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Thanks George
My goodness,it seems so long ago since you first introduced the
passage from the Principia into the discussion and while I have moved on and expanded on the subject beyond all recognition you now would not dare discuss Newton's absolute/relative time definition like you did years ago,I guess the progress can be gauged now by what you,as a relativist, can and cannot discuss and this is the price of intellectual slavery. You forget that I did not set out to disprove or prove anything and the trajectory of postings from years ago is the true means by which material and topics evolve.Again,I can point out that I geometrically explained the appearance of the supernova rings in 1990,long before the images emerged in 1994 and I assure you that work has quite a bit in common with the present topic of geometry,clocks and astronomy. You have the advantage that nobody at present associates absolute/relative time with the EoT and this says more of the poor intellectual atmosphere than it does true opposition and I alone remain confident that eventually Newton's purpose and intent of absolute/relative time,space and motion will be rediscovered as the development of accurate clocks for measuring distance was rediscovered. It just takes a tiny spark. "Oriel36" wrote in message m... "George Dishman" wrote in message ... "Oriel36" wrote in message om... snip Seconds are a count of the cycles of a frequency characteristic of a caesium atom. In simplistic terms, they used to be defined as a fraction of a year but now we use something more stable but of the same nominal duration. What you lot have done is turn a clock from an approximation of a geometric system into an idealised standard where the geometry is an approximation.Given that the basis for the development of clocks originated from geometry it is extremely important to consider how 1 second reflects distance within this system.It has nothing to do with 'time intervals' or 'duration',it strictly operates on the principle that 1 second is a proportion of distance traveled through a cycle. Here is how a second and by association a clock works. snip display related stuff ... when relativity emerged however and forced a 'time' dimension into existence through clocks it combined seconds as the measure of the passage of 'time' with the more objective and geometric seconds as a proportion of distance through a cycle. snip historical development the less likely "clocks measure time" can be Why are you still inventing your own childish version of that quote? Because clocks do NOT measure a seperate quantity that relativity designates as a dimension called 'time'. I still don't see what that has to do with your reversing the meaning of the quote. You could state it accurately and then say you disagree. At least I would get the idea you knew what you were talking about. However, that is a minor, if annoying point. You make a fundamental mistake in thinking that Relativity altered the view of time. I have repeatedly pointed out that this was the same view as held by Newton but you steadfastly refuse to even acknowledge what I say. Perhaps this quote will entice you to look into the matter: "Hitherto I have laid down the definitions of such words as are less known, and explained the sense in which I would have them to be understood in the following discourse. I do not define time, space, place and motion, as being well known to all. Only I must observe, that the vulgar conceive those quantities under no other notions but from the relation they bear to sensible objects. And thence arise certain prejudices, for the removing of which, it will be convenient to distinguish them into absolute and relative, true and apparent, mathematical and common. I. Absolute, true, and mathematical time, of itself, and from its own nature flows equably without regard to anything external, and by another name is called duration: relative, apparent, and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time; such as an hour, a day, a month, a year." The above is from Newton's Principia, published in 1687. http://members.tripod.com/~gravitee/...tions.htm#time In particular note: "Absolute, true, and mathematical time ... by another name is called duration" "relative, apparent, and common time ... is commonly used instead of true time; such as an hour, a day, a month, a year." A few paragraphs later he says: "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; ... It may be, that there is no such thing as an equable motion, whereby time may be accurately measured. All motions may be accelerated and retarded, but the true, or equable, progress of absolute time is liable to no change. The duration or perseverance of the existence of things remains the same, whether the motions are swift or slow, or none at all: and therefore, it ought to be distinguished from what are only sensible measures thereof; .." This entire definition emphasises the fundamental difference between the "pure progress of absolute time" he also describes as "duration or perseverance of the existence of things", and the common but flawed measure of time such as hours and days. Newton talks of the apparent motion of celestial bodies merely as a means to measure something quite independent, "Absolute time". It would really help this conversation if you read that page, there is a lot more I haven't quoted. snip Poincare originally based chaos on the premise that left to their own devices seemingly simple rules become rapidly complex,the heading of this thread is an example of that. That is why I have split the thread. This post relates to the fundamental disagreement, that of time as a dimension. The other covers the more general topic of intuition vs. the scientific method and the specific points on displays. I do not intend to pursue those themes to any degree. -- George Dishman The arrow of time points in many directions. |
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Thanks George
"Oriel36" wrote in message m... (George G. Dishman) wrote in message . com... You made occassional comments that didn't seem to fit with your other views, but it was hard to find where the problem lay. ... is all historically documented how a day is defined using the Sun alone as a reference. That's right, the apparent (geocentric) motion of the Sun defines the 24h day. Without that definition of why and how astronomers attributed an equable 24 hour pace to the axial rotation of the Earth as this alone provides the basis of clocks as physical rulers of distance. You are again forgetting the contribution of the Earth's orbital motion, oh but I forgot, you are with Ptolemy on this. I now understand you have an almost Ptolemaic view of the solar system which explains many of your errors. The error is not in treating axial rotation as a seperate motion to orbital motion. Your error was in denying that orbital motion exists: "Oriel36" wrote in message om... "Goes around the Sun" or 'falling around the Sun' is ill-defined,the Earth does no such thing .. Until you resolve this contradiction in your statements, nothing you say will make sense. Either the Earth orbits the Sun or it doesn't, make up your mind. As a siderealist you treat the Earth's axial rotation and orbital motion as one movement ... No, that's what you just did above. When you said "astronomers attributed an equable 24 hour pace to the axial rotation of the Earth..", you neglected the orbital contribution and treated it as all due to the Earth's rotation. Of course you have to do that as long as you deny the Earth orbits the Sun. Since the solar day is 24h and the year is 365.25 days, as you calculated the orbital motion of the Earth around the Sun accounts for 3m 56s of that 24h and that leaves only 23h 56m 4s for the rotation of the Earth. It is your own calculation Gerald, you cannot deny it. I became familiar long ago with the most fundamental rotation of all,the rotation of the Earth on its axis,one full revolution corresponding to 24 hours.You believe the value to be 23 hrs 56 min 04 sec and this constitutes an error. It constitutes the only logical conclusion to your own argument that the orbital motion contributes to the day, but of course you also deny that the Earth orbits the Sun as well as insisting I take it into account. Along time ago, the Ptolemaic model said the Earth was static and the Sun and stars revolved around it in 24h and 23h 56m 4s respectively. The Copernican model that replaced it said the Earth both spun on its axis and revolved around the Sun. Historically our understanding moved from no rotation to one rotation per sidereal day, and AFAIK nobody but you has imagined the Earth rotates 360 degrees in 24h with the stars spinning round us once a year. George |
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Thanks George
"George Dishman" wrote in message ...
"Oriel36" wrote in message m... (George G. Dishman) wrote in message . com... You made occassional comments that didn't seem to fit with your other views, but it was hard to find where the problem lay. ... is all historically documented how a day is defined using the Sun alone as a reference. That's right, the apparent (geocentric) motion of the Sun defines the 24h day. Only after the EoT is applied and that computation is actually an adjustment to the variation in the Earth's orbital motion derived from Kepler's second law which causes the variation in the natural day from noon to noon.I am defining a day by the motions of the Earth on its axis and its motion around the Sun,you are defining axial rotation of the Earth as though it were spinning alone against the background stars for that is what the sidereal is and does. Without that definition of why and how astronomers attributed an equable 24 hour pace to the axial rotation of the Earth as this alone provides the basis of clocks as physical rulers of distance. You are again forgetting the contribution of the Earth's orbital motion, oh but I forgot, you are with Ptolemy on this. Let me show you how the EoT equalises the orbital motion of the Earth to a constant orbital displacement