Centripetal forces and gravity

In summary, the conversation discusses the relationship between centripetal forces, gravity, and frame-dragging around a rotating black hole. It is suggested that the velocity of frame-dragging should be included when calculating the centripetal acceleration required to maintain a stable orbit. The concept of rotating within frame-dragging and the perception of centrifugal forces is also brought up.
  • #1
stevebd1
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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-

[tex]v=\sqrt{(a_{g} -a_{c}) r}[/tex]

v = velocity required to maintain stable orbit, [tex]a_{g}[/tex] = gravity acceleration, [tex]a_{c}[/tex] = 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
 
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  • #2
@stevebd1 did you find any more insight on this topic?
 

1. What is the difference between centripetal force and gravity?

Centripetal force is a force that causes an object to move in a circular path, while gravity is a force that attracts objects towards each other. Centripetal force is necessary for circular motion, while gravity acts on all objects with mass.

2. How are centripetal forces and gravity related?

Centripetal force is often described as a "center-seeking" force, and gravity is the force that keeps objects in orbit around a center point. In fact, gravity is one type of centripetal force that keeps planets in orbit around the sun.

3. What is the formula for calculating centripetal force?

The formula for calculating centripetal force is: Fc = mv²/r, where Fc is the centripetal force, m is the mass of the object, v is the velocity of the object, and r is the radius of the circular motion.

4. Can centripetal force and gravity be balanced?

Yes, centripetal force and gravity can be balanced in certain situations. For example, in a stable orbit, the centripetal force of the object's motion is balanced by the gravitational force of the larger object it is orbiting around.

5. How does centripetal force affect the speed of an object?

The greater the centripetal force acting on an object, the faster it will move in its circular path. This means that as the radius of the circular motion decreases, the speed of the object must increase to maintain the same centripetal force.

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