Paul wrote:So when the earth rotates it's not rotating along the same line as the ecliptic.

Yes, that's the main point. Thanks for the illustrations, Paul. Software is useful, but for those of us with poor visualization skills, I find an old-fashioned armillary sphere hard to beat. Just giving my desk-sized one a whirl as I write this, and watching the zodiac ring wobble -- most illuminating!

Thanks for the reply Paul. I knew it had to do with the angle between the ecliptic and equator line, but my doubt was why it reached the max and min peaks on the equinoxes instead of the solstices.

So I downloaded Stellarium as well, and the "key" to the solution seems to be that the angle between the ecliptic and equator is maximum in the equinox, contrary to what I was visualizing..

I have to look at this a little bit better, still haven't made "the click"!

Edit: Ok, I got it now! Here's a sketch that I made to understand, maybe it can help someone as well! It's for someone at a northern latitude, and the lines of projection from ecliptic to equator mark the beginning and end of the sign.

Thanks to Paul for the great visuals
A nice video of an armillary sphere in operation, and the the diurnal path of the sun in the sky at spring equinox and the solstices:

https://www.youtube.com/watch?v=M0chCdFEaP0

Along with Paul's clips, this makes things clearer, though unforunately it doesn't show the autumn equinox solar path - this is what intrigues me, why is it the opposite of the spring one? The penny will drop, I'm sure, but I might need an armillary sphere...
Graham

Paul's animated graphics suggest that the more appropriate words would be

-rising upright versus creeping up or
-standing tall versus crouching.

I just need to re-write some greek manuscripts

Thanks to Joao for the drawings, which also make things clearer.
The other point which I've realised is that I presume the opposite thing will happen as the given sign sets: the spring equinox ecliptic degree will rise fast and oblique and it will set slowly and upright, so it equals out over the day. The autumn equinox will be the opposite. The solstices will be equal at each end (I think).
I'd unconsciously confused "rising" with "overall movement during the day".
Graham

Graham F wrote: Can anyone point me at a post or an article on the net to help me understand why the summer solstice > winter solstice signs should be longer and straighter, and the the winter > summer ones more oblique and shorter (in time)? i can't manage to visualise why the peaks of fast and slow rising (and of obliquity and straightness) should be at the equinoxes. I can see that this is true with an astronomy program, but can't work out why.
...
Along with Paul's clips, this makes things clearer, though unforunately it doesn't show the autumn equinox solar path - this is what intrigues me, why is it the opposite of the spring one? The penny will drop, I'm sure, but I might need an armillary sphere...

jventura wrote: I'm with Graham, in the sense that I can't understand why the rising times peak (high/low) in the equinoxs. Is there any mention on the text for which time of the year this table was calculated?

Okay let me try again, I think I know where the stumbling block is. You are probably thinking, okay, so the angle between the ecliptic and the equator is 23.5ish degrees at Aries, when it rises, but it's the same 23.5ish degrees at Libra, when it rises. Therefore if the angle between them is the same, why are they rising at different angles!?

I hope I understand the confusion correctly.

To answer let me reiterate something from my last post - the straightness and crookedness is not formed between the angles of the ecliptic and equator. It is instead formed between the horizon and the ecliptic, or, to be more accurate, it is the projection of the ecliptic, along the diurnal arc, keeping note of the angle between the ecliptic and the horizon.

So far as clear as mud right?

Well consider the below diagram which shows the maximum declination of the Sun on the winter solstice and the summer solstice from a northern hemisphere perspective.
We can imagine the top sun, running through the red line, is the sun at the position of the summer solstice at midday. The red line is the ecliptic. Notice how high up the sky the sun is and therefore the wide, steep angle the red line makes to the horizon (the black line).
Similarly the lower sun is the sun at midday on the winter solstice. Much lower in the sky. The blue line is the ecliptic, and notice how shallow the angle is, the angle is much smaller. The closer the lines get to the horizon, the smaller the angle between the ecliptic and horizon will be there, the higher up, the wider the angle.
So let's do a thought experiment, or a real one if visualising is difficult. Imagine you take out a large coin, in england we have large ?2 or 2p coins, so imagine you take out the largest coin you have. If you can't imagine that, imagine instead the lid of a tin of pain, or a frisbee or something similar.

