doesn't have an exactly 365 day year, which is why we have to change times and add a leap year every 4 years.

Sidreal Day = 23.933333 hours
Sidreal Year = 365.25636 days

365.25636 days per year / 2 = 182.62818 days in 6 months
23.933333 hours per day x 182.62818 days = 4370.90104712394 hours in 6 months
4370.90104712394  / 360 (since the sun rotates around the earth 360 degrees in one day) = 12.14139179 hours offset

Earth should be offset by 12.14139179 hours? NYC should be in night?

--- --- ---

Napkin Calculation 3

Some sources say that the earth "actually" rotates 360.98 degrees per day.

360.98 degrees in a day x 182.62818 days in 6 months
= 65925.1204164 degrees in 6 months
ans / 360.98 = offset is 183.62818 degrees.

Earth should be offset by 183.62818 degrees? NYC should be in night?

--- --- ---

Corrections with the 360.98 figure

Using 360.98 degrees per day in the second calculation, replacing 360 with 360.98, gives an offset of 12.1082 hours. The offset still says that NYC should be in night.

Replacing 360 with 360.98 in the third calculation gives an offset answer of 182.625 degrees. The offset still says that NYC should be in night.

---

I may be going about this entirely wrong. Can I have some help with this seemingly glaring problem?

Why should the time it takes for the earth to spin on its axis fit in to how long it takes the Earth to orbit the Sun?

I must be misunderstanding something here otherwise you've gotten yourself into a muddle.

[AATW]

Why should the time it takes for the earth to spin on its axis fit in to how long it takes the Earth to orbit the Sun?

I must be misunderstanding something here otherwise you've gotten yourself into a muddle.

Yes, I think this is another fine mess he has got himself into.

There is no reason to think that the ratio between the time it takes the planet to orbit the sun and the time it takes the planet to rotate on its access should be an integer. The fact we need leap days and even leap seconds to keep things synced is indication that is is not exact.

[Jura-Glenlivet]

Turns out that the other planets days and years don't throw up integers either, what is going on?

https://www.universetoday.com/37481/days-of-the-planets/

[Tom Bishop]

If a Solar Day can't fit into a Solar Year, that is a huge problem. Where are those extra hours coming from?

If a Solar Day is how long it takes the earth to rotate on its axis.
And a Solar Year is how long it takes the earth to orbit the sun.

Why must the ratio of those be an integer? That implies that for every orbit the earth makes of the sun it rotates exactly 'x' times, and x is an integer.
Why should it be? The rotation speed (which, by the way, does change over time, very slowly) and orbit speed are determined by all kinds of things, there is no reason the ratio should be an integer.

Division of the number of days in a year and the number of hours in a day ( Days in a Year / Hrs in a Day ) must be a whole number because each Day in the Year is a representative of 24 Hours. If this is true then the ratios must relate.

Imagine that we had a planet with a Solar Day that was a 10 hour day.

Imagine that that the Solar Year year of this planet was 100 days.

Lets define Solar Year as the time it takes for the Sun to return back to the same place in the sky in Solar Time. This means that each of the days in the year must be full rotations.

Does a Solar Day fit into a Solar Year?

100 / 10 = 10. Yes. A solar day fits into a Solar Year.

If we mess around those numbers, a solar day no longer fits into a Solar Year.

142 / 10 = 14.2. A solar day does not fit into a Solar Year.

100 / 7 = 16.6. A solar day does not fit into a Solar Year.

A result of a whole number shows that the second value fits into the first value. The only types of Years a 10 hour day would return whole numbers in such a division.

A 10 hour day can fit into a 10 day year (10 / 10 = 1), a twenty day year ( 20 / 10 = 2 ),  but not a 25 day year ( 25 / 10 = 2.5 ).

Each 10 doesn't fit nicely into the 25, and the result is 2.5. The Solar Days have not been completed by the time the planet makes its way to the end.

It doesn't make a difference if we call them planets and years or dimes and pennies. The relationship is defined and must be maintained.

