Sun Travel

[SKF]

Hi Everyone,

 

I'm wondering how many arcseconds the Sun "travels" in one Tropical Year. I think it travels 1296000 in one day.

 

Mark

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Merged post follows:

Consecutive posts merged

So, this is from the reference point of someone standing on the solid Earth in one spot all year.

 

We could say that the sun starts at 90 degrees, goes down and up and back to 90 degrees(of course as the seasons change, the angle changes but that doesn't effect the calculation of angle travelled, and it does this 365 times, eventually coming back to the same position in the sky. 360 degrees times 365 days.

 

Here are my calculations:

 

One year: 131400 degrees, which is

 

7884000 arcminutes, which is

 

473040000 arcseconds.

 

I believe that is 473040000 arcseconds of angle traveled by the Sun from the reference point of someone standing on the solid earth in the same spot all year.

 

If someone could check my numbers, I would appreciate it.

 

Mark

[D H]

Not this nonsense, again!

 

Discussed ad nauseum here:

http://www.physicsforums.com/showthread.php?t=361891

http://www.physicsforums.com/showthread.php?t=362282

 

Mark, if you are trying to resurrect your disproof of the concept of a sidereal year, this thread will get the same treatment it got at physics forums. We are quite open to discussion here if, on the other hand, you truly do want to understand the concept.

[SKF]

I'm still just looking for the number of arcseconds, and thought that I would get more help here. Seriously, that's all I want to find out in this discussion. This, to me, seems a basic of astronomy. Yes, I have my own answer, but I want others to confirm the number.

[D H]

In other words, you are a crackpot on an agenda, or at least that is the appearance you give. You've been told multiple times that you are wrong, but rather than try to learn something you are taking the hidden agenda approach.

[SKF]

In any case, it's not up to me. It's up to the moderators of this forum if they want this topic to be discussed. Of course, if they don't want to discuss this topic, there is nothing more for me to say.

[Cap'n Refsmmat]

How many arcseconds the Sun travels from what reference frame?

[SKF]

Standing on the Earth in one spot all year....

[D H]

In any case, it's not up to me.

It is entirely up to you. The choice is yours. You can (a) argue that the concept of a sidereal year is wrong, or (b) try to learn something. Choose option (a) and this thread is toast. I strongly suggest you choose option (b).

[SKF]

Right.

 

So, I get for my calculations 473040000 arcseconds that the Sun travels through the sky in one year.

 

I did 1296000'' x 365 days.

 

Corrections welcome!

[mooeypoo]

But the above is wrong, and the two links D H posted explain why.

 

Let's try to see this again, SKF - You seem to be choosing one reference frame (a crappy one at that, for this type of calculation, seeing as it mixes up the rotation of the earth around itself WITH the rotation of the earth around the sun) and expect the answer to fit a different reference frame (just the rotation around the sun).

 

Things don't quite work this way. It's also confusing to answer. And it's definitely not yielding the simplistic calculation you posted.

 

So.. can you clarify here? What reference frame are you talking about?

 

Let me try and understand: Do you mean we look up at 00:00 on day X and take a "picture" of the sun's location in respect to a specific post, then we wait a full year (365 days) and take the same picture at 00:00 on day X a year later, then compare the position of the sun?

 

Is that what you mean?

 

Or rather, do you mean how it moves apparently to us while we're looking up? Because if you mean the second, then the sun appears to move because the Earth rotates around itself, on top of the fact that it seems to move because the Earth is moving around the sun.

 

When we calculate the differences and the sun's apparent movement, we don't usually mix the two up because mixing them up is useless. We calculate either-or, from a reference frame that isn't rotating around itself.

 

Is that clearer?

[SKF]

Hi,

 

Thanks for your response.

 

Of course, we know that the Earth moves around the sun. But from a reference frame of standing on the Earth, the Sun is travelling through the sky.

Let me try and understand: Do you mean we look up at 00:00 on day X and take a "picture" of the sun's location in respect to a specific post, then we wait a full year (365 days) and take the same picture at 00:00 on day X a year later, then compare the position of the sun?

