Because the payload is in free fall, and the tether is rotating, the payload and grapple vehicle will experience a relative acceleration equal to"
12.
In a small environment such as a freely falling lift, this relative acceleration is minuscule, while for skydivers on opposite sides of the Earth, the effect is large.
13.
In this geometric description, tidal effects the relative acceleration of bodies in free fall are related to the derivative of the connection, showing how the modified geometry is caused by the presence of mass.
14.
Looking back at our graph of the metric tensor, we can see that the tidal tensor produces small sinusoidal relative accelerations with period, which are purely transverse to the direction of propagation of the wave.
15.
However, four fictitious forces are defined for frames accelerated in commonly occurring ways : one caused by any relative acceleration of the origin in a straight line ( rectilinear acceleration ); two involving rotation : centrifugal force and Coriolis force; and a fourth, called the Euler force, caused by a variable rate of rotation, should that occur.