Hold it out right on front of you so that you are holding it in two hands, your left hand holding it on the left side, the right hand holding it directly opposite on the right side. Imagine you are looking at it full on so you can't see any of the edge. Now rotate it with your fingers, so that the top part of the coin is rotate back away from you, with the bottom coming up toward your eye line such that you can start to see the bottom edge of the coin. Make it so that you can only see this bottom edge. In our analogy the rim of the coin is the ecliptic. Were you to start turning your hands slowly in a clockwise direction, like you would if you were holding a steering wheel and turning right, you will see that very suddenly the entirety of the left edge rises above your eyeline all at once.

In our analogy, the eyeline is the horizon, so imagine the bottom half of the coin, beneath where you are holding it, is hidden beneath the horizon, we can only see the top half.

Put it back so that you are looking at straight on again, with no edge visible, and holding it on the left and right again. Were you to rotate it again, you will see it takes much longer to rotate the coin enough for a segment of the edge to completely rise above the eyeline.

So now look at the image of the solstices again, and try to rotate the coin always back and away from you so you only ever can see the bottom rim/edge of the coin.

You will notice that the angle the rim of the coin makes with the 'horizon line' becomes shallower and closer to 0? the more you bring the top edge down, and it becomes closer to 90? the more you bring it up until you are looking at it full on.

Well the thing is that when Aries rises, the rest of the ecliptic runs up into the sky and down to the southern extreme, in fact it moves to basically the same place as we can imagine the sun is at on the winter solstice. That shallow angle is made. And when Libra rises, the rest of the ecliptic runs up to the north toward where the summer solstice sun is.

What this means is that because we are not on the equator and looking above our heads but are instead looking down south at this, we are basically looking at the ecilptic making an angle either away from us, down south, closer to the horizon like the blue line, or we're looking at it so that the ecliptic runs more toward our position, more north, and so the angle is wider.

Of course the angle of the ecliptic and equator remains the exact same, but that is not what we're looking or focusing at, instead we're focusing on the angle the ecliptic makes with the horizon - keeping in mind that the ecliptic runs at an odd angle to the equator, north and south of it.

As a result, if we follow the zodiac along the ecliptic along these angles, we'll notice that when Aries rises, the angle the ecliptic makes to the horizon is shallow, it is closer to the horizon, and the angle it makes at Libra is wide, it is furthest from the horizon, and closer to being over head. The more north we go, the further south these points will be.

Now go back to my previous post and notice these same angles - the angle between the horizon and the ecliptic is much shallower with aries rising, and much larger with libra rising. Take note again of the animations to see the effect this has when the earth is spinning, and doing so parallel not to the eclipitc, but to the equator.

I hope this makes more sense now.

Graham F wrote:Thanks to Paul for the great visuals
A nice video of an armillary sphere in operation, and the the diurnal path of the sun in the sky at spring equinox and the solstices:

https://www.youtube.com/watch?v=M0chCdFEaP0

Along with Paul's clips, this makes things clearer, though unforunately it doesn't show the autumn equinox solar path - this is what intrigues me, why is it the opposite of the spring one? The penny will drop, I'm sure, but I might need an armillary sphere...
Graham

Try this, Graham

I found the xplanatons helpful.

https://www.youtube.com/watch?v=D8QVq7v ... iousLiving

Thanks Paul!

I think I know where the stumbling block is. You are probably thinking, okay, so the angle between the ecliptic and the equator is 23.5ish degrees at Aries, when it rises, but it's the same 23.5ish degrees at Libra, when it rises. Therefore if the angle between them is the same, why are they rising at different angles!?

Yes, that was precisely what foxed me. and this makes it all clear:

the thing is that when Aries rises, the rest of the ecliptic runs up into the sky and down to the southern extreme, in fact it moves to basically the same place as we can imagine the sun is at on the winter solstice. That shallow angle is made. And when Libra rises, the rest of the ecliptic runs up to the north toward where the summer solstice sun is.

Graham

(Pankadjubey: thanks for the link, but it's very slow and I can't get any sound and the optional subtitles look like a google translate, but I'll try again tomorrow, when I have more time.)