 

Not this.

 

Just how much angle the Sun travels through that sky in one year to get back to point X.

 

Or rather, do you mean how it moves apparently to us while we're looking up? Because if you mean the second, then the sun appears to move because the Earth rotates around itself, on top of the fact that it seems to move because the Earth is moving around the sun.

 

Right, as I mentioned above. But we're taking the reference frame of standing on the Earth. Of course it is an apparent movement.

 

Mark

[mooeypoo]

Hi,

 

Thanks for your response.

 

Of course, we know that the Earth moves around the sun. But from a reference frame of standing on the Earth, the Sun is travelling through the sky.

Due to the rotation of the Earth around itself, which is a different frame of reference.

 

You're mixing two frames of reference up, and then take the answer based only ONE frame and compare it, declaring it to be false.

 

See the problem?

 

Not this.

 

Just how much angle the Sun travels through that sky in one year to get back to point X.

Again, this is too vague. The sun travels in the sky because the Earth rotates around itself.

The sun changes position relatively to the Earth (regardless of rotation) within a year but then it doesn't quite "travel in the sky".

 

You are mixing two frames.

 

 

Right, as I mentioned above. But we're taking the reference frame of standing on the Earth. Of course it is an apparent movement.

 

Mark

No, you seem to be mixing the two. What I stated was a reference frame *NOT* from the surface of the Earth (I ignore rotation around itself). You say "yes" to my description but include the rotation of the Earth around itself. That would not be a 'Right', to my description: it would be a wrong.

 

You're mixing two frames. Again.

 

Choose one.

[SKF]

Hi,

 

It's tracing a circle in the sky. Not sure how it matters what else is going on if I'm only looking for the total angle traced in the sky by the Sun.

 

Mark

[mooeypoo]

Hi,

 

It's tracing a circle in the sky. Not sure how it matters what else is going on if I'm only looking for the total angle traced in the sky by the Sun.

 

Mark

SKF, this is very simple: You need to specify an inertial frame, otherwise this calculation makes no sense. There are an infinite amount of answers depending on infinite amount of reference frames.

 

You seem to use a certain number of seconds and claim that's the movement of the sun. It may well be, but it is *not* in the reference frame you claim it is.

 

If you mix reference frames, you make no sense. That's really quite simple.

 

You were told this fact multiple times in here and in the other forum.. I am hoping that this is due to some fundamental misunderstanding you have about the need for reference frames, so I am being patient and really trying to understand what you mean -- but it's very hard when your descriptions are so confusing.

 

Which scenario are you talking about?

 

(A) Stationary camera on the surface of the Earth, looking at the visible sky, making a "movie" of the sun every day for one year.

 

(B) Satellite orbiting the Earth in a point where it always faces the sun above the Earth - on a fixed point between the Earth and the Sun - taking a snapshot once, then a year later another snapshot, and you want to calculate the difference (the "sum" of movement in relation to the Earth).

 

These are two different reference frames.. one speaks of the apparent movement of the sun in the sky (A) and the other describes the apparent movement of the Sun relative to the earth as a whole (B).

 

Pick one.

[D H]

Even more importantly, Mark, are you still hung up on the idea of somehow disproving the concept of a sidereal year? Both the sidereal year and the tropical year are clearly definable and easily measurable quantities. That these two quantities differ by about 20 minutes is a fact known to the ancients.

 

If you are having difficulties understanding these concepts and how they relate to general precession, fire away. Your fixation on the motion of the Sun from the perspective of an Earth-fixed frame is hindering your understanding.

[StringJunky]

Mark: From a fixed position on the Earth the sun moves in a figure of eight pattern (not a circle as you mentioned)during the course of one year. This phenomenon is called an Analemma:

 

 

Time-lapse photograph taken from the same position, same time, every week for a year

 

I don't know if this is relevant but thought I'd mention it as you are working from a flawed mental image about the apparent movement of the sun through the sky.

 

Hope this helps.

