Equation Help: Gravitationally Bound Rubble Pile Asteroid Orbit

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Discussion Overview

The discussion revolves around the dynamics of a gravitationally bound rubble pile asteroid, specifically focusing on the conditions under which surface material can achieve a circular orbit after exceeding critical spin. Participants explore the relationship between centripetal force, gravitational force, and the necessary initial velocity for orbital motion.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • David introduces the scenario of a rubble pile asteroid and seeks the minimum initial velocity for surface material to achieve a circular orbit after exceeding critical spin.
  • One participant suggests that once critical spin is exceeded, loose rocks will enter circular orbit, although they may collide with other rocks and potentially end up in random elliptical orbits.
  • David expresses confusion regarding the relationship between critical spin velocity (2.28 m/s) and escape velocity (3.28 m/s), noting that at critical spin, surface objects are effectively weightless but higher velocities would launch them off.
  • Another participant argues that escape velocity is not relevant for achieving orbit, emphasizing that a projectile does not necessarily return to the surface if it maintains sufficient horizontal velocity.
  • The discussion touches on the concept of angular momentum and its role in the dynamics of the surface material once it is disconnected from the asteroid.

Areas of Agreement / Disagreement

Participants express differing views on the relevance of escape velocity in the context of orbital motion, indicating a lack of consensus on the relationship between critical spin, escape velocity, and the conditions for achieving a stable orbit.

Contextual Notes

There are unresolved aspects regarding the assumptions about the behavior of surface material once it exceeds critical spin and the implications of angular momentum in this context.

higginsdj
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Hi all,

I have a gravitationally bound rubble pile asteroid. This asteroid reaches and exceeds 'critical' spin where centripetal force exceeds gravitational force and surface material is launched off the surface.

At what minimum initial velocity would the surface material need to be to achieve a circular orbit? Just looking for the equation or a reference site.

Cheers

David
 
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Hi David! :smile:

As soon as it exceeds critical spin, any loose rock (on the top of the highest "mountain", say) will go into circular orbit (hopefully just missing the mountain on its return!).

(In practice, it'll collide will other rocks, and either crash, or get thrown out into some random elliptical orbit, where it will continue to collide with other rocks and eventually they'll all settle down to some regular pattern.)
 
I though this to, but then I might have confused myself. ie for my object, at Critical spin, the surface of the primary is traveling at 2.28 m/s. BUT escape velocity is 3.28 m/s. At the surface Fg = 0.00706 m/s^2. So when I spin fast enough for Fc = 0.00706, The surface object is traveling at 2.28 m/s and will effectively just be weightless on the surface where it is, higher velocities will actually launch it.

BUT, if the object is now disconnected from the parent, Fg will still be acting on it, the more distant the object gets from the parent the slower it's orbital velocity and thus like a projectile it should return to the surface so I am assuming this all has something to do with Angular Momentum BUT I am having trouble connecting all the dots.

Cheers

David
 
Hi David! :smile:
higginsdj said:
I though this to, but then I might have confused myself. ie for my object, at Critical spin, the surface of the primary is traveling at 2.28 m/s. BUT escape velocity is 3.28 m/s.

Escape velocity is irrelevant … it's the velocity for reaching infinity, not for orbiting.
BUT, if the object is now disconnected from the parent, Fg will still be acting on it, the more distant the object gets from the parent the slower it's orbital velocity and thus like a projectile it should return to the surface so I am assuming this all has something to do with Angular Momentum BUT I am having trouble connecting all the dots.

A projectile doesn't have to return to the surface, it only has to keep falling.

As Isaac Newton pointed out, if you throw an apple hard enough horizontally, it will go into orbit … it keeps falling, but the Earth curves away beneath it fast enough to counter the falling.
 

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