Relationship: 100 pennies is 10 dimes. There are 10 pennies in a dime.

We have 142 pennies and 10 dimes. Does the relationship work?

142 pennies / 10 dimes = 14.2. This is not a whole number. 10 dimes does not fit into a value that is 142 pennies.

100 pennies / 7 dimes = 16.2. This is not a whole number. 7 dimes does not fit into a value that is 100 pennies.

10 dimes can fit into 10 pennies (10 / 10 = 1), 20 pennies (20 / 10 = 2), but it cannot fit into 25 pennies (25 / 10 = 2.5).

10 dimes doesn't fit nicely into the 25, and the result is 2.5.

[Devils Advocate]

Turns out that the other planets days and years don't throw up integers either, what is going on?

https://www.universetoday.com/37481/days-of-the-planets/

So a day on Mercury is longer than a year on Mercury.......Tom get your calculator out, I think you can prove Mercury doesn't exist 

[Devils Advocate]

If a Solar Day can't fit into a Solar Year, that is a huge problem. Where are those extra hours coming from?

If a Solar Day is how long it takes the earth to rotate on its axis.
And a Solar Year is how long it takes the earth to orbit the sun.

You're answering your own question Tom. The day is the time it takes for earth to rotate and the year is how long it takes for the earth to orbit the sun. These are two independent events with no logical reason why they should fit snugly into an equation together. Humans have jammed and manipulated them to fit in our calendar as best as we can but its not perfect because the universe isn't mathematically perfect. If it was then Pi would be a whole number.
 

[Edgar Alan Hoe]

If a Solar Day can't fit into a Solar Year, that is a huge problem. Where are those extra hours coming from?

If a Solar Day is how long it takes the earth to rotate on its axis.
And a Solar Year is how long it takes the earth to orbit the sun.

Why must the ratio of those be an integer? That implies that for every orbit the earth makes of the sun it rotates exactly 'x' times, and x is an integer.
Why should it be? The rotation speed (which, by the way, does change over time, very slowly) and orbit speed are determined by all kinds of things, there is no reason the ratio should be an integer.

Division of the number of days in a year and the number of hours in a day ( Days in a Year / Hrs in a Day ) must be a whole number because each Day in the Year is a representative of 24 Hours. If this is true then the ratios must relate.

Imagine that we had a planet with a Solar Day that was a 10 hour day.

Imagine that that the Solar Year year of this planet was 100 days.

Lets define Solar Year as the time it takes for the Sun to return back to the same place in the sky in Solar Time. This means that each of the days in the year must be full rotations.

Does a Solar Day fit into a Solar Year?

100 / 10 = 10. Yes. A solar day fits into a Solar Year.

If we mess around those numbers, a solar day no longer fits into a Solar Year.

142 / 10 = 14.2. A solar day does not fit into a Solar Year.

100 / 7 = 16.6. A solar day does not fit into a Solar Year.

A result of a whole number shows that the second value fits into the first value. The only types of Years a 10 hour day would return whole numbers in such a division.

A 10 hour day can fit into a 10 day year (10 / 10 = 1), a twenty day year ( 20 / 10 = 2 ),  but not a 25 day year ( 25 / 10 = 2.5 ).

Each 10 doesn't fit nicely into the 25, and the result is 2.5. The Solar Days have not been completed by the time the planet makes its way to the end.

It doesn't make a difference if we call them planets and years or dimes and pennies. The relationship is defined and must be maintained.

Relationship: 100 pennies is 10 dimes. There are 10 pennies in a dime.

We have 142 pennies and 10 dimes. Does the relationship work?

142 pennies / 10 dimes = 14.2. This is not a whole number. 10 dimes does not fit into a value that is 142 pennies.

100 pennies / 7 dimes = 16.2. This is not a whole number. 7 dimes does not fit into a value that is 100 pennies.

10 dimes can fit into 10 pennies (10 / 10 = 1), 20 pennies (20 / 10 = 2), but it cannot fit into 25 pennies (25 / 10 = 2.5).

