Observations/Perspective

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Perspective

The appearance to the eye of objects in respect to their relative distance and positions, for example the way that objects appear smaller when they are farther away and the way parallel lines appear to meet each other at a point in the distance (Vanishing point).

Vanishing point

The vanishing point is the point in the distance where parallel lines seem to meet, due to perspective. We know that trains tracks don't actually get narrower they further they go because the train would derail. This narrowing / vanishing effect is due to perspective and the way our eyes work.

Crepuscular Rays

Crepuscular rays occur when objects such as mountain peaks or clouds partially shadow the sun's rays. The name crepuscular means "relating to twilight" and these rays are observed at sunrise and sunset. Crepuscular rays appear to diverge outward from the setting sun, and are visible only when the atmosphere contains enough haze or dust particles so that sunlight in unshadowed areas can be scattered toward the observer.

Anti-crepuscular Rays

Have you ever witnessed rays of sunlight seemingly converging in the opposite direction of the setting sun? These fascinating rays, known as anti-crepuscular rays, create a mesmerizing display in the sky. While crepuscular rays appear to converge on the sun itself, anti-crepuscular rays appear to converge towards the anti-solar point, which is directly opposite the sun in the sky.

To observe anti-crepuscular rays, you must position yourself with your back to the sun or sunset point. As you gaze towards the horizon opposite the sun, you may be fortunate enough to witness these parallel shafts of sunlight streaming through gaps in the clouds. The seemingly peculiar directions of these rays are actually a result of perspective. Just like a straight road appears to converge towards the horizon, anti-crepuscular rays appear to converge towards the opposite horizon.

While anti-crepuscular rays are not necessarily rare, they do require careful observation. When you notice crepuscular rays illuminating the sky, it's time to turn around and search for their opposite counterparts. By shifting your focus away from the sun, you may be rewarded with the breathtaking sight of anti-crepuscular rays stretching across the sky.

Azimuthal grid of vision

If you took all these facts on how perspective works and apply it to every direction you can look, apply the same rule of perspectve to all the directions you can see. You might not see parallel lines in the sky, but the same rule of perspective applies. The net effect of your "personal perspective" in all directions result is called a "dome of vision", "arc of the horizon", or an "Azemuthal grid of vision".

It is important to realize this "dome of vision" is not the firmament or a dome over earth, it is an invisible region of the limitations of how far we can see in any given direction.

How perspective was hijacked to create the globe

Have you ever seen Earth curve and distance dependent angular resolution? What if they are the same thing?

Since globularists noticed the 69 miles per degree relationship and declared that this effect happened solely because of the curve of the earth. For the sky solely because of the curve of the earth, but for mountains, well... that is because of perspective. And for streetlights on a long straight road... also perspective. And of course tall buildings that compress into the horizon with distance, well that happens because of perspective too. But the stars and the sun the moon are all because of earth curvature. Essentially, the globular position has to be that this effect happens for everything on earth due to perspective, but it happens to everything in the sky for a completely different reason. ^[1]

Earth curve or angular resolution limit?

To find the arc angle representing the section of your spherical vision which undergoes the optical drop rate over 3 miles is calculated as 8 inches per mile squared or approximately 0.666 feet per mile squared. The angular resolution limit for the Raleigh criterion is given as 0.0316° (or 0.000552 radians).

If the Earth was flat but our vision curved the calculations and measurements related to viewing distance, horizon, and angular resolution would likely remain consistent.

Ways to optically derive radius:

Determine the distance to the horizon

Determine the distance to the horizon for a 6-foot observer by using the formula ( $d=1.22{\sqrt {h}}$ ), where ( $d$ ) is the distance to the horizon in miles and ( $h$ ) is the height of the observer in feet. Plugging in a height of 6 feet, we get:
$d=1.22{\sqrt {6}}$
$d=1.22\times 2.45$
$d\approx 3miles$
Therefore, the horizon for a 6-foot observer is approximately 3 miles away.

Derive the radius based on the angular resolution limit

To derive the radius value of 3,959 miles based on the angular resolution limit of 0.0316° and the optic drop over a distance of 12 feet across 3 miles (using a drop rate of 8 inches per mile squared), we can calculate it as follows:
Calculate the drop rate for the given drop over distance: For 12 feet over 3 miles, the drop rate is 8 inches per mile squared, or 8/12 feet per mile squared, which is approximately 0.666 feet per mile squared. ^[2]

Using the angular resolution limit of 0.0316° (or 0.000552 radians) for the Raleigh criterion, we can calculate the radius value by equating the angular resolution to the tangent of the arc angle: Arc angle = 0.0316° = 0.000552 radians tan(0.000552) = R / 3 miles, Solving for R, we get R ≈ 3,959 miles.

Therefore, based on the given information and calculations, the derived radius value to meet the angular resolution limit of 0.0316° is approximately 3,959 miles.

This can also be converted to a drop from 0 ft to -6 ft over 3 mi:
To derive the angular resolution limit based on the previously calculated radius of 3,959 miles, we can use the formula that relates the radius of a circle to the arctangent function.

Given the radius as 3,959 miles, we can calculate the angular resolution limit (θ) by solving the formula:
$\tan(\theta )={\frac {R}{3{\text{ miles}}}}$

Plugging in the radius value of 3,959 miles:
$tan(\theta )={\frac {3,959}{3}}$
$tan(\theta )\approx 1,319.67$
By taking the arctangent of 1,319.67 (in radians), we can determine the angular resolution limit corresponding to the previously derived radius of 3,959 miles.

Angular resolution calculation

The angular resolution limit is a measure of the ability of an optical system, like the human eye, to distinguish between two separate points or objects that are close together. It is typically expressed in terms of the angle subtended by the smallest resolvable detail or feature.

To determine the angular resolution limit, you can use the formula:
$\theta ={\frac {\lambda }{D}}$
where:

θ is the angular resolution limit.
λ is the wavelength of light (often provided in nanometers).
D is the diameter of the aperture (e.g., the pupil diameter of the eye).

By plugging in the appropriate values for λ and D, you can calculate the angular resolution limit for the given optical system.

Summary

Earth's curvature is perceived through optical angles, horizon distances, angular resolution, and object descent rates in the field of vision.
Calculation of Earth's radius involves angular measurements and drop rates over distances utilizing geometric or trigonometric approaches.
The perspective shift due to lower observer height sets the horizon closer in view, affecting the descent and angular compression rates.
Proportional angle pairs diminish together based on the observer's position relative to the surrounding elements.
The concept of a "ceiling/floor" model determines the horizon based on the nearest reference point, impacting visual perception.
The descending objects' height adjustments and distances create a parabolic function reflecting the curvature's observable rate.
The visual perception is influenced by the nearest ceiling or floor, setting the horizon, and the steeper descent rate affects the interpretation of depth in the field of vision.
The rate of curvature is 6 feet lost at 3 miles from a 6-foot observer height
The angular resolution limit is closely approximated within the curved perspective
Two crossover points occur at 0 miles and 3 miles in the observations
Size changes are exponential within the observer's perspective
The observer perceives a 6-foot descent over 3 miles, with corresponding angle changes in observer height
The arc angle calculation from a 3-mile arc length or a 12-foot drop over 3 miles determines the Earth's radius to be approximately 3,978 miles
Exponential drop rate adjustments result in a parabolic height change with distance in the observer's field of view
The radius of 3959 miles leads to an angular resolution limit of approximately 1.57 radians as derived from the arctangent calculation