Michel Jullian wrote: > Indeed in an inertial frame the fictitious force vanishes (from the analysis) > as a force, but it also magically reappears as mass times acceleration, simply > going from the left hand side to the right hand side of F=ma while changing > sign, so the equations remain the same mathematically. > > For example if one analyses the motion of a satellite on a circular orbit in > its rotating frame, the satellite is at rest i.e. the sum of the inwards > gravitational force Fg and of the fictitious outwards centrifugal force mv^2/r > is zero: > > F = m*a > > Fg - m*v^2/r = 0 > > If one now analyses the satellite's motion in the (assumed inertial) frame of > the Earth, the centri_fugal_ force -mv^2/r moves to the right while changing > sign to become m times the centri_petal_ acceleration +v^2/r : > > F = m*a > > Fg = m*v^2/r > > Same equation mathematically, so both approaches yield the same result for > orbital speed as a function of radius as would be expected.
mv^2/r is the _derived_ centripetal force on an object rotating relative to an inertial frame of reference. If the Earth is assumed to be rotating then v = 0 for the satellite and the satellite's equation of motion is: GMm/r^2 - ma = 0, and a = GM/r^2 If the satellite is assumed to rotating then the derived force mv^2/r may be assumed to be _functionally equivalent_ to the gravitational force GMm/r^2. Functional equivalency does not necessarily establish physical equivalency. Harry
