SCIENCE EXPLAINS

Cue (NZERS), Issue 8, 30 September 1944, Page 13

SCIENCE EXPLAINS

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THE fact that this terrestrial globe, on which man lives is a slightly flattened sphere is now generally accepted. ’ This was not always the case, and in the dim past men of science who first suggested that the world was spherical and not flat were received with hostility and with threats. ’

What, then, are the proofs to establish beyond question that the earth is approximately spherical in shape ?• They . may be given briefly, as follows:• — (1) -■ It is possible to circumnavigate the world in any direction from a given starting point and return to the same, point by maintaining the initial direction. This is impossible except on a globe of spherical shape, remembering that ’ this does' not necessarily prove a true sphere. It , could be egg-shaped. This objection disappears when it is noted that the circumference, in whatever direction it is measured, is . approximately the same. In fact, the difference between equatorial and polar circumferences is Only , about 85 miles. This, then, must be on an almost spherical body. (2) ; Then there is also the wellknown argument —the curvature at sea. ; ’ ~ • Fig. 1 illustrates three floats, A, B and C, with a vertical pole on each, and spaced on the surface of a calm sea, with a distance of say 600-800 yds between A and and the same distance between B and C. The top of each pole is exactly

the same height from the surface of the water. If a line is- now taken between the top of mole A and the top of pole C, it *is found that the top of the middle pole, B, projects

above this line. The amount is small, measured in inches, but it indicates curvature on the surface of the water. The important observation is that, in whatever direction- the

line of poles faces, or in whatever part of the world this is tried, the same curvature is observed. The only solid which has the same surface curvature on any part whatsoever of its surface is a sphere. The mathematically inclined can calculate the radius of the sphere from these observations. . ‘ ' (3) Observations from any point at sea show that ships approaching from any direction come into view masthead first, then superstructure and finally the hull. This can happen only on a body of spherical shape. If on a plane surface, all the ship would be visible at the same time, and every part from masthead to hull would increase in size as distance away decreased. Figure 2 illustrates this. Consider a ship approaching a point of observation P. At location C, only the mast is visible, as the superstructure and hull are below the observer’s horizon. At location B, the mast is visible, with superstructure just appearing above the horizon, while at location A, the hull . has appeared above the horizon.. This could not barmen on a flat st face. - * _

On a flat surface, as in Fig. 3, the real horizon is at infinity and the line of sight is parallel with the plane surface. Whole objects can be seen .at any distance, their apparent size being governed by perspective. Further, zif , the earth were flat the sun would rise or set at the same time all over the world. That is not the case. (4) The increase in size of the circular horizon is another interesting proof of spherical shape for this terrestrial planet. The higher

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the altitude of a point of observation, the greater is the diameter of the circular, horizon. . This diameter increases at a mathematical rate compatible only with observation above a sphere. (5) In an eclipse of the moon, the earth’s shadow cast on the surface of the moon is always circular in shape. Only a sphere will cast a circular shadow in any direction. (6) The approximately constant weight of a body, when weighed by spring balance methods on all parts of the earth’s surface, is a proof that the . body is being weighed on a large sphere. It is. a. well-known axiom in physics that every particle of matter in the universe attracts

every other particle in the universe with , a force which is directly proportional to their respective, masses, and inversely proportional to the square of their distances apart. : Expressed mathematically:— >•A A & F’G '

Where • F = force of attraction between two bodies Ml, M2. < ■ G = ’gravitational constant. Ml — mass of one body. M 2—2 — mass of second body. ’ D = distance apart. The weight of a body on the surface of the earth is really the force with which the earth attracts this body towards its centre. Remembering this, now, consider the weight of an object when weighed at different parts of the earth’s surface. < Observation shows the -weight for the object to be nearly the same at all places. Then, calling the first weight Fl, and the second weight, at a different location, F2, then

1 F» “Fa ) i-x Therefore G lU#* ~

Ml = mass of object. M2 = mass of the earth. DI = distance between centres of Ml and M2 in first case: ‘7 . D2 .= distances apart in second case. . —and since, G, Ml and M2 are constants (no substance being lost from the object or from the earth). • ; D? - Da orDr-D« —And so the distance from the

centre of the object to the centre of the earth is the same in both cases. In the same way, it can be shown that distance to the centre of the earth is nearly the same from all parts of its surface. The earth, therefore, must be nearly a sphere. As a matter* of fact, an object weighs just slightly more at the

poles, because the poles are nearer the centre of the earth than the equator. To be more correct, the earth is thus an oblate spheroid. (7) The apparent motion and behaviour of the planets > and the stars can be accounted for only on the assumption that the earth is spherical. (8) Another proof by «inference » can be put forward from the fact that the earth is one of the nine planets of the solar system. The planets are, in order of proximity to the sun, Mercury, Venus, ■ Earth, Mars, Jupiter, Saturn, Uranus, Neptune and Pluto. Eight of these planets are known to be spherical by actual observation. It is, therefore, a

fair assumption that the earth,, which came into being in the same way as the others, and obeys the same laws, would be like them in form. Finally, a few interesting mathematical facts about the earth:— . Mass: 6,596 million million million tons (6.596 X 1021 tons). Volume: 249,300 million cubic miles (2.493 X 10 Hy, cubic miles). Area: 197 million square miles. Polar radius: 3949.99 miles; equatorial radius 3963.34 miles. ) Density: 5.522 grams per c.c.— i.e., 5.522 times as heavy as a similar sphere all water.