We all know from General Relativity theory that movement of objects around, for example, a star actually straight in spacetime continuum. It just time distortion causes the movement to curve.
Considering this, I have the following questions:
Whether the force is Coriolis or centrifugal, or if the planet accelerates radially is frame dependent. For mass $m$ planet revolving at speed $v$ in a radius of $R$:
In an inertial frame, there are no fictitious forces, and the centripetal force caused by gravity is:
$$ F_g = \frac{mv^2} R $$
which keeps the planet in orbit
In a rotating frame ($\omega=v/R$) in which the planet is fixed, there is a centrifugal force:
$$ F_{cent} = {m\omega^2}R = {m(v/R)^2}R = \frac{mv^2}R = F_g$$
Since the planet is stationary, there is no Coriolis force. The total fictitious force balances gravity, and the planet remains fixed.
In a frame moving at $\omega'=\omega/2$, there is a centrifugal force:
$$ F'_{cent} = \frac{m\omega'^2} R = \frac{mv^2}{4R} $$
In this frame, the planet's velocity is:
$$ v' = v - R\omega' = v-v/2 = v/2 $$
The Coriolis force is:
$$ F'_{cor} = 2m\omega' v' = 2m(v'/R)v' = \frac{mv^2}{2R}$$
which is in the anti-radial direction (see Eötvös effect, in while the motion is manifest as a change local gravity).
The total fictitious force is:
$$ F'_{fact} = F'_{cor} + F'_{cent} = \frac 3 4 F_g $$
Hence,the planet experiences a radial force:
$$ \frac 1 4 F_g = \frac{mv'^2} {R} $$
which keeps it on its orbit.
The latter analysis holds for any $\omega'$.
