The force of attraction exerted by the sun acts not only on a load in a pair of scales, but also on the earth, and therefore it imparts identical acceleration to both scales and load (neglecting tidal effects, see preceding problem). Therefore the force of attraction of the sun does not alter the strain in the springs, i.e, it does not affect the reading of the scales. Just as the earth's attractive force does not stretch the spring if the load, together with scale and spring, falls freely to earth, so the sun's attractive force does not stretch the spring, since the scale "falls", together with the earth towards the sun. This "fall" expresses itself in the fact that the earth, in its orbit round the sun, has a centripetal acceleration, which is in fact equal to the acceleration of free fall, which it or any other body would have if placed on the earth's orbit without initial velocity. Consequently the weight of bodies on the earth is the same day and night.
114. (1) According to the universal theory of gravitation, the acceleration acquired by a body is in inverse proportion to the distance squared. Therefore a body which has been raised to a height of 500 km and which therefore is at a distance of 7000 km from the centre of the earth, will have a gravitational acceleration of
980 × 6500²/7000² = 845 cm/sec²...
(2) For the body to be able to describe a circle about the earth the acceleration imparted to it by the earth must be equal to the required centripetal acceleration. Therefore
845 = v²/(7000 × 10⁵)
Hence we get that v = 7.7 km/sec.
(3) At the velocity we have found, one revolution about the earth will be completed in a time equal to
(2π × 7000)/(7.7 × 3600) hr,
or approximately 1 hr. 40 min.
VII. Oscillation, Waves, Sound