What makes a trajectory (orbit) bound?

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Homework Help Overview

The discussion revolves around the conditions that determine whether a trajectory, specifically an orbit, is bound. Participants explore concepts related to gravitational forces and energy levels in orbital mechanics.

Discussion Character

  • Conceptual clarification, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants question the role of energy in defining bound orbits, with some suggesting that total energy must be less than or equal to zero. Others inquire about the conditions for orbits to be closed and the relationship between orbital periods.

Discussion Status

The discussion is active, with various interpretations being explored regarding the relationship between energy and the nature of orbits. Some participants have provided insights into the conditions for boundedness and closure of orbits, but no consensus has been reached.

Contextual Notes

There is an underlying assumption about the nature of gravitational forces, specifically referencing an inverse square law, which may influence the discussion on the types of bounded orbits.

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What makes a trajectory (orbit) bound?
 
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Not exactly sure what the question is.

Gravity?
 
What are the conditions on energy? Does it have to be less than or equal to 0?

Also what makes an orbit closed?
 
Yes, if the total energy (kinetic energy plus potential energy) is negative (In orbital problems, potential energy is typically taken to be 0 at infinity) then there is not enough energy for the vehicle to go "to infinity" so the trajectory must be closed.
 
The energy by itself determines whether an orbit is bound or not, but not whether it is closed. If the ratio of the orbital period to the period of radial oscillations (something like this...) is not an integer, then the orbit does not eventually have to close in on itself.
 
True, but assuming an inverse square law acceleration (i.e. gravity) the only bounded orbits are ellipses and so are closed.
 

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