The Circle of the Earth

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Introduction

In the Bible it is written, “It is he that sitteth upon the circle of the earth, and the inhabitants thereof are as grasshoppers; that stretcheth out the heavens as a curtain, and spreadeth them out as a tent to dwell in.(Is 40:22) Some site this verse as evidence that Earth is flat and not a sphere, or a ball, since a different Hebrew word would be used here if the author wanted to describe a ball rather than a circle.

However, if we read the text carefully, it does not say that Earth is a circle, but it implies that Earth has a circle. The Hebrew word circle is also translated circuit (Job 22:14) and compass. (Pr 8:27) The Scripture appears to teach that both Earth and its Heaven (atmosphere) have a circuit, or a circular route that they travel together … an orbit if you will … an idea that is consistent with our modern heliocentric model of Earth, and long preceded our modern discoveries of it.

This should come as no surprise since there can be no real conflict between Science and Scripture if God is the Author of both. (1Ti 6:20) Only a Spherical Earth (SE) model accounts for the sun actually rising and setting from an earthly perspective while also providing for 24 time zones, disproving any Flat Earth (FE) model by contradiction. Direct proof of the size and shape of Earth is found in considering the consistent behavior of the stars.

The Sun’s Behavior

Sunsets are amazing; as the sun is setting it is often still so bright we can only watch it unprotected for a very short time, as the orb of the sun is finally disappearing from view. The sun appears to sink below the horizon as it goes beyond our ability to see any farther west, a function of the terrain and our height above sea level.

Just after sunset we can still enjoy its brilliant glow; sunlight can still reach us by reflecting off particles in the atmosphere. This happens in every sunset, from every mountain top and coastline; it is not merely due to uneven terrain.

We can also prolong sunsets: increasing our elevation by a few feet will bring the sun back into view for a few more seconds, and flying west can add hours to a day. In fact, the sun is always visible to someone on Earth; it never actually goes down behind anything, as any who travel internationally or connect with those along distant meridians (north-south lines measuring east-west position) know very well.

And as the sun traverses our skies, ranging between the 24th parallels (east-west lines measuring north-south position), both its size and speed appear to be constant throughout each day.

These facts have significant implications for any model of Earth; a valid FE model must account for all of them.

Implications

Time Zones

Firstly, the fact that the sun only appears to set from the perspective of a relatively stationary person, since the sun never actually does drop behind the edge of the earth, at once explicitly contradicts any type of FE model where the sun orbits perpendicularly about a FE, lighting Earth during the day and going subterranean, below the FE at night (BFE). While a BFE model accounts for sunsets and a constant size and speed of the sun as it traverses the sky, it cannot provide for the sun always shining somewhere on Earth.

So if Earth is flat the sun must always stay above the FE (AFE), and travel in a circular pattern around either the North or South Pole, maintaining a constant height above the plane of the earth within the two 24th parallels. The AFE model type is our only other FE option, and it does account for time zones. However the remaining facts about our sun directly contradict any AFE model on three  conspicuous levels: the AFE cannot explain [1] sunset (night), or the constant [2] size or [3] speed of the sun.

Sunsets

Perhaps the most obvious problem in an AFE model is how to account for sunsets and nights since the sun never dips below the plane of the earth. Sunsets occur every day on every mountain top and coastline, so they cannot be explained by uneven terrain. So then how do we explain sunsets on an AFE?

Typical AFE models, as in Fig. 1 below, simply depict the sun shining on a relatively small area and leaving most of the earth in darkness. Is this realistic, or just wishful thinking?

Fig 1

Fig. 1

We know that as the sun moves farther away from us on an AFE that [1] its brightness and size will diminish due to distance and the dispersion of light in the atmosphere, and [2] that it will appear to move closer to the horizon due to laws of perspective. So we should be able to find the tallest point in our area and watch the sun getting closer and closer to the horizon, but never dropping below it, gradually decreasing in size and brightness until it looks like a star twinkling in the night, and finally fading into the darkness. At such locations sunset should occur at the same time at any elevation, whether we are on the ground, in a hot air balloon, or flying in a plane miles above ground.

