31
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

32
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.)

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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

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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.
"The only true wisdom is in knowing you know nothing" - Socrates

https://heavenlysphere.com/

35
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