Edited December 12, 2009 by StringJunky

[D H]

Mark: From a fixed position on the Earth the sun moves in a figure of eight pattern (not a circle as you mentioned)during the course of one year. This phenomenon is called an Analemma:

Mark (SKF) was alluding to the figure traced out over one day. To see the analemma take shape, one must remove this daily motion by recording the position of the Sun at a fixed time each day.

[mooeypoo]

Sidereal year and tropical year are both definitions created by humanity to define two different situations... I'm to sure I understand how one can argue they're physically wrong or, for that matter, what difference it would make for our understanding of physics, if they are our own definition.

 

It's as if we realized that "sobbing" and "crying" are only slightly different, and then argued the distinction is false, isn't it? we're the ones making that definition from different points of view. We defined them differently from the beginning.

 

The differences between them are also the reason we add an extra day each four years (February 29th).

 

It's a logical result of two slightly different definitions of a year.. not sure I get why this difference is such a big deal?

[StringJunky]

Mark (SKF) was alluding to the figure traced out over one day. To see the analemma take shape, one must remove this daily motion by recording the position of the Sun at a fixed time each day.

 

Ok. Thanks DH.

[SKF]

It's a logical result of two slightly different definitions of a year.. not sure I get why this difference is such a big deal?

 

Hi Mooeypoo,

 

I actually agree with you It doesn't make much difference to science. It is interesting though, at least to me.

 

Back to the topic...

 

(A) Stationary camera on the surface of the Earth, looking at the visible sky, making a "movie" of the sun every day for one year.

 

This one

[D H]

The differences between them are also the reason we add an extra day each four years (February 29th).

You are thinking of the roughly 1/4 day difference between 365 days and the tropical year. The sidereal year and tropical year differ because of the precession of the equinoxes.

 

The Earth's rotation axis is tilted at about 23.44° with respect to its orbital angular momentum vector. It is this axial tilt that results in the seasons. As we want our calendars to be based on the seasons, we use the mean time between successive vernal equinoxes as the defining characteristic of a year. This is the vernal equinox year, which was 365.24237404 days long at epoch J2000.0 (ask, but only if you want to be confused further). The reason we need to add leap days is because that 365.2424 days is not an integer. Julius Caesar introduced the Julian calendar, which inserted one leap day every four years. The Julian year is 365.25 days long on average. This is a marked improvement, but is still off a bit. Our current calendar omits the leap day on years that are divisible by 100 but not by 400. This makes for an average year of 365.2425 days, which is very close to the mark.

 

If the Earth's rotational axis was a constant vector, the vernal equinox would occur at the same location on the Earth's orbit about the Sun every year. However, both the angle and the orientation of the Earth's rotation axis with respect to the Earth's orbital plane changes slowly over time. Ignoring the change in the angle for now, the Earth's rotational axis undergoes a slow precession, the precession of the equinoxes, about the Earth's orbital angular momentum vector. A full cycle takes about 25,771.5 years to complete. This slow precession means that in terms of the Earth's orbit about the Sun, the anomalistic angle between successive vernal equinoxes is about 50 arcseconds shy of 360 degrees.

 

The time it takes to cover a full 360 degrees is of interest as well. This is the sidereal year. The sidereal year was 365.256363004 days long at epoch J2000.0. The difference between the vernal equinox year and the sidereal year means that the constellations used by astrologers now appear in different months than they appeared in when Babylonian astrologers first developed astrology.

 

What about the tropical year? The time between successive vernal equinoxes is 365.242374 days and is growing with time. The time between successive autumnal equinoxes is 365.242018 days and is shrinking with time. The tropical year, 365.242190 days, is the average of the time between successive points over the whole year. So why is the time between vernal equinoxes growing and the time between autumnal equinoxes shrinking? The answer lies in the shape of the Earth's orbit, and this will introduce a fifth definition of the year.

 

The Earth's orbit is elliptical. The anomalistic year is the time between successive perihelion passages. Because the Earth orbits the Earth-Moon center of mass, the exact timing of the Earth's closest approach to the Sun varies a bit year to year. Ignoring this bouncing around, one would expect the perihelion passage to occur at the same point on the Earth's orbit every year. This isn't the case. The anomalistic year, 365.259635864 days at epoch J2000.0, is about 282.771 seconds longer than the sidereal year largely thanks to Jupiter.

