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Art and geocentricity

Anne Day of the United Kingdom reported the following in a fax: “I saw a most interesting TV art programme a couple of days ago, comparing the style of painting from various times. What was striking, and it was noted in the commentary, was the change which happened at the same time that the heliocentric idea was taking root. Before this came large portraits, filled with sturdy, confident detail — people who were at ease with themselves while God was in his heaven and all was (relatively) right on the earth. Even the children have big, bold eyes and look at us all in the eye. They knew where they stood and the rules they must obey. But compare this with the pictures which follow, when geocentricity is pushed aside. The people have disappeared into the landscapes and are diminished by huge skies. We are no longer at the centre of things but mere specks in the universe.”

A towering riddle

Jim Hanson sent the following riddle involving the tower of Babel. The question is: What is the greatest height to which the Tower of Babel could have been raised, before the materials carried to the summit lost all their gravity?1

”To answer this mathematical pleasantry, which belongs as much to the physical part of astronomy as to mechanics, we must observe:

”1st. That the gravity of bodies decreases in the inverse ratio of the squares of their distance from the centre of the earth. A body, for example, raised to the distance of a semi-diameter of the earth above its surface, being then at the distance of twice the radius, will weigh only 1/4 of what it weighed at the surface.

”2d. If we suppose that this body partakes with the rest of the earth in the rotary motion which it has around the axis, this gravity will be still diminished by the centrifugal force; which, on the supposition that unequal circles are described in the same time, will be as their radii. Hence at a double distance from the earth this force will be double, and will deduct twice as much from the gravity as the surface of the earth. But it has been found, that under the equator the centrifugal force lessens the natural gravity of bodies 1/289th part

”3d. In all places, on either side of the equator, the centrifugal force being less, and acting against the gravity in an oblique direction, destroys a less portion, in the ratio of the square of the cosine of the latitude to the square of radius.

”These things being premised, we may determine at what height above the surface of the earth a body, participating in its diurnal motion in any given latitude, ought to be to have no gravity.

”But it is found by analysis that under the equator, where the diminution of gravity at the surface of the earth, occasioned by the centrifugal force, is exactly 1/289, the required height, counting from the centre of the earth, ought to be 2891/3, or 6 semi-diameters of our globe plus 65/100, or 5 semi-diameters and 65/100 above the surface.

”Under the latitude of 30 degrees, which is nearly that of the plains of Mesopotamia, where the descendants of Noah first assembled, and vainly attempted, as we learn from the Scriptures, to raise a monument of their folly, it will be found that the height above the surface of the earth ought to have been 6 27/100 semi-diameters of the earth.

”Under the latitude of 60 degrees, this height above the surface of the earth ought to have been 9 47/100 semi-diameters of the earth.

”Under the pole this distance might be infinite; because in that part of the earth there is no centrifugal force, since bodies at the pole only turn round themselves.”


1 The question and answer are from Recreations in Mathematics and Natural Philosophy: containing amusing dissertations and enquiries concerning a variety of subjects the moset remarkable and proper to excite curiosity and attention to the whole range of the mathematical and philosophical sciences. M. Ozanam. Enlarged by M. Montucla. Translated into English by Chas. Hutton. Vol. 4 (of 4). (London: G. Kearsley), 1803. Pp. 40-42.

Translated from WS2000 on 3 September 2005 by ws2html.