10 dimes doesn't fit nicely into the 25, and the result is 2.5.

So you're saying there should be some fixed relationship between a planets orbit around the Sun and a planets rotation on its own axis, is that right?

[Tumeni]

Division of the number of days in a year and the number of hours in a day ( Days in a Year / Hrs in a Day ) must be a whole number because each Day in the Year is a representative of 24 Hours.

No.

Divide 7 (days in a week) by 24 (hours) and you get 0.29166. So what? Does that mean weeks are wrong?

If there are 20 shillings in one pound, and 12 pence in one shilling, there's (20*12) 240 pence in one pound.

Divide 20 by 12 and you get 1.6666. What does that MEAN to you, in this context, if anything?

If you divide 240 by 12, you get 20, but you have to divide similar units to do this. You're dividing different units, and coming up with something meaningless.

[AATW]

Division of the number of days in a year and the number of hours in a day ( Days in a Year / Hrs in a Day ) must be a whole number because each Day in the Year is a representative of 24 Hours. If this is true then the ratios must relate.

OK...firstly, the number of hours in a day being 24 is completely arbitrary. It's a definition. I actually don't know where that definition came from but there is nothing magic about the number 24. I guess it was defined as such because it's so divisible, you can divide it by 2,3,4,6,8 and 12 exactly, I suspect this is also why there were 240 pennies in an old British pound, but I digress.

The length of a year and the length of a day are a defined by
a) How long a planet takes to orbit its star
b) How long a planet takes to revolve on its axis

respectively. That applies to any planet.
These are two independent motions, the ratio of them does not need to be exact. We need leap days and leap seconds because it is not exact.

Imagine that we had a planet with a Solar Day that was a 10 hour day.
Imagine that that the Solar Year year of this planet was 100 days.

Lets define Solar Year as the time it takes for the Sun to return back to the same place in the sky in Solar Time. This means that each of the days in the year must be full rotations.

Does a Solar Day fit into a Solar Year?

100 / 10 = 10. Yes. A solar day fits into a Solar Year.

Well, again, the definition of hours in a day is arbitrary. You could still have 24 hours in a day. The important part of your scenario is that the year (how long the planet takes to go around the sun) is an exact number of days (how long the planet takes to rotate).

In that scenario then because 100 is an integer, if we imagine I'm in space above that planet and I'm completely stationary (let's ignore any movement of stars and galaxies). I take a photo of the planet as it is right in front of me and then exactly 100 of that planet's days later I take another photo. In that time the planet has gone around its star once and rotated 100 times while I have stayed exactly where I was. Those two photos should exactly match because 100 is an integer, whatever side of the planet was facing towards me the first time should be facing towards me the second.

If the number of days in a year is not an integer though, as it isn't on earth, then if I took the second photo an exact solar year after the first of earth then the photos would not match, the earth would not be in exactly the same orientation as it was before. What I'm confused about is why you think that's an issue? Who says it has to be? As I said, if that was the case on earth we wouldn't need leap days or seconds, the ratio between the length of earth's year and day would be exact. But it isn't.

The speed the earth orbits the sun and the speed it rotates on its access are completely independent of one another, as someone else has pointed out one of the planets in our solar system actually has a longer day than it does a year, it spins so slowly that it has gone round the sun more than once before it makes a complete revolution around its access.

I don't understand why you think that's an issue.

[Tom Bishop]

They aren't independent variables.

1 Year = 365.24 Days

24 hours = 1 Day

The related variable is Days.

The relationship isn't really any different than 100 pennies = 10 dimes, as demonstrated in my previous post.

The math doesn't need to know about the concept of money or rotations or years. The equation is a simple relationship ratio.

IF there are 24 hours in a day then it only fits into certain kinds of years. Visualize it.

Can a 24 hour day fit into a year that is 0.5 days long? NO

Can a 24 hour day fit into a year that is 2.5 days long? NO

The above examples should be easy to visualize. Very easy. The earth has not finished rotating by the time it reaches those points.