But the sun does not at all behave like this, contradicting every AFE in three basic ways: [1] the sun always moves toward the horizon at a constant rate and then appears to drop below it out of sight, [2] we can always prolong a sunset merely by elevating ourselves above the ground, and [3] we can always see sunlight illuminating the atmosphere just after sunset. These three behaviors cannot be explained by any AFE.

Even so, just to be complete, let us carefully answer two basic questions about the sun on an AFE: [1] Would the sun ever fade from view? and [2] Would the sun ever approach the horizon?

On our first question, brightness is measured in lux and varies by the inverse of the distance squared, so if we double the distance we get a fourth of the brightness. Late afternoon sunshine on a clear day is about 110,000 lux and a full moon on a clear night is about 0.25 lux. In no AFE model will the sun ever triple its distance from us between late afternoon and midnight, so at midnight in a clear sky on any AFE the sun will still be at least 10,000 lux, thousands of times brighter than a full moon; it will never fade away.

On our second question, we can measure the sun’s closeness to the horizon: its angle α above the horizontal, as in Fig. 2 below, is the inverse tangent (Tan-1) of the ratio of its vertical height (h) and its horizontal distance (d).

Fig. 2

For the sun’s angle to be 1above a flat horizon, as when it sets over an ocean or on a mountain top, its distance must be 57 times its height. Can this happen on an AFE? Let’s find out.

We know the sun’s latitude (numbered lines parallel to the equator, spaced about 69 miles apart) at any given time of year, so we can calculate d, the sun’s distance from us at sunset at any given location on an AFE model. Then given any height h we will know the altitude α of the sun at sunset.

For example, on Monday, June 20, the summer solstice of 2016, the sun’s latitude was 23.5oN, so the radius of the circle it was traversing was about 4,588 (69×[90-23.5]) miles. In Dallas TX, at a latitude of 33oN, sunset was about 9 p.m., so in an AFE (centered at the North Pole) the sun would have been above a point on Earth about 3/8 the way around this circle from Dallas, or 7727 miles away (per triangle calculator), as in Fig. 3.


Fig. 3

If the sun’s height is 4,000 miles (typical for an AFE model), then its altitude α in the sky at sunset on that date would have been about 27o (Tan-1[4000/7727]), which is nowhere near the horizon. At a height of 1000 miles the altitude would have been 7o, which is closer but still well above the horizon. In order for the sun to come within 1o of the horizon on such an AFE it would need to be about 130 miles above our earth.

Sun Size

Yet if the sun were so close to Earth that it appeared to sit on the horizon at sunset, this would create a second fundamental problem: the sun’s size appears to be constant all throughout its circuit, implying that changes in its distance from us as it appears to move across the sky are dwarfed by its actual distance from us the entire time.

The sun appears to be about ½ a degree in size (when viewed through a protective, non-distorting filter), and for such a small angle α the size (s) of an object compared to its distance away (d) can be approximated by the formula α = 57(s/d), so we may approximate the sun’s distance-to-size ratio d/s by a constant: d/s = 2×57 = 114.

In the example sunset above, if the sun were 130 miles above the earth then the sun’s distance d from us at sunset could be computed using the Pythagorean theorem to be 7,728 miles, and therefore the size s of the sun can be estimated to have a diameter of about 68 miles (7728/114). But this implies that at noon, when the sun is overhead in Dallas and only 130 miles away, it will appear immense, its angular size α would be 28o (Tan-1[68/130]), about 56 times bigger … it would take up nearly one sixth of the sky, an obvious problem for any AFE model.

In order for the sun to appear to be consistently small as it crosses the sky in an AFE it must be extremely far away, much farther away than 4,000 miles, such that its maximum change in distance from us throughout its circuit is minuscule compared to its actual distance from us; but if the sun is that far away in an AFE then it will never get anywhere near the horizon.

