Oriel36

Could you please explain, without using cut and paste and without quoting Newton or Einstein or anyone else, why is it so important that the Earth rotate about its axis in exactly 24 hours???

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SeanF wrote;"Okay, not only does that not answer my question, but it doesn't even make any sense. The Earth is simply rotating on its axis as it revolves around the Sun. There is no "orbital elliptical rotation" that is somehow separate from the "axial rotation." It rotates around its axis, and it revolves around the Sun."

This is where all the problems get resolved,the sidereal figure of 23 hours 56 min combines the axial and annual orbital motions whereas the EoT isolates the axial to 24 hours and clocks are based on the Earth's rotation.

By way of an analogy.Take two threaded bars or bolts of equal lenght,for those who do not know what it looks like here is an image.

http://www.indiamart.com/precisionfasteners/

If a ball or sphere is allowed to run in the groves,each rotation marks out an equal lenght which can be marked off a scale parallel to the bar.This represents the rotation of the Earth in 24 hours if the pitch or the distance between threads on the bar were constant.

If you were to compare the axial rotation of the Earth (the sphere)
against the path of the Earth in its elliptical path (the groves in the bolt) for each rotation through 360 degrees as it would occur naturally and with Kepler's second law in mind,the pitch of the threads would be variable,they would be finely space corresponding to the motion near the aphelion and widely spaced near the perihelion.With each axial rotation of the ball around the bar,it marks off an unequal divisions parallel to the bar.

If the two bars are placed side by side,both the spheres will traverse the total lenght of the bolt in the same period even though as the spheres traverse the bolts,one sometimes be ahead and then sometimes fall behind.

The axis of the bolt represents its orbital path,the axis of the sphere represents the rotation of the Earth,unless you want to play with words and argue over rotate and revolve,there are two rotations involved in the Earth's annual motion and the analogy above will suffice.

SeanF wrote;"Well, the apparent movement of the Sun against the background stars amounts to about .00068 degrees per minute, so during the duration of a 5 minute eclipse, there wouldn't be enough movement to measure.

But you don't need to do it during an eclipse.

Right now, you can't see the star Spica because it's very close to the Sun. In six months, Spica will be easily visible high in the sky at midnight, 180 degrees away from the Sun. Six months after that, Spica will again be right near the Sun and not visible. How does Spica move 180 degrees away from the Sun in six months if it doesn't move about a degree away every day? "

Those who have seen a solar eclipse say that it is awe inspiring,for a few minutes the veil is lifted and we see things as they truly are,our Sun is just one of billions of Suns rotating around the galactic axis.The night sky and stellar circumpolar motions distorts or rather conditions this view,only polaris maintains its position to the Sun but the rest is conditioned by the rotations of the Earth on its axis and its rotation around the Sun.I cannot imagine why you would trade the true motion of our Sun and the rest of the Suns around the galactic axis for circumpolar motion,the insight of the true motion of the stars around the galactic axis has been with us for almost 80 years,Spica does'nt move,the Earth does,Spica maintains its position to our Sun in their majestic sweep around the galactic axis.

SeanF wrote;"So, you're saying you agree with me? During one axial rotation (360 degrees), the Earth moves through its elliptical path (with the distance moved varying throughout the year), so the Earth has to rotate a little bit farther to get to the solar transit again."

Those minds who are capable of sorting out the rotations of the Earth,on its axis,around the Sun and around the galactic axis would have little patience to remain with those who attribute just one rotation to the cyclical annual orbital motion of the Earth and place some significance to circumpolar motion which obstructs the ability to deal with true stellar rotation around the galactic axis and its consequences for wider cosmological modelling.

Those who accomplish most learn to deal with their impatience,those who accomplish least are patient but are so unoriginal that it does'nt matter,at least in terms of astronomy,the real enigma is not nature or the universe,it is man himself and that much I have come to understand.

It's not "playing with words," Oriel. It should be obvious that if you are using words to mean something different than I am, we're not going to be able to talk to each other. That's why it's important that we use the word "rotate" to mean the same thing.

So, let's look at this ball around the threaded bolt thing. Let's have the bolt standing on its end, and we'll look straight down from the top. So, we just see the circle end of the bolt and the ball moves around it, right?

Now, let's say there's a line drawn straight across the circle end of the bolt.

There's also a line drawn from one pole to the other of the ball. So, when we're looking at it from the top, it looks like a straight line that goes from the center of the ball to the edge and is rotating about the center of the ball as the ball rolls around the bolt. Okay.

