As far as the moon landings are concerned, Bill Kaysing first refuted them in the 1970's with his book 'We Never Went to the Moon.' David Percy, Bart Sibrel, and numerous others have produced books and videos about this since. Lloyd Mallan wrote an expose of the Russian space program as a farce designed to improve the Soviet image. More recently, a Hungarian writer wrote an informative book about Yuri Gagarin showing that the alleged first man in space lied for the party and the entire thing was Soviet propaganda that never occurred. Corroboration of this comes from Albanian communist leader Enver Hoxha who wrote against Soviet science teams whom he found diseeminating falsified information in his country which is one of the reasons he went with China. While Mao was still alive, the Chinese press asserted that the moon landings are a lie and nuclear weapons are a paper tiger, and the schools in Cuba and other socialist Latin countries maintain that today.
The consensus of the early Church endorsed the flat earth cosmology even before Constantine came to power. It was the pagan scholars who argued for a globular geocentric earth. Christians writers like Lactantius wrote emphatically in favor of a flat earth. What unambiguously unified the Church Fathers was the concept of antipodes which they were against. The existence of antipodes refers to feet on the opposite side of a globe where it rains upwards and men are upside down and plants and trees grow downwards as Lactantius wrote.
'Of the Antipodes, The Heaven, and the Stars'
Divine Institutes Book III, Chapter XXIV
The Church Fathers such as Saint John Chrysostomos declared that it is unacceptable to bleieve in the antipodes. However, I should say that although most Christians at that time believed the earth to be flat, what Saint Chrysostomos had in mind theologically was the teaching of another race of men on the other part of the world who were not descended from Adam. The distinction is important because belief in whether the earth is flat or rounded is not important to salvation as Saint Basil declared. I feel that I should mention that the english translation of the word "world" or "Universe" as rounded or hemispherical in Saint Basil's Hexameron must be viewed as referring to the firmament or heavens in order to be consistent with other Church Fathers who viewed the earth as flat as the heaven as domed.
Venerable Bede of England is the first I have found that unequivocally blieved that the earth is globular rather than flat. I suspect that the influence of Islamic science (which preserved the globular teachings of the greeks) had some influence by that time as a close observation reveals that Saint John of Damascus's Exact Exposition of the Orthodox Faith was more influenced by contemporary science than was earlier Christian writers - probably because he rightly did not consider the natural sciences as essential as the theology. If he did not make any mistake with regard to theology, but only on natural science then the book is good. I would question what Saint John of Damascus wrote in one passage where he wrote that lunar eclipses occur because the moon passes into the earth's shadow. However, I have read that lunar eclipses have been observed in which the sun is still visible in the sky. IF that is the case, then then the darkness overcoming the moon is not the shadow of the earth. I belive the moon is a vessel in the sky which emits light (not reflects it) which is how Saint Basil describes it. Genesis 1 says that the sun and moon are both lights in the sky.
Cosmas Indicopleustes was a monk of the Sinai monastery at the time of Saint John Climacus who wrote a book entitled 'Christian Topography' which refuted the pagan concept of a globular earth. A ninth century copy of this book is on display at the Sinai monastery, and it is mentioned in books published with the monastery's blessing by the American University in Cairo. The ancient Church of Saint George in Madaba, Jordan has a sixth century mosaic map of the world which contains the most ancient map of Jerusalem known to exist. The most exhaustive study of this map was done by Piccirillo using the archives of the Patriarchate of Jersusalem, and he asserts that this mosaic map was commissioned by Cosmas Indicopleustes as was another one in Gaza. He also asserts that Emperor Justinian agreed with Cosmas and publicly spoke to that effect.
By Cosmas Indicopleusteshttp://www.sacred-texts.com/earth/ct/index.htm
Online Chapter of Piccirillo's Madaba Map Bookhttp://126.96.36.199/www1/ofm/mad/index.html
Circa 400 A.D., Saint Jerome also translated and paraphrased a flat earth cosmological book by a Scythian pilgrim named Aethicus of Istria. Modern infidels have questioned Jerome's authorship of this since about 1850, but prior to that it was accepted.
Cosmography of Aethicus of Istria
Translated and Paraphrased by Saint Jeromehttp://www.amazon.com/The-Cosmography-A
According to this kind of cosmos, the sun and stars are much smaller than imagined by modern astronomy and are only a few few hundred miles away. Jerusalem is located at the geographical center of the earth as the psalm says that God worketh salvation in the navel of the earth. This refers to the crucifixion and resurrection of Christ just outside of the Jerusalem city gate which coresponds to Jerusalem's layout at the time of Christ. The exact geographical centre of the world is a specific place in the navel of the Church of the Holy Sepulchre called the Omphalos. It is literally a few feet north of Golgotha and a few feet east of the Tomb of Christ.
This cosmos also includes a great mountain in the far north which is the one the Devil was referring to when he boasted in Isaiah 14. The height of this mountain is taller than the orbit of the sun, moon and stars which revolve around it. Cosmas asserted that the shadow cast by this mountain creates night on the opposite side of the world.
The world is surrounded by a vast sea which is hemmed in on four sides by the four walls of heaven, and the roof is a dome. The Garden of Eden is an actual geographical location in the East. Along the four sides of the world are located the twelve storehouses of the winds - three on each side.
The river that flows west from the garden of eden splits into four riverheads that proceed underground and resurface in this world and flow to the sea. These are the Nile, Euphrates, Tigris, and the Ganges according to most authors. It is possible that underground tributaries of these rivers account for most or all of the world's aquifers. I have been to the cave in the Himalayas from whence the Ganges gushes forth. It is quite striking. I have also been to the source of the Blue Nile in Ethiopia which also originates from an underground river.
Although the book of Enoch is mentioned in Jude's Epistle, it was expunge from Holy Scripture at the Synod of Pergamos because of interpolations. It survived in the Ethiopian bible and has vestiges of the original book. The most notable astronomical part within the Book of Enoch is the Book of the Heavenly Luminaries which describes the twelve storehouses of the winds.
Twelve storehouses of winds are mentioned in 'A Cosmological Tract' attributed to first century Saint Dionysios the Areopagite and has been preserved in Syriac.
A Cosmological Tract
By Dionysios the Areopagitehttp://www.sacred-texts.com/journals/jras/1917-07.htm
A movement by devout protestants in nineteenth century England revived flat earth belief in a modified model. The foundational book of that movement was a book by Samuel Rowbotham that refuted modern science's objections to the flatness of the earth.
'Earth Not a Globe'
By Samuel Rowbothamhttp://www.sacred-texts.com/earth/za/index.htm
I might also mention that the most original and ancient cosmology of every nation in the world is a a flat earth cosmology. This was attested by the zealous albeit erudite nineteenth century science historians like Draper or the atheist Andrew Dickson White in his book 'The History of the Warfare of Science With Theology in Christendom':http://masi.cscs.lsa.umich.edu/~crshali
Finally, the most popular Flat Earth Society website is a poorly regulated and agnostic oriented satire where serious posters are less than one in a million.