# Centripetal forces and gravity

1. Apr 29, 2008

### stevebd1

On a couple of occasions I've seen it stated that centripetal forces cancel out gravity where centripetal force is v^2/r (expressed in m/s^2 as with gravity). Based on this, if the angular velocity of frame-dragging near a 3 sol BH (spin parameter a = 0.95) was 54,226,630 m/s (0.181c) at the photon sphere (r = 13,291.65 m) and the gravity was ~4.006e12 m/s^2, would the velocity of the frame-dragging be included when calculating the centripetal acceleration required to maintain a stable orbit?

frame-dragging centripetal acceleration= v^2/r = 2.2123e11 m/s^2

in order to maintain a stable orbit, velocity required of an object within rotating frame might be expressed as-

$$v=\sqrt{(a_{g} -a_{c}) r}$$

v = velocity required to maintain stable orbit, $$a_{g}$$ = gravity acceleration, $$a_{c}$$ = centripetal acceleration, r = radius

in this case, 224,290,519 m/s (0.748c)

Is it considered acceptable to include the frame-dragging's angular velocity when calculating the velocity required to retain a stable orbit at a specific radius around a rotating BH?

Also, if you were rotating within the frame-dragging without any input (i.e. rotating the black hole as a static object within the rotating frame) and you had some form of propulsion directed towards the black hole that counteracted the gravity, would you be aware of centrifugal forces induced by the rotating frame or is the fact that the frame itself is rotating and technically not you mean that no centrifuge would be perceived?

Steve

Last edited: Apr 29, 2008