Now, we start at a point where the two lines are sitting end-to-end, pointing straight along the same path. The ball begins moving along the grooves, rotating as it goes. We eventually reach the point where the line on the ball has gone all the way around and is again pointing in the same direction it started, parallel to the line on the bolt but no longer end-to-end with it. This is one complete rotation of the ball, 360 degrees.

But notice that because the ball has also moved along the groove, our ball line is not pointed at the center of the bolt. Do you see that? The ball has to rotate (and move) a little bit farther to get to the point where the ball line is pointing at the center of the bolt. But then the ball line is no longer parallel to the bolt line.

By the time the ball has moved a quarter of the way around the bolt, its line will be perpendicular to the bolt line when it's pointing at the bolt center.

Now, here are the key points.

Each time the ball line again becomes parallel to the bolt line, pointing in its original direction, is one sidereal day. It is one complete 360 degree rotation of the ball.

Each time the ball line again points at the center of the bolt is one solar day. It is slightly more than 360 degrees of rotation of the ball.

Why did I know when I wrote that that you would think I was talking about proper motion?

I'm talking about the apparent motion of the Sun against the background stars. Right now, Spica appears very close to the Sun, and so cannot be seen in the daylight glare. In six months, Spica will appear very far from the Sun, and be easily visible in the late night dark sky. Therefore, Spica appears to move about one degree a day relative to the Sun.

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SeanF

"Ask to understand, but don't challenge unless you have the knowledge."--NEOWatcher

The contents of this post are ©2008 by SeanF and may not be copied or retransmitted in any form without the express written consent of SeanF

SeanF

The ball and bolt analogy serves the purpose of explaining the Equation of Time via Kepler's second law and especially the variation in distance the Earth covers in its elliptical path against a mean distance.The emphasis is always on the motions of the Earth,the axial and orbital rather than the Sun,the Sun acts only as a reference for the variation in the natural day for each axial rotation,the Equation of Time reflects the variation in distance covered by the Earth in its annual orbital rotation.

The irony is that Newton after going out of his way to distinguish between the natural unequal day and the equalble clock day in terms of the EoT or the difference between absolute and relative time,did'nt clue in that Flamsteed was supplying him with figures based on the sidereal figure,no wonder he could'nt make sense of Flamsteed's data.After informing his readers that the 'vulgar' do not understand the difference between the natural day and the 24 hour clock day,Newton did'nt recognise why Kepler's figures made sense and Flamsteed's did not.

The upshot of all this is that the sidereal value has the Earth rolling around the Sun as though it were a sphere rolling around the surface of a balloon,great if you love 'warped space' but awful if you wish to consider the rotation of the Earth on its axis,its rotation around the Sun and its rotation around the galaxy and the implications of that greater rotation.

SeanF wrote;I'm talking about the apparent motion of the Sun against the background stars. Right now, Spica appears very close to the Sun, and so cannot be seen in the daylight glare. In six months, Spica will appear very far from the Sun, and be easily visible in the late night dark sky. Therefore, Spica appears to move about one degree a day relative to the Sun."

If you wish to consider the rotation of the stars around the galactic axis and the changing orientation of the remaining galaxies to this rotation you have to jettison the following sidereal picture.

http://www.ldeo.columbia.edu/~small/...ages/Stars.jpg

The astronomical heritage which I admire had always enough sense to distinguish that the observed motions of the Sun,planets and stars were conditioned by the motions of the Earth regardless of what reference was used.The 24 clock is built using the Sun as a reference,at the very least it is easier to comprehend Newton's use of absolute/relative time via the Equation of Time and why minutes and seconds were added and subtracted at noon depending on where the Earth was in its annual orbit.

That picture does not represent a sidereal frame of reference.

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"We do not require reality to conform to the expectations of the ignorant"

Astro wrote;http://www.ldeo.columbia.edu/~small/...ages/Stars.jpg
That picture does not represent a sidereal frame of reference"

Do you know how much this 'frame of reference' nonsense has gotten everyone into trouble and makes us all look like idiots.

You can base the sidereal value on 23 hours 56 min but only if the Earth's axial rotation is based on 24 hours.The safest way to know why the rotation of the Earth is based on the 24 hour clock and visa versa is to go back and review how clocks were developed for determining position on the planet via the longitude problem.Next,look at Kepler's second law and then Newton's gravitational laws and one cannot work without the other.

Here is Newton expressing the Equation of Time -

"Absolute time, in astronomy, is distinguished from relative, by the equation or correlation of the vulgar time. For the natural days are truly unequal, though they are commonly considered as equal and used for a measure of time; astronomers correct this inequality for their more accurate deducing of the celestial motions. It may be, that there is no such thing as an equable motion, whereby time may be accurately measured"Principia


Here is where Newton gets it wrong and this is where you get into hot water with indiscrimate 'frames of reference'.As there is no celestial motion corresponding to 24 hours,Newton decides to switch to the sidereal figure which is the only way to determine that the Earth around the Sun and Sun around the Earth are equivalent.