http://ircamera.as.arizona.edu/NatSc...res/kepler.htm The circular orbit is the basis for your sidereal value with its constant .986/3 min 56 sec orbital displacement http://www.absolutebeginnersastronomy.com/sidereal.gif Pity that you have to define a 24 hour day first before you decide to divide a day into an annual cyclical orbit for only then will you know why the difference between the natural unequal day and the constant 24 hour day uses only the Sun and the EoT to obtain the objective of defining a day. I now understand you have an almost Ptolemaic view of the solar system which explains many of your errors. The error is not in treating axial rotation as a seperate motion to orbital motion. Your error was in denying that orbital motion exists: There are no errors in the historically supported reasoning,the determination of a 24 hour day came long before the determination of the sidereal day,the EoT retains the natural day as a component (noon determination) but the sidereal value is entirely artificial and after the fact that a 24 hour day was defined first without the use of circumstellar rotation. "Oriel36" wrote in message om... "Goes around the Sun" or 'falling around the Sun' is ill-defined,the Earth does no such thing .. Until you resolve this contradiction in your statements, nothing you say will make sense. Either the Earth orbits the Sun or it doesn't, make up your mind. Too imprecise on your part,the Earth has both an axial rotation and an orbital motion acting in concert,the axial rotation is constant and the orbital motion varies for each axial rotation,the EoT is the means to isolate axial rotation to 24 hours/360 deg from the variation in its orbital component and provide a seamless transition from one 24 day to the next.As a clock is used to gauge the axial cycle at a constant pace whereas the natural pace as determined by a shadow varies for each axial rotation,it is an automatic deduction that the EoT equalises the variation in the natural unequal pace to a constant 24 hour pace. As a siderealist you treat the Earth's axial rotation and orbital motion as one movement ... No, that's what you just did above. When you said "astronomers attributed an equable 24 hour pace to the axial rotation of the Earth..", you neglected the orbital contribution and treated it as all due to the Earth's rotation. Of course you have to do that as long as you deny the Earth orbits the Sun. Again,astronomers when they accomplished heliocentric modelling reduced their observation of the primary planets and their satellites from observance made through the natural unequal day to a constant 24 hour day,relative time to absolute time,if you choose to use Newton's terminology. "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." Principia It would have been impossible for Roemer to determine finite light distance from the motion of Io without the EoT as the observed motions of the other planets are skewed by the motions of the Earth in its own elliptical orbit around the Sun.Albert simply tied the motion of Mercury to the 'fixed stars' and thinks that you get an elliptical orbit but heliocentric modelling by Kepler and Roemer is an enormous task which compensates for the restriction placed by the Earth's own motion and particularily the natural inequality in a day. Since the solar day is 24h and the year is 365.25 days, as you calculated the orbital motion of the Earth around the Sun accounts for 3m 56s of that 24h and that leaves only 23h 56m 4s for the rotation of the Earth. It is your own calculation Gerald, you cannot deny it. I became familiar long ago with the most fundamental rotation of all,the rotation of the Earth on its axis,one full revolution corresponding to 24 hours.You believe the value to be 23 hrs 56 min 04 sec and this constitutes an error. It constitutes the only logical conclusion to your own argument that the orbital motion contributes to the day, but of course you also deny that the Earth orbits the Sun as well as insisting I take it into account. Along time ago, the Ptolemaic model said the Earth was static and the Sun and stars revolved around it in 24h and 23h 56m 4s respectively. The Copernican model that replaced it said the Earth both spun on its axis and revolved around the Sun. Historically our understanding moved from no rotation to one rotation per sidereal day, and AFAIK nobody but you has imagined the Earth rotates 360 degrees in 24h with the stars spinning round us once a year. George Historically,astronomically and geometrically,the development of accurate clocks relied on the principle that the Earth axially rotates through 360 degrees in 24 hours exactly,the pace of this clock where meridian differences correspond to 'time' difference emerge from the equalising of the natural day gauged by the motions of the Earth using the Sun as a reference to a 24 hour equality . You are not insulting me,you are insulting John Harrison who said "I think I may make bold to say," wrote Harrison, "that there is neither any other Mechanism or Mathematical thing in the World that is more beautiful or curious in texture than this my watch or timekeeper for the Longitude." John Harrison http://www.inference.phy.cam.ac.uk/t.../images/H4.gif The next thing I need to hear from you is why you choose to go against this true genius who based his clock on the work other brilliant men,if it is incapacity then just say so but I assure you the rotation of the Earth through 360 degrees is 24 hours exactly.I admire stubborness in a man but not insincerity for the is the creed of a slave. |
