Ecliptic Longitude Measurement

[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 verticle 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 verticle 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.

 

[sardar]

I appreciate your creativity and ingenuity in coming up with a method to measure the ecliptic longitude using a sundial type device. However, I must caution that this method may not be entirely accurate and may require further testing and refinement before it can be considered a reliable measurement tool.

The ecliptic longitude is a measure of the position of an object along the ecliptic, which is the apparent path of the Sun on the celestial sphere. While your method does take into account the tilt of the Earth and the position of the flag pole, it may not accurately account for the curvature of the ecliptic and the varying angles of the Sun's path throughout the year. Additionally, the shadow point crossing the coordinate circle twice in a day could also introduce potential errors in the measurement.

To truly measure the ecliptic longitude, a more precise and sophisticated instrument would be needed, such as a telescope or a specialized equatorial mount. These devices are designed specifically for astronomical observations and can provide more accurate measurements of celestial objects and their positions.

In conclusion, while your idea is intriguing, it may not be entirely accurate in measuring the ecliptic longitude. I encourage you to continue exploring and experimenting with different methods, but also to consult with experts in the field to ensure the validity and accuracy of your measurements.