Гравитациялық және инерциялық масса теңдігін зерттеу эксперимі

the experiment to test the equality of gravitational and inertial mass

The Eötvös effect is the change in measured Earth's gravity caused by the change in centrifugal acceleration resulting from eastbound or westbound velocity. When moving eastbound, the object's angular velocity is increased (in addition to Earth's rotation), and thus the centrifugal force also increases, causing a perceived reduction in gravitational force.

In the early 1900s, a German team from the Geodetic Institute of Potsdam carried out gravity measurements on moving ships in the Atlantic, Indian, and Pacific oceans. While studying their results, the Hungarian nobleman and physicist Baron Roland von Eötvös (Loránd Eötvös) noticed that the readings were lower when the boat moved eastwards, higher when it moved westward. He identified this as primarily a consequence of Earth's rotation. In 1908, new measurements were made in the Black Sea on two ships, one moving eastward and one westward. The results substantiated Eötvös' claim.

To calculate what it takes for the internal weight of a gravimeter to be neutrally suspended when it is stationary with respect to the Earth, the Earth's rotation must be taken into account. At the equator, the velocity of Earth's surface is about The amount of centripetal force required to cause an object to move along a circular path with a radius of 6378 kilometres (the Earth's equatorial radius), at 465 m/s, is about 0.034 newtons per kilogram of mass. For a 10,000 gram internal weight, that amounts to about 0.34 newtons. The amount of suspension force required is the mass of the internal weight (multiplied by the acceleration of gravity) minus those 0.34 newtons. In other words: any object co rotating with the Earth at the equator has its measured weight reduced by 0.34 percent, thanks to the Earth's rotation. When cruising at 10 m/s due East, the total velocity becomes 465 + 10 = 475 m/s, which requires a centripetal force of about 0.0354 newtons per kilogram. Cruising at 10 m/s due West the net velocity is 465 − 10 = 455 m/s, requiring about 0.0325 newtons per kilogram. So if the internal weight is neutrally suspended while cruising due East, after reversing course it will not be neutrally suspended any more: the apparent mass of the 10,000 gram internal weight will increase by about 3 grams, and the spring of the gravimeter must extend some more to accommodate this greater weight. In high performance meteorological models, this effect needs to be taken into account on a terrestrial scale. Air masses with significant velocity with respect to the Earth have a tendency to migrate to another altitude, and when the accuracy demands are strict this must be taken into account.

The mathematical derivation for the Eötvös effect for motion along the Equator explains the factor 2 in the first term of the Eötvös correction formula. What remains to be explained is the cosine factor. Because of its rotation, the Earth is not spherical in shape, there is an Equatorial bulge. The force of gravity is directed towards the center of the Earth. The normal force is perpendicular to the local surface. On the poles and on the equator the force of gravity and the normal force are exactly in opposite direction. At every other latitude the two are not exactly opposite, so there is a resultant force, that acts towards the Earth's axis. At every latitude there is precisely the amount of centripetal force that is necessary to maintain an even thickness of the atmospheric layer. (The solid Earth is ductile. Whenever the shape of the solid Earth is not entirely in equilibrium with its rate of rotation, then the shear stress deforms the solid Earth over a period of millions of years until the shear stress is resolved.) Again the example of an airship is convenient for discussing the forces that are at work. When the airship has a velocity relative to the Earth in latitudinal direction then the weight of the airship is not the same as when the airship is stationary with respect to the Earth. If an airship has an eastward velocity, then the airship is in a sense "speeding". The situation is comparable to a racecar on a banked circuit with an extremely slippery road surface. If the racecar is going too fast then the car will drift wide. For an airship in flight that means a reduction of the weight, compared to the weight when stationary with respect to the Earth. If the airship has a westward velocity then the situation is like that of a racecar on a banked circuit going too slow: on a slippery surface the car will slump down. For an airship that means an increase of the weight. The first term of the Eötvös effect is proportional to the component of the required centripetal force perpendicular to the local Earth surface, and is thus described by a cosine law: the closer to the Equator, the stronger the effect.