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Thanks George
"Oriel36" wrote in message om... "George Dishman" wrote in message ... "Oriel36" wrote in message m... ... is all historically documented how a day is defined using the Sun alone as a reference. That's right, the apparent (geocentric) motion of the Sun defines the 24h day. Only after the EoT is applied ... No, the EOT only deals with the variation of the day from the mean. The original definition of 24h was just the solar day, that is based on the Sun as you say, but later it was refined to be the mean solar day. and that computation is actually an adjustment to the variation in the Earth's orbital motion derived from Kepler's second law which causes the variation in the natural day from noon to noon.I am defining a day by the motions of the Earth on its axis and its motion around the Sun, The day is not yours to define, nature does that for us. Without that definition of why and how astronomers attributed an equable 24 hour pace to the axial rotation of the Earth as this alone provides the basis of clocks as physical rulers of distance. You are again forgetting the contribution of the Earth's orbital motion, oh but I forgot, you are with Ptolemy on this. Let me show you how the EoT equalises the orbital motion of the Earth to a constant orbital displacement The EOT does not affect the motion of the Earth, it is merely a factor that allows us to calculate natural noon from civil time or vice versa. However, what I am talking about is the the contribution the orbital motion makes to the _mean_ day, not the variation of specific days from that mean. http://ircamera.as.arizona.edu/NatSc...res/kepler.htm Good, now look at the box entitled "Kepler's First Law: The orbits of planets are ellipses with the sun at one focus of the ellipse." and notice that the blue line representing the Earth's orbit 'goes round' the red symbol representing the Sun: "Oriel36" wrote in message om... "Goes around the Sun" or 'falling around the Sun' is ill-defined,the Earth does no such thing .. Until you resolve this contradiction in your statements, nothing you say will make sense. Either the Earth orbits the Sun or it doesn't, make up your mind. Too imprecise on your part, Then look at the diagram above if you are struggling to understand what I am saying, it's really not that hard. Kepler's First Law requires that the path of the Earth emcompasses the Sun, your statement above requires that it does not, yet you claim to accept Kepler's Laws. That contradiction in your ideas makes it very hard to talk to you. Along time ago, the Ptolemaic model said the Earth was static and the Sun and stars revolved around it in 24h and 23h 56m 4s respectively. The Copernican model that replaced it said the Earth both spun on its axis and revolved around the Sun. Historically our understanding moved from no rotation to one rotation per sidereal day, and AFAIK nobody but you has imagined the Earth rotates 360 degrees in 24h with the stars spinning round us once a year. Historically,astronomically and geometrically,the development of accurate clocks relied on the principle that the Earth axially rotates through 360 degrees in 24 hours exactly, The original development of clocks was of course based on the arbitrary choice to break the solar day into 24 hours and if the varied from day to day, it didn't matter much. You said as much in the first paragraph quoted above. When navigation came to rely on clocks, that situation changed and the variation could not accepted, so the correspondence was refined to be between 24 hours and the mean solar day, with the EOT describing the deviation from the mean. the pace of this clock where meridian differences correspond to 'time' difference emerge from the equalising of the natural day gauged by the motions of the Earth using the Sun as a reference to a 24 hour equality . You are not insulting me,you are insulting John Harrison who said "I think I may make bold to say," wrote Harrison, "that there is neither any other Mechanism or Mathematical thing in the World that is more beautiful or curious in texture than this my watch or timekeeper for the Longitude." Exactly, he didn't say ".. than this my watch or timekeeper for the rotation." You need to learn the difference. John Harrison http://www.inference.phy.cam.ac.uk/t.../images/H4.gif The next thing I need to hear from you is why you choose to go against this true genius who based his clock on the work other brilliant men,if it is incapacity then just say so but I assure you the rotation of the Earth through 360 degrees is 24 hours exactly.I admire stubborness in a man but not insincerity for the is the creed of a slave. I will just stick with what Harrison said, longitude, not rotation, and defend him against your perversion of his work. I don't think you do it out of malice, just ignorance. George |