Sun Speed

A third obvious problem with any AFE model is that basic laws of perspective imply that the rate at which the sun moves across the sky must be much slower when it is farther away from us, morning and evening in an AFE model, than when it is more directly overhead at noon.

The sun’s angular motion in any AFE model must be a constant 15o per hour (360o/24), so in the above example in Fig. 3 the change in the sun’s position per hour at sunset, the angle α in Fig 4 below, is about 8o. Yet when the sun is overhead near Dallas its speed will appear to be about 12 times faster, measured by angle β in Fig. 4, or about 90per hour.

Fig 4

Fig. 4

Yet anyone can observe that the angular rate at which the sun crosses the sky is essentially the same morning, noon and evening, implying that it’s distance from us is not actually changing significantly throughout the day. This property of the sun is accounted for in the BFE, but it disproves every AFE model.

Flat Earth Disproved

There are only two possible FE options: BFE models that can’t handle time zones, and AFE models that can’t handle sunsets or the constant size and speed of the sun. There are no other options, and there is no uncertainty or ambiguity in any of these facts. It should come as no surprise then that no FE model addresses these simple problems. They cannot; it is impossible.

While many get bogged down in other types of phenomenon that are more difficult to explain, we find that Earth cannot possibly be flat using commonly available facts which anyone can easily verify for themselves.

It is wise to acknowledge that one only needs to formally disprove FE once to nail the coffin shut, and the above analysis appears at once to be conclusive proof by contradiction. But we need not rest in merely contradicting all possible FE models with high school math and science; the motion of the stars in our skies positively confirms the shape and size of our earth.

Spherical Earth Proof

the celestial north pole

If we take a time-lapse photograph of the sky at night directly overhead at the North Pole, we will get an image similar the following, regardless of the time of year.

Fig 4

Fig. 5

The stars appear to be revolving counter-clock-wise about a single point – the North Celestial Pole (NCP) — directly above us, generally associated with the North Star, the bright star closest to it. The stars at the horizon rotate around us and this NCP, never rising or setting; they are each visible all night (circumpolar). They make a complete rotation every 24 hours just like our sun, and appear to be in a fixed orientation with each other; the distances between them never change. In a FE model this implies that either earth is spinning beneath the heavens, or the stars are spinning counter-clockwise above the earth (or perhaps both), about an axis of rotation that aligns with a vertical line at the NCP directly above us, as in Fig 6.

Fig 5_

Fig. 6

pole Altitude Changes with Latitude

Yet as we move south in any direction and take similar photographs, say from Ogden UT at a latitude of 41oN, we find the stars still rotating about the same NCP but the location of the pole has dropped from an altitude of 90o down to 41o, same as our latitude.

6ab

North – Fig. 7a Ogden, UT – East

6cd

South- Fig. 7b Ogden, UT – West

FE proponents would explain the NCP’s drop in altitude in the same way they try to explain the sunset, by “parallax,” or perspective. We have moved south about 3,381 miles (69×[90-41]) miles, a bit more than half way from the North Pole to the Equator, so if the NCP is not too far above us then it could appear to move like that as we travel. In fact, since we know the distance we have traveled south and the angle of the NCP, we can calculate its height in the same way we determined the sun’s altitude: TAN(41)*3381 = 2,939 miles, as in the right diagram in Fig 8 below.

Fig. 8

Circular Rotation Persists

There is, however, a problem with the parallax explanation: the star trajectories remain circular; they are not distorted like we would expect them to be if the NCP’s apparent decrease in altitude were due to the distance we had traveled away from it.

If we had departed from the axis of rotation at the NCP by traveling horizontally away from it on an AFE, we would expect to see the circular patterns of the star trajectories change from our new southern perspective. How they would change would depend on the shape of the dome containing the stars; if the surface were relatively flat, like the ceiling of a room, the trajectories farther away from us than the North Star would appear to be compressed more than those lower in the sky or nearer to us because we would be looking at the entire rotational pattern from a side view, as in the left diagram in Fig 8 above.

