Can a Sundial Measure Ecliptic Longitude Accurately?

[Helios]

I have an idea how to measure the ecliptic longitude with a sundial type device. Ecliptic longitude is a astronomical variable so I chose this forum.

Suppose we have a vertical flag pole poised on the equator of the Earth.
A "coordinate circle" is drawn that surrounds the flag pole, radius = ( flag pole height )*tan( e ), e = 23.4393° = tilt of Earth.
So when the shadow point crosses the coordinate circle, the altitude of the Sun is 66.5607°.

Now with some doodling, I have a conjecture to offer.

When the shadow point crosses the coordinate circle, the ecliptic longitude will equal the azimuth of the Sun measured from due east as 0° and positve going counter-clockwise. Take care to note that due east azimuth for the Sun is due west for the shadow point.
It is obvious that the shadow point usually crosses the circle twice in a day, so it is assumed that the observer knows to use the reading closest to 24 hours from the previous one.

Is this correct? Is what that is being measured the ecliptic longitude?

 

[Philosophaie]

The elliptical longitude of the Earth is measured at the extremes distances:

max = a*(1+e)
min = a*(1-e)

a - Semi-Major Axis
e - Eccentricity

The elliptic longitude is measured by three factors:

eclLong = N + w + t

where:

N - Longitude of the Ascending Node
w - Argument of the Periapsis
t - True Anomaly

 

[Helios]

Philosophaie, not that what you say isn't true, but it's not relevant. The task is to prove that one can measure elliptic longitude with a vertical pole on the equator just as I describe.

I think this sundial is remarkable and so simple. Yet I don't think it has ever been discovered before. That's why I wish someones would look into it and verify my math.

 

[Philosophaie]

On the Greenwich Meridian the Azimuth is equal to the Ecliptic Longitude which makes ludicris because the azimuth is North-South and the ecl Long is along 23.4393deg from the equator and the equinox point.

The azimuth must be close to 90deg because the pole can only be so high making the ecl Long approximately equal to 90deg minus the radius of pole location.

The altitude of the sun casts a shadow when close to the eastern hemisphere 2X a day.

The measured ecliptical longitude will be somewhere a close to 90deg witha negative ecliptic lonitude when it travels from the outer part of the circle to the center on the equator.