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Thanks George
"Oriel36" wrote in message m... (George G. Dishman) wrote in message . com... (Oriel36) wrote in message . com... My goodness,it seems so long ago since you first introduced the passage from the Principia into the discussion and while I have moved on and expanded on the subject beyond all recognition you now would not dare discuss Newton's absolute/relative time definition like you did years ago, When we previously discussed it, I assumed you were familiar with the simpler aspects of astronomy. I became familiar long ago with the most fundamental rotation of all,the rotation of the Earth on its axis,one full revolution corresponding to 24 hours.You believe the value to be 23 hrs 56 min 04 sec and this constitutes an error. Excuse me for joining in, but what exactly are you saying? The earth orbits the sun once every 365 1/4 days - which we call a year, and it makes a total of 366 1/4 rotations in that time. This means that in an average 24 hours the earth has to rotate more than 360 degrees. If the daily rotation of the earth is measured against a 'fixed' frame, i.e. the fixed stars; then clearly the true 360 degrees is achieved in 23hrs, 56m, 04 sec. The equation of time is an unrelated concept, being the adjustment made to smooth out the Solar clock to take into account the elliptical orbit relected in the solar analemma. It enables us to have equal length seconds, minutes days etc, throughout the year. Newton's comments about absolute time are intended to lay out the difference between the 'imperfect' solar time and the 'perfect' absolute time. The point that is made is that all perfect times are equally perfect. Clearly sidereal time, being regulated by the rotational momentum of the earth is much closer to perfection than solar time. In terms of these ideas, could you explain where your view differs. Thanks |
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Thanks George
"OG" wrote in message ...
"Oriel36" wrote in message m... (George G. Dishman) wrote in message . com... (Oriel36) wrote in message . com... My goodness,it seems so long ago since you first introduced the passage from the Principia into the discussion and while I have moved on and expanded on the subject beyond all recognition you now would not dare discuss Newton's absolute/relative time definition like you did years ago, When we previously discussed it, I assumed you were familiar with the simpler aspects of astronomy. I became familiar long ago with the most fundamental rotation of all,the rotation of the Earth on its axis,one full revolution corresponding to 24 hours.You believe the value to be 23 hrs 56 min 04 sec and this constitutes an error. Excuse me for joining in, but what exactly are you saying? The earth orbits the sun once every 365 1/4 days - which we call a year, and it makes a total of 366 1/4 rotations in that time. You have to define a constant 24 hour day FIRST before you divide the axial cycle into the annual cycle(the capitalisation is not done out of irritation or loss of patience but because of it is of the utmost importance). The astronomical means to derive a constant 24 hour day is from the natural unequal day and the EoT computation using ONLY the Sun as a reference for the motions of the Earth. This means that in an average 24 hours the earth has to rotate more than 360 degrees. The noon determination occurs at any given moment at a longitude meridian location on the Earth,the determination of the exact moment when a longitude meridian rotates to face the Sun directly (noon) varies from one complete axial rotation to the next and constitutes the natural unequal day. The EoT, with its positive and negative values facilitates the transition from one constant 24 hour day to the next and astronomically this was made from the noon determination,we still retain the AM and PM prefix when the astronomical day began at noon. http://ourworld.compuserve.com/homep...powers/EoT.htm If the daily rotation of the earth is measured against a 'fixed' frame, i.e. the fixed stars; then clearly the true 360 degrees is achieved in 23hrs, 56m, 04 sec. No,you have already lost the significance of the 24 hour/360 deg equivalency which provides the basis for the sidereal figure of 23 hours 56 min 04 sec.The original purpose for determination of the 24 hour day allied to civil longitude coordinates remains based on the axial rotation of the Earth isolated from the variation in orbital motion. It stands to reason that axial rotation acting in concert with the orbital motion reflected by Kepler's second law generates an inequality registered by the variation in the pace of a shadow across the face of a sundial.The EoT equalises the shadow's natural