Kepler's 3rd Law: Constant Orbital Velocity Around Black Holes?

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Discussion Overview

The discussion revolves around the applicability of Kepler's 3rd law in the context of orbital motion around black holes, particularly under conditions of strong gravity and high velocities. Participants explore whether the law holds true when considering the effects of relativistic speeds and gravitational forces near black holes.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • One participant questions the constancy of mass in the context of Kepler's 3rd law when an object orbits a black hole, suggesting that this may imply a violation of the law.
  • Another participant notes that Kepler's laws are derived from Newtonian mechanics and may not be valid in strong gravitational fields or at relativistic speeds, mentioning the concept of the Innermost Stable Circular Orbit (ISCO).
  • A participant seeks a general relation that could apply in all realistic scenarios regarding the relationship between time period and radius for orbits around black holes.
  • One participant expresses skepticism about finding astronomical cases where Kepler's laws fail, suggesting that in relativistic scenarios, each case must be evaluated individually.
  • Another participant speculates that objects in strong gravitational fields may be torn apart by tidal forces before any calculations can be made, indicating potential limitations in applying Kepler's laws.
  • A follow-up comment reiterates the concern about tidal forces and suggests that while small objects might experience negligible tidal effects, their trajectories could still deviate significantly from Newtonian predictions.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of Kepler's laws in extreme conditions, with some suggesting that they may not hold while others argue that they generally work well in most realistic cases. The discussion remains unresolved regarding the specific conditions under which Kepler's laws may or may not apply.

Contextual Notes

Participants acknowledge the limitations of applying Kepler's laws in scenarios involving strong gravitational fields and relativistic speeds, but do not reach a consensus on a unified relation that would apply universally.

Suraj M
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While proving Kepler's 3rd law we get the equation
$$ \frac{ΔA}{Δt} = \frac{2L}{m}$$
we say L and m are constant,so aerial velocity is constant!
But consider a body going around a black hole really quickly, then the mass would not be constant, right?
So is Kepler's 3rd law violated or am i missing something?
 
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Kepler's laws are a consequence of Newtonian Mechanics. They don't hold in the case of strong gravity or velocities close to the speed of light. For example as you get close to a black hole, there is a radius (clued the ISCO, for Innermost Stable Circular Orbit) within which there are no possible stable orbits. This is still outside of the event horizon.
 
Oh Okay, is there some defined relation that works in all realistic cases, relating Time period and radius?
 
Kepler's laws work really well in almost all realistic cases. I suspect it is very difficult to find an astronomical case where the velocity is so high or the gravity so strong that Kepler's laws don't apply. In the relativistic case (velocities close to the speed of light, or very strong gravity), I don't think there is any general rule like Kepler's laws. You have to work out each case.
 
phyzguy said:
In the relativistic case (velocities close to the speed of light, or very strong gravity)
I guess the object would just get torn apart due to the gravitational force, before we calculate anything!
 
Suraj M said:
I guess the object would just get torn apart due to the gravitational force, before we calculate anything!
The object could be small which would make tidal forces negligible, but its trajectory could still be highly non-Newtonian.
 

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