[Tom Bishop]

Division of the number of days in a year and the number of hours in a day ( Days in a Year / Hrs in a Day ) must be a whole number because each Day in the Year is a representative of 24 Hours.

No.

Divide 7 (days in a week) by 24 (hours) and you get 0.29166. So what? Does that mean weeks are wrong?

There is a rule in division that the larger group on the left side needs to be a bigger number than the smaller group on the right side for this to work.

7 / 24 = 0.29166  < --- This is not a valid equation for the purpose

If we change that around to "1 Day is 3 hours. Does a 3 hour day fit into a 6 day week?"
 
6 / 3 = 2. Whole Number. Works.

Does a 3 hour day fit into a 7 day week?

7 / 3 = 2.33. Not a whole number. A 3 hour day does not fit neatly into a week that is 7 days long. The earth has not finished rotating by the time it reaches that point.

[AATW]

Again, there being 24 hours in a day is a definition. An hour is a completely made up concept.
A day and a year are not, they have definitions which relate to the movement of the planet, an hour is not it is just an arbitrary sub-division of a day.
Why you think days / hours should be a whole number is beyond me.

[Curious Squirrel]

They aren't independent variables.

1 Year = 365.24 Days

24 hours = 1 Day

The related variable is Days.

The relationship isn't really any different than 100 pennies = 10 dimes, as demonstrated in my previous post.

The math doesn't need to know about the concept of money or rotations or years. The equation is a simple relationship ratio.

IF there are 24 hours in a day then it only fits into certain kinds of years.

Can a 24 hour day fit into a year that is 0.5 days long? NO

Can a 24 hour day fit into a year that is 2.5 days long? NO

The above examples should be easy to visualize. Very easy.

A year an a day, only have as much relation to one another as humans have decided they do. Your two examples are incorrect. The length of a day doesn't care how long the length of a year is, and vice versa. There's no mathematical relationship/ratio required between them.

Earth takes 365.24 days to go around the sun. It takes 1 day to go fully rotate around it's axis. All that means is the rate of rotation and the orbital rate are not a perfect match. Which completely expected. As mentioned previously, this is why we have leap days and leap seconds. To keep our calendar roughly on track.

If I have $4.21 in my pocket right now, I can't divide that equally into dimes. Looks like our money system is broken. I can't divide it equally into quarters either! Dear god help us, the economy is ruined! /s

Division of the number of days in a year and the number of hours in a day ( Days in a Year / Hrs in a Day ) must be a whole number because each Day in the Year is a representative of 24 Hours.

No.

Divide 7 (days in a week) by 24 (hours) and you get 0.29166. So what? Does that mean weeks are wrong?

There is a rule in division that the larger group on the left side needs to be a bigger number than the smaller group on the right side for this to work.

7 / 24 = 0.29166  < --- This is not a valid equation for the purpose

If we change that around to "Does a 3 hour day fit into a 6 day week?"
 
6 / 3 = 2. Whole Number. Works.

Does a 3 hour day fit into a 7 day week?

7 / 3 = 2.33. Not a whole number. A 3 hour day does not fit neatly into a week that is 7 days long.

Does a 24 hour day fit into a 7 day week?

24/7 = 3.429 Not a whole number, a 24 hour day doesn't fit into a 7 day week. Clearly our whole concept of time is broken Tom. Help us figure it out, will you?

[AATW]

Does a 3 hour day fit into a 7 day week?

7 / 3 = 2.33. Not a whole number. A 3 hour day does not fit neatly into a week that is 7 days long.

Does a 24 hour day fit into a 7 day week?
Does a 52 week year fit into a 365 day year?

IF I said "there are 168 hours in a week and 24 hours in a day" and 168 didn't divide by 24 THEN you would be able to say
"But that means there aren't an exact number of hours in a day" and you'd be right.

But expecting arbitrary definitions like 7 days in a week and 24 hours in a day to correlate to number of days in a year and it have to be a whole number is meaningless.