pace to a constant pace and 24 hour clocks were developed to keep a constant pace as a product of the EoT ,the equable 24 hour day which it generates and subsequently the division of the 24 hour day into subdivisions of hours,minutes and seconds. Again,you have to define a 24 hour day first and subsequently hours minutes and seconds before you determine that the annual cycle is 365.25 days.This is where the error exists in linking the Earth's axial rotation directly to the stellar circumpolar figure. The equation of time is an unrelated concept, being the adjustment made to smooth out the Solar clock to take into account the elliptical orbit relected in the solar analemma. It enables us to have equal length seconds, minutes days etc, throughout the year. Without the EoT you have no 24 hour clocks,with no 24 hour clocks you cannot make the determination of the sidereal value,the value for the annual cycle or the pace of anything else. Newton's comments about absolute time are intended to lay out the difference between the 'imperfect' solar time and the 'perfect' absolute time. The point that is made is that all perfect times are equally perfect. Newton's definitions and distinctions between absolute and relative time contain a definite mathematical component,the EoT.He is being pragmatic for he is aware that astronomers base their calculations and modelling of the motions of the primary planets on the constant 24 hour day from observances conditioned by the natural unequal day. "The duration or perseverance of the existence of things remains the same, whether the motions are swift or slow, or none at all: and therefore, it ought to be distinguished from what are only sensible measures thereof; and out of which we collect it, by means of the astronomical equation." In his description of absolute time he remarks accurately that there is no observed equable motion corresponding to the pace of a 24 hour clock yet a more sensitive examination of the material reveals that the constant day is based solely on the axial rotation of the Earth free of the variation in the natural unequal day,the variation is due to Kepler's second law. Clearly sidereal time, being regulated by the rotational momentum of the earth is much closer to perfection than solar time. The overall importance of countering the direct linkage of the rotation of the Earth to stellar circumpolar motion or what amounts to the same thing - sidereal time,is that the original determination of the 24 hour day via the EoT permits the isolation of constant axial rotation from its orbital variation.The sidereal value creates a stellar circumpolar framework whereas the original absolute time(as Newton phrasedit) reflects only the axial rotation of the Earth without any outside reference.Crucially,it is easier to begin with axial rotation,then consider orbital motion around the Sun and then consider the Earth's along with the rest of the solar system's rotation about the galactic axis. In terms of these ideas, could you explain where your view differs. Thanks It is a geometric treatment of clocks and their historic and observational relationship to geometry and astronomy. |
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Thanks George
"Oriel36" wrote in message You have to define a constant 24 hour day FIRST before you divide the axial cycle into the annual cycle(the capitalisation is not done out of irritation or loss of patience but because of it is of the utmost importance). The astronomical means to derive a constant 24 hour day is from the natural unequal day and the EoT computation using ONLY the Sun as a reference for the motions of the Earth. The problem with your approach is that using ONLY the sun it is not possible to determine the EoT. Using ONLY the sun, you can ONLY determine a non-constant 'day'. This means that in an average 24 hours the earth has to rotate more than 360 degrees. The noon determination occurs at any given moment at a longitude meridian location on the Earth,the determination of the exact moment when a longitude meridian rotates to face the Sun directly (noon) varies from one complete axial rotation to the next and constitutes the natural unequal day. The EoT, with its positive and negative values facilitates the transition from one constant 24 hour day to the next and astronomically this was made from the noon determination,we still retain the AM and PM prefix when the astronomical day began at noon. Imagine yourself as an ancient astronomer; how can you determine a 'constant' time frame if you use ONLY the sun? If the daily rotation of the earth is measured against a 'fixed' frame, i.e. the fixed stars; then clearly the true 360 degrees is achieved in 23hrs, 56m, 04 sec. No,you have already lost the significance of the 24 hour/360 deg equivalency which provides the basis for the sidereal figure of 23 hours 56 min 04 sec.The original purpose for determination of the 24 hour day allied to civil longitude coordinates remains based on the axial rotation of the Earth isolated from the variation in orbital motion. There is no 