A number of Muslims believes that the Qur'an talks about the earth as being spherical [actually 'eggshaped'] and not flat as supposedly everybody in Muhammad's life time believed. This is claimed as another "scientific miracle" confirming the divine origin of the Qur'an. Also that the moon does not shine by its own light but only reflects the light is hailed as a "miraculous" insight. As it turns out, the answers to these two questions are related.
If really all people in Muhammad's time had believed that the earth was flat, this might indeed have been an astonishing factoid about the Qur'an. Some Muslim speakers claim the sphericity has not been known until Columbus sailed to America or Magellan sailed around the earth.
But it is not true. The spherical shape of the earth has been known since about 900 years before the Qur'an. The property that the moon only reflects light and doesn't shine by itself is only mentioned in passing since this is a completely obvious fact for anybody who has watched the moon for a while and sees the different phases. The only explanation that some parts of moon don't shine most of the time, is that it only reflects and we see only the part that is currently reached by the light of the sun.
In the following I am quoting from George O. Abell, Exploration of the Universe, 4th edition, New York: Holt, Rinehart and Winston, pages 16 and 18.
... Pythagoras (who died ca. 497 B.C.) also believed that the earth, moon, and other heavenly bodies were spherical. It is doubtful that he had a sound reason for this belief, but it may have stemmed from the realization that the moon shines only by reflected sunlight, and that the moon's sphericity is indicated bv the curved shape of the terminator, the demarcation line between its illuminated and dark portions. If he had so reasoned that the moon is round, the sphericity of the earth might have seemed to follow by analogy.
Another member of the Pythagorean school was Philolaus, who lived in the following century. He may have been the first person to introduce the concept that the earth is in motion. Apparently he held that it is too base to occupy the center of the universe; he assigned a central fire to that position. About the fire revolved the earth and other planets...
Philolaus regarded the celestial sphere as motionless and its apparent rotation as the result of the revolution and rotation of the earth. He proposed that the sun, the moon, and the planets moved in their respective spheres outside the orbit of the earth. It was an imaginative concept based entirely on fancy and cannot be regarded as a forerunner of the heliocentric theory. Nevertheless, the concept of a moving earth had been introduced, although in a completely erroneous manner. It was a bold idea that may have had some influence on later Greek thought. Other Greek philosophers of the sixth to fourth centuries B.C. who are said to have believed in a moving earth are Hicetas, Heracleides, and Ecphantus...
So, far from being an unknown thought, this was an opinion held by a considerable number of the Greek astronomers. But even if those were speculations, Aristotle definitely has given a sound reasoning for his theories, over 900 years before the Qur'an. And Aristotle is not some obscure writer, but his works have been read in all centers of higher learning in antiquity.
Another important topic discussed by Aristotle (384-322 B.C.) was the shape of the earth. He cited two convincing arguments for the earth's sphericity. First is the fact that during a lunar eclipse, as the moon enters or emerges from the earth's shadow, the shape of the shadow seen on the moon is always round. Only a spherical object always produces a round shadow. If the earth were a disk, for example, there would be some occasions when the sunlight would be striking the disk edge on, and the shadow on the moon would be a line.
As a second argument, Aristotle explained that northbound travelers observe the stars near the north celestial pole to be higher in the sky than is observed at home, and different stars pass throulh the zenith. Conversely, when one travels to more southern latitudes the stars near the north celestial pole are seen lower in the sky, and some stars that are never above the horizon at home are seen to rise and move across the southern sky. The only possible explanation is that the travelers' horizons had tipped to the north or south, respectively, which indicates that they must have moved over a curved surface of the earth....he also advanced a theoretical argument that material falling to a center would take on a spherical shape - an idea consistent with the gravitational theory of Newton two millennia later.
Some might argue that even if some scholars knew that the earth was a sphere the general public would still have believed that the earth is flat and in particular the illiterate Muhammad would not have had access to the learning of the scholars.
This is effectively rebutted by the existence of many ancient coins which show the earth as globe. Muhammad was a merchant and he might not have read the books of astronomers but he has handled money as nearly everybody would have at many times of his life and even more than today people would be interested to know what was printed on the coins they are using. Through these coins, the knowledge of the earth as globe has certainly spread widely even to the common people of this time.
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