Paul
Thinking about your image of the red and blue arcs:
http://i.imgur.com/MgL6lCN.gif
isn't it more an illustration of the diurnal path of the sun at the equinoxes rather than at the solstices (except for the sun being shown at the top), since both arcs start and end at the same points on the horizon?
So the summer solstice arc would start further east and finish further west than the upper red (autumn equinox) arc, but would go just as high, so it's obliquity would be greater and its speed faster, making those "middling".
And the winter solstice arc would start and finish further south than the lower blue arc (spring equinox), but would again go just as high, so its obliquity would be less and its speed slower than the latter, so again it would be "middling".
If this is right, I now understand why the solstices are middling and the equinoxes (different) extremes of obliquity/straightness, and speed.
Graham

Graham F wrote:Paul
Thinking about your image of the red and blue arcs:
http://i.imgur.com/MgL6lCN.gif
isn't it more an illustration of the diurnal path of the sun at the equinoxes rather than at the solstices (except for the sun being shown at the top), since both arcs start and end at the same points on the horizon?

Wrote a reply and removed it, cos I want to try to make this as clear as possible.

Firstly in the diagram of the solstices, with the red and blue lines, those lines are the ECLIPTIC on those respective days, not the diurnal arc.

In the diagram of the solstices, the 'length' of the ecliptic above the horizon is the same - 180? - so the length of the red and blue lines are the same. So in order for that to be true, we can imagine that the blue semi-circle (going from east to west), the ecliptic on the day of the winter solstice, is angled down closer to the southern horizon, creating a kind of foreshortening effect.

But it is still 180? of ecliptic. The red line is the just at a less tight angle to the southern horizon - so there's less foreshortening. It is higher up in the air. And that is because the Ecliptic runs north to south, crossing over the ecliptic twice. When the sun is at these extreme north or south places, as far north or south as the ecliptic goes, these are the solstices. When the sun crosses the middle bit over the equator, it is the equinox. The sun never leaves the ecliptic, so the ecliptic itself moves up a certain amount north and a certain amount south.

But whether the sun is there or not, the ecliptic is still always going north and south - even if we can't see it. We call the most extreme point north it can go 0 Cancer, and the most extreme point south it can go as 0 Capricorn.

So that's always happening, imagine that it never moves - which it doesn't for our sake (but in fact we know it's slowly moving, or rather we are, so that it looks like it moves by 1 degree in 72 years. But for our sake let's keep it static and unmoving).

Try to actually visualise this in your head.

If that maximum point north that the ecliptic can go is 0 Cancer, then think about it on the day of the summer solstice, the sun is on the most extreme part north. So if that's true, then when the Sun is rising on the day of hte summer solstice it is rising as much north as it will ever rise, but every single degree which follows it cannot be any more north than that, because the sun was at the most extreme north possible, and we know the ring of the ecliptic itself is running north to south. So every degree that rises after it will be subsequently rising more and more to the south of the position the sun was at when it rose.

So by the time the Sun has risen enough to be on the MC, then the degrees rising in the east at that time must be considerably further south than the the Sun was when it rose. In fact it's half way through it's two extremes. In other words when 0 Cancer is on the ascendant, then 0 Libra is on the ascendant. And when 0 Capricorn is on the MC, 0 Aries is rising. Try it out, choose any year ever.

But the point with that diagram was to show that the ecliptic is at an angle with the horizon when the ecliptic goes to 0 Capricorn. I am putting the sun on 0 Capricorn just as a visual aid and because we have experience of noticing the sun being at 0 Capricorn in the winter time and at noon it is never really all that much off the horizon (depending on your latitude), but in summer it's up high in the sky. But in both cases there is the same amount of ecliptic, there is still half the zodiac above the horizon, it's just that the angle the ecliptic/zodiac makes with the horizon is tighter and tighter and closer and closer to the horizon in winter, than summer.

But the key point is that when Aries rises, and 0 Capricorn is on the MC, then with this diagram, we can easily spot how low in the sky 0 Capricorn is, cos we know where the sun is at 0 Capricorn, and we know the Sun is always on a point of the ecliptic, so when Aries rises we know that the ecliptic is very low to the ground as it were, it's closer to the horizon (like the sun is closer to the horizon when it is at 0 Capricorn).

So we know it's making a very tight angle then to the horizon.

Thanks Paul - I see now that the arcs in your diagram are the ecliptic and not the diurnal arcs, and I think I've got it.
I was trying to understand this relationship obliquity/speed. I think my misunderstanding of your arcs as being diurnal in a way helped me grasp why obliquity is positively correlated with speed of rising and VV, and why the greatest and least obliquity/speed are at the equinoxes, and the middling values at the solstices. That was what was niggling me, as you correctly diagnosed. I misunderstood the arcs, but it's clear now.
Graham