If the dome were more hemispherical then the pattern would be reversed; the trajectories nearer to and above us would appear to be more compressed than they were at the North Pole since we have moved off center and are nearer the edge of the dome. But our math actually tells us that if the dome is a hemisphere then we are already outside it at the 41st parallel since the altitude of the NCP has dropped to less than 45o. If there is a dome containing the stars it must be much wider than it is high, more of an oval shape perhaps, and relatively flat on top.

In any case, this is not what we find; we see the stars as if the axis of rotation of their movement has itself rotated while we traveled, such that we are still within it. As in Fig 9, this axis is no longer vertical like it was at the NCP; it appears to have rotated 49o.

Fig 8_

Fig. 9

new stars appear

The stars on the horizon no longer circle around us like they do at the North Pole, as we would expect in any AFE; the stars that were below 49o in altitude at the North Pole are no longer circumpolar: just like our sun, they now disappear (set) below the western horizon for part of the night and then re-appear (rise) above the eastern horizon. New stars are now visible which were continually below the horizon at the North Pole. How can this be on an AFE?

One thing we know for certain: the view from the North Pole has not changed, so neither the earth nor the heavens have shifted in their orientation in relation to each other: the only thing that has changed is our position on Earth, and along with it our orientation with respect to the axis of rotation of the stars.

As we moved south what we call up and down, the directions aligned with the pull of gravity, have changed in relation to the rotational axis of the stars; our perception of vertical is changing with respect to the heavens and the earth as we move around on Earth’s surface – when nothing else changes.

orientation a function of location

This implies the directions up and down are relative to and dependent on our position on Earth. This can only be true if up and down are directions perpendicular to a surface having a constant curvature; this is, by definition, a sphere. There is no other way this can happen; it cannot happen in any FE model.

Not only has our movement resulted in an apparent shift of the axis itself, our 3,381 mile trip has not moved us outside of this axis at all as far as we can tell; we still appear to be aligned with its center. This implies that the stars are so far away from us that our journey southward has not changed our perceptions of their distances from each other or from us, as in Fig 10.Fig 9_

Fig. 10

the south celestial pole

Additionally, the new stars now visible in the southern sky are not rotating counter clock-wise about the NCP as the northern stars are; the southern stars appear to be revolving clock-wise around a different point in the southern sky, the South Celestial Pole (SCP), directly opposite (180o) from the NCP. It was is impossible for any type of dome to model this behavior above an AFE.

As we move farther south to the equator we see the pattern continue in another time-lapse photograph spanning 180o of the horizon. Both NCP and SCP are on the horizon; no stars are circumpolar; they all rise in the east and set in the west like the sun.

Fig 10

Fig. 11

Only here, along the equator, can we see all the stars surrounding Earth as they rotate across the sky between the two poles; their brightness is constant and their positions relative to each other are unchanged; none of the constellations are distorted.

Nothing has changed but our location on Earth; traveling a bit more than 6,000 miles (69×90=6210) south has shifted our vertical orientation toward the heavens a full 90o … but neither the earth nor the heavens have moved with respect to each other.

From our observations at the 41st parallel, the AFE implies the NCP is about 2939 miles high, so its altitude should now be 25o (Tan-1[2939/6210]). To get the NCP within 1o of the horizon we should have needed to travel over 150,000 miles … but the NCP is on the horizon … and we are still within the rotational axis, evidently half way between two celestial poles … all impossible on any kind of FE, but perfectly consistent with a SE.

we cannot be on a Flat Earth

We must be on a sphere about 25,000 (4×6210 = 24,840) miles in circumference. We have moved away from the axis of rotation about 4,000 miles, Earth’s radius, yet like the sun, the stars are so far away that changes in their positions relative to us and each other are imperceptible – so they must be very, very far away.

The pattern continues as we move farther south into northern Chile at the 23oS latitude.

Fig 11

Fig. 12 Almacama Telescope, Northern Chile

We see the SCP clearly now, about 23o in altitude as expected, and distinctly different from its northern counterpart since no nearby star is bright enough to help us locate it. Star trajectories remain perfectly circular, so we are still within the axis of their rotation. No stars have dimmed in their brightness along the way; the NCP is now below the horizon, no longer visible.

