What makes a trajectory (orbit) bound?

In summary, the conditions for a bound trajectory (orbit) include having negative total energy and obeying an inverse square law acceleration. Additionally, a closed orbit is one where the ratio of the orbital period to the period of radial oscillations is an integer and the orbit is limited to an ellipse.
  • #1
yxgao
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0
What makes a trajectory (orbit) bound?
 
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  • #2
Not exactly sure what the question is.

Gravity?
 
  • #3
What are the conditions on energy? Does it have to be less than or equal to 0?

Also what makes an orbit closed?
 
  • #4
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.
 
  • #5
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.
 
  • #6
True, but assuming an inverse square law acceleration (i.e. gravity) the only bounded orbits are ellipses and so are closed.
 

1. What is a trajectory (orbit)?

A trajectory, also known as an orbit, is the path an object takes as it moves around another object due to the force of gravity.

2. What makes a trajectory bound?

A trajectory is considered bound when an object is constantly orbiting around another object without ever leaving the gravitational pull. This means that the object's velocity and distance from the central object are balanced, creating a stable orbit.

3. What factors affect the boundness of a trajectory?

The boundness of a trajectory is affected by the mass and distance of the central object, as well as the velocity and mass of the orbiting object. If any of these factors change, the trajectory may become unbound and the object will escape the gravitational pull.

4. Can a trajectory be bound around any object?

Yes, a trajectory can be bound around any object that has enough mass to create a gravitational pull. This includes planets, moons, stars, and even black holes.

5. How do scientists calculate the boundness of a trajectory?

Scientists use mathematical equations, such as Newton's Law of Universal Gravitation, to calculate the boundness of a trajectory. They also take into account the initial conditions, such as the object's position and velocity, to determine the shape and stability of the trajectory.

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