page_title: Eötvös effect
section_title: Motion along 60 degrees latitude
hierarchical_section_title: Eötvös effect / Physical explanation / Explanation of the cosine in the first term / Motion along 60 degrees latitude
context_page_description: The Eötvös effect is the change in perceived gravitational force caused by the change in centrifugal acceleration resulting from eastbound or westbound velocity. When moving eastbound, the object's angular velocity is increased, and thus the centrifugal force also increases, causing a perceived reduction in gravitational force.
  In the early 1900s, a German team from the Institute of Geodesy in 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 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. Since then, geodesists use the following formula to correct for velocity relative to Earth during a measurement run.
  Here,
  is the relative acceleration
  is the rotation rate of the Earth
  is the velocity in longitudinal direction
  is the latitude where the measurements are taken.
context_section_description: The same gravimeter is used again, its internal weight has a mass of 10,000 grams.
  Calculating the weight reduction when stationary with respect to the Earth: 
  
  An object located at 60 degrees latitude, co-moving with the Earth, is following a circular trajectory, with a radius of about 3190 kilometer, and a velocity of about 233 m/s. That circular trajectory requires a centripetal force of about 0.017 newton for every kilogram of mass; 0.17 newton for the 10,000 gram internal weight. At 60 degrees latitude, the component that is perpendicular to the local surface (the local vertical) is half the total force. Hence, at 60 degrees latitude, any object co-moving with the Earth has its weight reduced by about 0.08 percent, thanks to the Earth's rotation.
  Calculating the Eötvös effect: 
  
  When the airship is cruising at 25 m/s towards the east the total velocity becomes 233 + 25 = 258 m/s, which requires a centripetal force of about 0.208 newton; local vertical component about 0.104 newton. Cruising at 25 m/s towards the west the total velocity becomes 233 − 25 = 208 m/s, which requires a centripetal force of about 0.135 newton; local vertical component about 0.068 newton. Hence at 60 degrees latitude the difference before and after the U-turn of the 10,000 gram internal weight is a difference of 4 grams in measured weight. (Popularly spoken as the weight is a force being measured in newtons, not in grams.)
  The diagrams also show the component in the direction parallel to the local surface. In meteorology and in oceanography, it is customary to refer to the effects of the component parallel to the local surface as the Coriolis effect.
caption: The Eötvös effect for an object moving westward along 60 degrees latitude. The object tends to be pulled towards the Earth's axis.
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