"PHÆNOMENON IV.
That the fixed stars being at rest, the periodic times of the five
primary planets, and (whether of the sun about the earth, or) of the
earth about the sun, are in the sesquiplicate proportion of their mean
distances from the sun.

This proportion, first observed by Kepler, is now received by all
astronomers; for the periodic times are the same, and the dimensions
of the orbits are the same, whether the sun revolves about the earth,
or the earth about the sun."

[Principia]

http://members.tripod.com/~gravitee/...tions.htm#time


Maybe all this is too tough to untangle for everyone but fundamentally clocks are based on a day which in turn is based on the axial rotation of the Earth through 360 degrees,in other words it rotates on its axis once in 24 hours.I thought the whole thing intriguing and I will grant that it is intricate in places but ultimately it was always about the process of incorporating the consequences of the rotation of the local stars around the galactic axis and setting up new rules by using this rotation as a reference for wider cosmological modelling.

You would have a hard time doing any measurements without defining a frame of reference. So no, it's far from being nonsense - it's a requirement to perform any sort of physics.

Actually, the picture does very nicely show us the rotations of the Earth-fixed and sidereal frames of reference;
- In an Earth-fixed frame, the Earth is fixed, and the stars rotate at a constant rate.
- In a sidereal frame, the stars are fixed, and the Earth is rotating at a constant rate.

The key here is that the rotation rate is constant*. No similar constant rate exists relative to the sun, which is why we need to involve all this stuff with the Equation of Time to create such a standard artificially. If you determine your longitude by measuring against the stars, the problem becomes much simpler, as the only inconsistencies are due to stellar parallax and simliar, much smaller effects. The difficulty would lie mainly in determining a set of reference stars close to the celestial equator, not to mention problems with clouds and whatnot.

* Yes, I know, not quite constant but close enough for the level of precision we're discussing

Btw, many of your posts say that "the Earth's axial rotation is based on 24 hours". It's actually the other way around - the length of an hour is determined by the rotation period relative to the (mean) sun. This is not only nitpicking.
Do you realise that these two statements are equivalent?
These two statements are only true in a Galileian frame of reference; in no other, solar, Earth-fixed, etc do they match observations. And, as I've said before, to all appearances, the sidereal frame of reference does seem to be a Galileian one.
1) clocks are based on the day - agreed, no argument
2) the day is based on the rotation of the Earth - not quite; days are based on the rotation relative to the sun, which does not necessarily say anything about any 'true' rotation
3) Stars do not "rotate" around the galactic axis. The actual motions are rather intricate, and involve the spacial distribution of mass in the galaxy. I'm not sure if a Keplerian orbit can be applied at all, but even if possible, it would have to incorporate a HUGE precessional component.

As a side note, do you realise that stuff like that sounds awfully arrogant and condescending? Don't make assumptions about the intelligence of others - all it does is make them angry.

__________________
"We do not require reality to conform to the expectations of the ignorant"

Especially when he clearly doesn't know what he's talking about himself.....

Oh, my. Let's take an extreme example, and look at Mercury.

Oriel36, please read this page.

Now, let's take a look at the first diagram:



From the point labelled "Day 1" to the point labelled "Day 58" (these are Earth days, by the way) is one complete rotation of Mercury. Just look at the red pointers. It starts out pointing straight down, moves 90 degrees to Day 15, 90 degrees to Day 29, 90 degrees to Day 44, and 90 degrees to Day 58. One complete 360-degree rotation.

However, we can see that that point on Mercury's surface is in daylight during that entire time. The sun rises at Day 1, and doesn't set until Day 88. That point on the surface would then spend the next 88 days in darkness.

So, one Mercurial solar day, sunrise to sunrise (or solar transit to solar transit), takes 176 Earth days. However, one Mercurial sidereal day takes only 58 Earth days.

Now, Earth is rotating faster relative to its orbital speed than Mercury, but the general effect is the same - a solar day takes longer than a sidereal day because of the orbital movement around the sun.

Now, if you are going to continue to argue that one complete rotation of the Earth is not 23:56:04, then you're saying that Day 1 to Day 58 on that diagram is not one complete rotation of Mercury.

That simply and clearly makes no sense.

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SeanF

"Ask to understand, but don't challenge unless you have the knowledge."--NEOWatcher

The contents of this post are ©2008 by SeanF and may not be copied or retransmitted in any form without the express written consent of SeanF