 

The date at which perihelion passage occurs (e.g., January 3, 2010) advances about one day every 58 years. This advance is why the time between successive vernal equinoxes is growing but the time between successive autumnal equinoxes is shrinking.

 

Recap

 

[math]\aligned

&\text{\bf Year}&&\text{\bf Length (days)} \\

&\text{Julian}&&365.25 \\

&\text{Gregorian}&&365.2425 \\

&\text{vernal equinox}&&365.24237404 \\

&\text{tropical}&&365.24218967 \\

&\text{sidereal} &&365.256363004 \\

&\text{anomalistic}&&365.259635864

\endaligned[/math]

[mooeypoo]

You are thinking of the roughly 1/4 day difference between 365 days and the tropical year. The sidereal year and tropical year differ because of the precession of the equinoxes.

Yah.. by a quarter of a day,roughly... which I was sure is why we add a day every four years.. no?

 

The Earth's rotation axis is tilted at about 23.44° with respect to its orbital angular momentum vector. It is this axial tilt that results in the seasons. As we want our calendars to be based on the seasons, we use the mean time between successive vernal equinoxes as the defining characteristic of a year. This is the vernal equinox year, which was 365.24237404 days long at epoch J2000.0 (ask, but only if you want to be confused further). The reason we need to add leap days is because that 365.2424 days is not an integer.

Yup, and it's .24 which is almost a quarter, hence another day every 4 years. Indeed. My point is that *WE* defined the year this way, not the universe.. as far as the universe is concerned we're off with our count which is why we need to "correct" for the actual orbit, not the other way around.

 

We defined a unit of measurement, and the unit isn't really exactly precisely sufficient to describe our orbit time, so we have to play with it.. we add a day, we sometime extend a year by an extra second (like we did this year), etc.

 

That doesn't mean it's nature's fault, though. Nature's just fine. We defined our definitions *before* we knew how to measure these processions so now that we know they're inaccurate, we have to fix our definition.

 

I just don't understand what the big deal is.. what's so "earth shatteringly unphysical" with the difference of the definition *WE* created? It's not like the Earth is behaving in an inconsistent way, or is acting against the laws of nature -- it's perfectly fine.. we just need to define ourselves better.

 

Recap

 

[math]\aligned

&\text{\bf Year}&&\text{\bf Length (days)} \\

&\text{Julian}&&365.25 \\

&\text{Gregorian}&&365.2425 \\

&\text{vernal equinox}&&365.24237404 \\

&\text{tropical}&&365.24218967 \\

&\text{sidereal} &&365.256363004 \\

&\text{anomalistic}&&365.259635864

\endaligned[/math]

Yup. And all those are OUR definitions... it's like saying "Look! Here's a cube. It's also a square, when you look at it straight-on." and then go "OMG OMG I can't have both a square and a cube it's just not right it's impossible!"... well, it's possible because you are the one who made the definition twice: once as a three-d object, and once as a head-on view. therefore, the shape itself isn't different, it's just our measurement -- which we defined! -- is different.

 

Why is this surprising?

[Nikola]

If you went outside at exactly the same time every day and took a picture that included the Sun, how would the Sun appear to move? With great planning and effort, such a series of images can be taken. The figure-8 path the Sun follows over the course of a year is called an analemma. This coming Tuesday, the Winter Solstice day in Earth's northern hemisphere, the Sun will be at the bottom of the analemma. Analemmas created from different latitudes would appear at least slightly different, as well as analemmas created at a different time each day. With even greater planning and effort, the series can include a total eclipse of the Sun as one of the images. Here is a picture of what you are looking for. It has already been posted, but just wanted to add a NASA sponsered site.

http://antwrp.gsfc.nasa.gov/apod/ap091220.html

[iNow]

Well, thanks Nikola, but StringJunky already shared that image just a few posts back in post #16 (although it was not the APOD version), and DH has already explained why that is not relevant to the claims being made by the individual who opened this thread.