The equipotential surfaces form ellipsoidal shells around the center of the planet, while the surface of any ellipsoidal shell is always perpendicular to the effective gravitational acceleration at any point. An equipotential surface is a surface where the effective gravitational acceleration has the same magnitude everywhere. This has to do with the fact that the earth is mostly liquid and the surface of any liquid always is level to an equipotential surface. Why is it that the ellispoid has a shape just right so that the effective acceleration is everywhere perpendicular to the surface? This implies that the pure gravitational acceleration generally does not act perpendicular to the surface. The ellipsoid has just such a shape, so that the effective gravitational acceleration acts everywhere perpendicular to the surface of the ellipsoid. The effective gravitational acceleration at any point on earth is the vector sum of the pure gravitational acceleration due to gravity plus the centrifugal acceleraion due to earth's rotation. So the formulas to compute the effective gravitational acceleration on a point on earth is much more complicated. This means that the pure gravitational acceleration is dependent on the latitude and there is another component acting against gravity: the centrifugal acceleration a C, which is also dependent on the latitude. Now, the earth is not a perfect sphere but an oblate ellipsoid of revolution, also called an oblate spheroid, and is rotating with the angular speed ω around its minor axis. On a perfect non-rotating sphere the gravitational acceleration for each point on the surface of the sphere is according to Newton: It is prefered to use the gravitational acceleration instead of the force, because the acceleration is the same for any mass m, so m is not contained in the formula. Gravity can also be expressed as a gravitational acceleration g = F / m. On each point P on earth there is a gravitational force F acting on a mass m down to the center of the earth. This radius changes with position because the earth is an ellipsoid. R h: Distance from the center of the earth to to the point P h at altitude Alt, see (7). Depends on the rotational speed ω or the rotational period T and the radius r φ where r φ is the perpendicular distance of the point P h from the earth axis. V h: Tangential velocity at altitude Alt and at point P h. The radius r φ is the perpendicular distance of the point P h from the earth axis. This is dependent on the rotational speed or rotation period T and the radius r φ for the latitude Lat. the earth radius at latitude Lat plus the altitude Alt.Ī hC: Centrifugal acceleration at altitude Alt at point P h, see (19). Depending on the mass M of the earth and the distance R h from the center of the earth, i.e. G hG: Pure gravitational acceleration at altitude Alt at point P h, see (21). This is the vectorial sum of pure gravitational acceleration g hG and centrifugal acceleration a hC. G h: Effective gravitational acceleration at altitude Alt at point P h, see (17). W h: Weight of the test mass as displayed on the scale at altitude Alt at point P h. R o: Distance from the center of the earth to to the point P, see (6). Depends on the rotational speed ω or the rotational period T and the radius r φ where r φ is the perpendicular distance of the point P from the earth axis. V 0: Tangential velocity at the surface at point P. On the poles this radius is 0, on the equator it is equal to the radius of the earth at that location. The radius r φ is the perpendicular distance of the point P from the earth axis. Depending on the mass M of the earth and the distance R o from the center of the earth.Ī oC: Centrifugal acceleration on earth's surface at point P, see (11). G oG: Pure gravitational acceleration on earth's surface at point P, see (14). This corresponds to the vectorial sum of pure gravitational acceleration g oG and centrifugal acceleration a oC. G o: Effective gravitational acceleration on earth's surface at point P, see (9). W o: Weight of the test mass displayed on the scale at sea level at point P.
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