Implications

As we have traveled south our perception of vertical has also gradually changed in exactly the same way, proportional to the distance we traveled. The distance between each latitudinal line is exactly the same, and produces the corresponding change in the altitude of either the NCP or the SCP in the sky, depending on where we are. This change in latitude is therefore linearly proportional to the distance south we travel, and it is the same regardless which direction south we travel from the NCP, implying a consistent curvature of the surface of Earth.

There are thousands of time-lapse photographs of the stars showing this phenomenon, taken all over the earth by all types of people; we should not expect to find a single one that supports an AFE model.

The surface we are describing and experiencing is the surface of a sphere, the only shape that fits what we are seeing: the sphere, by definition, is the only object with a constant curvature across its entire surface.

Objections

As one would expect if SE is true, as proved conclusively above both directly and by contradiction, there can be no actual evidence for FE. So what shall we make of all the vigorous and apparently thoughtful literature supporting FE, much of which seems based on empirical observation and experimentation?

Evidently, those who support FE have not considered the above facts, but have essentially spent their time claiming proof of FE by:

  1. Results from superficial, incomplete testing of poor experimental designs, especially related to perspective and depth perception (parallax), gross ignorance of the most basic natural laws (related to friction and inertia), and the role of atmospheric refraction (logical fallacy: Non Sequitur),
  2. Debunking incomplete and/or inaccurate SE claims (logical fallacy: Straw Man),
  3. Their inability to explain certain atmospheric and/or physical phenomenon according an SE model (logical fallacy: Argument From Silence), and
  4. Asserting that a literal biblical hermeneutic requires an FE position (logical fallacy: A Priori).

The most convincing of the FE experiments are those which claim to prove Earth is flat by observing an object across an expanse of water that should be curved according to the SE model. If the theoretical curvature should hide the object and it can still be viewed, FE proponents declare the earth must be flat.

The flaw in such an argument is that when light passes through air of differing densities (due to changes in temperature and/or humidity) the light can bend; it’s called atmospheric refraction, and any experiment that does not take this into consideration is flawed by design.

So as we wade through the FE literature and consider their points one by one, we find the expected: their “proofs” and arguments never deviate from the above logical fallacies. It would take many pages and months of effort to fully demonstrate this, but it would not change the facts: there is zero actual scientific or scriptural support for any FE position.

If the above incontestable and easily observable solar and astronomical phenomenon are not convincing in themselves, since no reasonable scientific objection can be made and there is no ambiguity in their interpretation, no other type of experimentation can be more relevant to the debate and thus will likely not be any more convincing.

Conclusion

He stretcheth out the north over the empty place, and hangeth the earth upon nothing.” (Job 26:7) God did not set Earth on massive marble pillars, or float it on subterranean waters under a dome of brass; He set it out in empty space, open to the sun and stars, an engineering marvel that should move us all to worship. A spherical Earth is the only possible model consistent with both a rational biblical hermeneutic and also with reason and science.

The behavior of the sun violates all possible FE models, disproving FE by contradiction. We may then prove SE directly by traversing the earth any way we like and observing that [1] all the stars we can see at any given location maintain a constant brightness and distance from each other, fixed within constellations which do not change in size or shape, and rotate seamlessly about a single axis of rotation through two celestial poles from which we cannot escape, and that [2] our vertical orientation toward these poles and the heavens consistently and predictably changes as we move about on Earth. These phenomena can only be explained if earth is a sphere completely surrounded by stars so distant from us that our farthest earthly journeys are comparatively microscopic.

Since all motion is relative to some reference point, based on the above we could begin to describe our world from either a geocentric perspective in which the sun and stars revolve about Earth, or from a heavenly perspective where Earth revolves on its own axis and orbits the sun, a small blue spec in God’s amazing universe. What we have observed so far is consistent with either view, but a humble perspective is the heavenly one.

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