24hour/360degree equivalency in the earth's rotation. There _is_ something approaching such an equivalency in the solar clock, but this is uneven and inadequate for considering the true nature of time. Newton knew this. It stands to reason that axial rotation acting in concert with the orbital motion reflected by Kepler's second law generates an inequality registered by the variation in the pace of a shadow across the face of a sundial.The EoT equalises the shadow's natural pace to a constant pace and 24 hour clocks were developed to keep a constant pace as a product of the EoT ,the equable 24 hour day which it generates and subsequently the division of the 24 hour day into subdivisions of hours,minutes and seconds. So the EoT was a consequence of determining a TRUE constant time, better than the 24 hour dirurnal clock . To determine the EoT, you need a better clock. True? Again,you have to define a 24 hour day first and subsequently hours minutes and seconds before you determine that the annual cycle is 365.25 days.This is where the error exists in linking the Earth's axial rotation directly to the stellar circumpolar figure. But you cannot determine a constant 24 hour day without a better time-keeper. The EoT is the adjustment made to the solar clock once you have a better clock. Where else does the EoT come from? The equation of time is an unrelated concept, being the adjustment made to smooth out the Solar clock to take into account the elliptical orbit relected in the solar analemma. It enables us to have equal length seconds, minutes days etc, throughout the year. Without the EoT you have no 24 hour clocks,with no 24 hour clocks you cannot make the determination of the sidereal value,the value for the annual cycle or the pace of anything else. So you agree that without the EoT you don't have a constant 24 hour clock? THIS IS IMPORTANT - capitalized because it's important etc. Newton's comments about absolute time are intended to lay out the difference between the 'imperfect' solar time and the 'perfect' absolute time. The point that is made is that all perfect times are equally perfect. Newton's definitions and distinctions between absolute and relative time contain a definite mathematical component,the EoT.He is being pragmatic for he is aware that astronomers base their calculations and modelling of the motions of the primary planets on the constant 24 hour day from observances conditioned by the natural unequal day. But to get from 'the unequal day' to 'the equal day' you need the EoT, and the EoT needs 'an equal clock' to compare with 'the unequal day', and 'the equal clock' is 23:56:04 long and measured by the stars. "The duration or perseverance of the existence of things remains the same, whether the motions are swift or slow, or none at all: and therefore, it ought to be distinguished from what are only sensible measures thereof; and out of which we collect it, by means of the astronomical equation." In his description of absolute time he remarks accurately that there is no observed equable motion corresponding to the pace of a 24 hour clock yet a more sensitive examination of the material reveals that the constant day is based solely on the axial rotation of the Earth free of the variation in the natural unequal day,the variation is due to Kepler's second law. So we agree:- here you assert that the 'equal' day is based on the axial rotation of 23:56:04, rather than the solar day of 24:00:00. Can you see that you may be missing a step here. The solar day is 'in theory and practice' unequal, the sidereal day is 'in theory and practice' equal. Clearly sidereal time, being regulated by the rotational momentum of the earth is much closer to perfection than solar time. The overall importance of countering the direct linkage of the rotation of the Earth to stellar circumpolar motion or what amounts to the same thing - sidereal time,is that the original determination of the 24 hour day via the EoT permits the isolation of constant axial rotation from its orbital variation. You seem here to say that "We have to deny ("counter") a direct linkage between the earth's rotation and sidereal time" and "we have to do this because we ALREADY have an equation (the EoT) that links an imperfect clock to a perfect clock" If I have misunderstood, then please let me know. However - We do not have the EoT without a steady clock, and the steady clock is measured against sidereal time. The sidereal value creates a stellar circumpolar framework whereas the original absolute time(as Newton phrasedit) reflects only the axial rotation of the Earth without any outside reference.Crucially,it is easier to begin with axial rotation,then consider orbital motion around the Sun and then consider the Earth's along with the rest of the solar system's rotation about the galactic axis. In terms of these ideas, could you explain where your view differs. Thanks It is a geometric treatment of clocks and their historic and observational relationship to geometry and astronomy. |
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