The earth is spherical and spinning

Note: Sources (Numeric) and diagrams (Alphabetical) cited in comments. Direct Observation There most obvious proof of a spherical earth is direct observation, including the hundreds of astronauts in orbit, and thousands of pictures taken. These pictures are from the ESA[1], Russian Space Agency[2], NASA[3] the ISS live stream[4], amateur rocketry organizations[5], non-governmental space corporations such as Space X[6] and Scaled composites[7] pilots of high altitude planes, and James May, a former presenter of Top Gear [8]. That all of these images, videos, observers" amateur footage, and Captain slow himself, from unrelated and unaffiliated sources and in some cases hostile governments are all faking their pictures is neither credible nor possible. Geometry Relative observations of where the sun and moon are viewed from points a surface, despite my opponents contentions, are not unrelated, but CRITICAL to understanding the shape of the earth. Using these relative observations of objects at the same time allow you to determine relative positions, and relative orientations of different observers on the earth; these combine to reveal the overall geometry of the earth. So, to start, the moon has a constant angular velocity through the sky: meaning that it travels the same number of degrees when it appears as it does at any point through it"s arc [9][10]; it can also be shown that the moon does not change size by any significant margin as it moves across the sky; this is true for any observer. [11] If the moon was traveling in a direction that took it closer or further away from the earth as a substantial fraction of the distance from the earth to the moon it"s size, and velocity through the sky would deviate. This is indicated by basic geometry of an observer viewing the same object at different distances shown in [A] and [B] While the constant speed could be explained by continually changing speed over the course of its movement; this would cause wildly deviating angular speeds for different observers at differing locations [C], which is not observed and so can be ruled out. Optical atmospheric effects bending the light, or changing the moons position in the sky significantly can be ruled out: the moon passes in front of stars which must pass through the same atmosphere at the same time; if these are unaffected and undistorted throughout the night, then atmospheric refraction or effects that appreciably change the position or size the moon cannot be occurring. Also, Most atmospheric effects are relatively transient depending on conditions; natural variations in these conditions would cause repeated discrepancies, and aberrations that could be detected, and are not. So, due to these, the only possibility is that the distance from the moon to any other observer is approximately the same at all times it is visible; with the lack of change in size indicating the distance to the moon is significantly greater than the size of the earth. In other words, it must be travelling in an approximate circle for observations we see to be possible. [D] Other observers at different locations; will also observe the moon traveling in this constant angular motion and size, but at different angular position in the sky. [E] As it is not possible for the moon to physically be in two places at once, the distance between observers and the different viewing angle of the moon can be used work out the relationship between observers. As I have shown the path for moon must maintain constant distance from the two different observers, and thus can only be travelling in a roughly circular path, we can measure it"s position at different locations over time, and super impose these observations. [F][G] It is clear from the diagram shown in [G] that there must be an angular difference in orientation between the two observers to account for the observed position of the moon between them. IE: "straight up" for one, is offset by an angle from the "straight up" of the other. More observers can be added [H]; and using this same technique that shows that as you move in distance, the observers orientation can be demonstrated to change from 0, all the way through 360 degrees; a process that can be repeated for any direction they walk; the ONLY geometric surface in which this is possible, is a sphere. Thus, all other geometries of the earth other than a sphere can be ruled out through this observation. Given the above; and given the nature of total eclipses [12], that occur at different positions on the earth at varying times of day; we know the sun doesn"t change size appreciably either; there are variations in size, which correlate to the specific time of year the eclipse is, not the position in the sky at which the eclipse occurs. IE the sun appearing larger in January that it does in July, but larger at every point in the sky where such eclipse occur. It"s much harder to show photographic evidence by an amateur of the size of the sun, as the sun is an extraordinarily bright object with few features, and thus it is easy to fall foul of optical effects such as bloom[13], or poor focus[14] that obscures it"s true size in images. When decent solar filters, and good photographic equipment is used to take such images, they all show a constant angular size and speed of the sun too [15] Thus, repeating the geometric analysis I provided for the moon can be performed on the sun with the same results. Now that the geometry of the earth can be established: a sphere with the sun and moon travelling around the earth relative to observers; further calculations can be made and matched to other observations. Using this geometry; we can further calculate the phases of the moon [16]; together with an explanation for them. Locations of solar eclipses [17], lunar eclipses [18], the position of the sun in the sky for all observers on earth [19], and the position of the moon in the sky for all observers on earth [20]. All calculations that are reliant on the curvature of the earth, constant angular motion and an exact match between longitude and latitude degrees, distance, and the relative direction of "up". If the observers do not have an orientation that matches their position on the sphere, these calculations cannot not work: they depend both on the moons position, and the orientation of the observer. If the latter is wrong, the calculated lunar position of that observer will be wrong too. But they"re not. Even worse, these calculations all require a 1 degree change in viewing angle for the sun, the moon for every 69 degrees travelled in any direction at any point in earth; that is not possible in any other configuration other than a sphere with an approximate circumference of 24,000 miles [I][J][K]; without the sun being far enough away to be visible for all observers at once. As a result, the observations are not only consistent with the spherical earth, the above demonstrate that such observations are not physically possible if the earth is not a sphere of 24,000. Add to this, the visible horizon; and a maximum viewing distance from almost all positions and almost all times consistent with an earth curvature of 24,000 miles [21]; with objects appearing Below the horizon [22][23][24], which geometry and line of sight clearly shows cannot be significantly obscured by waves without them being higher than the height of the object being obscured, which should be observable. [L], The only possibility is the general sea level was physically higher between the two objects [L]; for this to be true at any location on earth; the earth must be a sphere. The sole exception to this, are artifacts such as mirages, mock mirages, looming and stooping[25][26]; where varying degrees of atmospheric refraction can bend light around the horizon, allowing you to see objects that should be too far away to see: [27][28] So, as we have established observation of the sun and moon, with geometry render it indisputable that the earth is a sphere; the last contention is whether the earth is spinning, or whether the sun revolves around the earth. As I have stated thus far, the sun appears to be revolving around the earth because of relative motion; the effect would appear the same to an observer on the earth for both. Gravity: Newton laws of motion, used throughout the world indicate that to produce acceleration on a mass, you need force [29]. As objects falling to earth are accelerated. While we may not understand what the force is, it is clear that earth exerts a force on all masses as a result. If the moon has mass, it either crashes to earth, flies off into space; or can orbit the earth through precisely defined periods [30]. For the planets to orbit around the earth, a convoluted system of extreme forces that are not measurable and unknown that produce no effect on earth, must be invoked to explain retrograde motion [31] due to Newton"s first law of motion. However, a force we already know exists combined with these laws of motion, allows us to determine that the existing force we understand allows planets to orbit around the sun with no other forces required. [32] As we can accurately determine the distance of the moon [33], we can discover that the speed of rotation using Newton's laws indicates the sun has a much larger mass than the earth; and the earth/sun has an orbital speed consistent with the earth orbiting around the sun, and totally inconsistent with a required equivalent orbital period of the sun moving around the earth [34]. Add to this parallax of stars [35]; indicating that they are in different positions in summer and winter, allows us to determine the earth is in a physically different location relative to other stars in summer and winter. All of these things together, make it incontrovertible that the sun is rotating around the sun; and thus to explain observations, the Earth must necessarily be spinning.