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. Derivation of the formula for simplified case Derivation of the formula for motion along the Equator. A convenient coordinate system in this situation is the inertial coordinate system that is co-moving with the center of mass of the Earth. Then the following is valid: objects that are at rest on the surface of the Earth, co-rotating with the Earth, are circling the Earth's axis, so they are in centripetal acceleration with respect to that inertial coordinate system. What is sought is the difference in centripetal acceleration of the surveying airship between being stationary with respect to the Earth and having a velocity with respect to the Earth. The following derivation is exclusively for motion in east–west