You mean smaller at aphelion?
Yes. My bad, I mistyped.
I have updated the post.
This is what i meant by speed while upper part is what i meant by orbit. But wouldn't faster orbital speed at smaller orbit cause sun to move more than few minutes that cause difference between solar and sidereal day? Sun would have to move little more than it does at aphelion. And it would set later/be more East in sky. Am i getting it right?
Yes.
It can be confusing with terms as you can consider it in a few different ways, and there are multiple terms.
If Earth wasn't rotating, then at perihelion, the sun would appear to move the fastest.
However, Earth is rotating and rotating in the same direction as the sun, but at a faster rate.
This means the sun appears to move in the opposite direction, so at perihelion, the sun appears to be moving slowest to us.
The other way of thinking about it is that as we have moved more in our orbit, the Earth needs to rotate more to face the sun.
So the sun would set later.
As for solar day vs sidereal day; there is also the mean solar day.
The mean solar day is 24 hours.
The solar day will vary, as it is literally just based upon where the sun is.
The sidereal day is the rotation of Earth.
This means at perihelion the solar day is longer than 24 hours, and at aphelion it would be shorter; at least it would be if there was no axial tilt.
However, there is axial tilt, and that has a larger effect.
We can also see this indirectly by looking at things like timeanddate:
https://www.timeanddate.com/sun/ecuador/quito?month=7&year=2023https://www.timeanddate.com/sun/ecuador/quito?month=1&year=2023In July, near aphelion, we see solar noon is 12:17 on the 1st, 12:18 on the 2nd and 12:19 on the 7th.
That means over the course of 5 days (2nd to 7th), the sun has fallen behind by 1 minute.
However in January, solar noon is 12:17 on the 1st, 12:18 on the 2nd and 12:19 on the 5th.
That means it has only taken 3 days (2nd to 5th) to fall behind by 1 minute.
The effect of axial tilt is comparable here, and this 2 day difference is due to perihelion vs aphelion.
(You can also go to the equinox to see it going the other way.)
Graph (equation of time) shows zeroes (for orbit) at exactly aphelion/preihelion, why is that? Wouldnt theise points be maximum/minimal instrad of zeroes? Also at that point, at "0" sun should have maximum angular speed due to "bouns" caused by effects i described earlier
The equation of time shows the cumulative effect.
At perihelion and aphelion, the slope is at the greatest magnitude, but the value is 0.
In some ways this is like moving around a circle.
When you are at y=0, your vertical position is 0 (modelled by sin), but your vertical speed is maximum (modelled by cos).
You can also consider this to be a starting point at 0.
As you move on from the perihelion, the sun still appears fast, but as a decreasing rate. However, that is without rotation. As rotation is in the opposite direction it means the sun appears to slow down, or that the Earth needs to rotate more to catch up to the sun.
This means the real clock goes ahead (equivalent to the sun being behind), but the amount it is getting ahead each day is decreasing.
But eventually you reach a point where the rate has decreased so much that it is now at the average, so the sun is now keeping track with the clock. This is the maximum on the graph.
Then after this point, the sun is appearing to go slower, but again with the rotation this means Earth needs to rotate less to catch the sun, meaning the real clock starts falling behind as the sun appear to be speeding ahead (but it starts from being ahead).
This change continues until you reach aphelion.
At this point the sun is going slowest. This means the real clock is falling behind the fastest.
But due to the symmetry of the orbit, you have fallen back to where you were at perihelion.
Then after that you have the real clock falling behind, but at an ever decreasing rate.
Eventually you again reach a point where the speed of the sun matches the average so you have reached the minimum.
After this point the sun starts speeding up again approaching perihelion, so the clock starts getting ahead, reaching 0 again at perihelion.
The reason these points need to be 0 is due to the symmetry.
The region approaching perihelion needs to be symmetric to the region after perihelion; as the orbit is symmetric.
Likewise, the region approaching aphelion needs to be symmetric to the region after aphelion.
So either both of these points are 0, or it will drift over time (e.g. perihelion will be 0 one year, then -10 s the next, then -20 s the next and so on.
How large is that shift? Wiki is unclear about what change is caused by different speed and orbital shape separately.
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I get that they should but i cant see them *both* being applied
The point is it makes no sense to apply them individually.
If you just want to focus on the speed, what distance would you use?
If you just want to focus on the distance, what speed would you use?
This is especially true when you can use Kepler's law to directly calculate an angle from a time.
That means you aren't considering velocity and distance and instead directly calculating the angle.
https://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion#Position_as_a_function_of_time