Closed Orbits

Definition

Closed orbits refer to the gravitational paths taken by objects that are bound to a central body, such as a planet orbiting a star or a satellite orbiting a planet. These orbits are closed, meaning the object repeatedly follows the same trajectory, forming a complete loop or ellipse.

5 Must Know Facts For Your Next Test

1. Closed orbits occur when an object's gravitational potential energy and kinetic energy balance, resulting in a stable, repeating trajectory.
2. The shape of a closed orbit is determined by the object's initial velocity and its distance from the central body, as described by Kepler's laws of planetary motion.
3. Closed orbits can be circular or elliptical, with elliptical orbits being more common in the real world.
4. The total energy of an object in a closed orbit is the sum of its kinetic and gravitational potential energies, which remains constant throughout the orbit.
5. Closed orbits are essential for the stability of planetary systems and the motion of artificial satellites around Earth.

Review Questions

• Explain how the balance between gravitational potential energy and kinetic energy leads to the formation of closed orbits.
  • Closed orbits occur when an object's gravitational potential energy and kinetic energy are in balance. As the object moves closer to the central body, its gravitational potential energy decreases, but its kinetic energy increases. Conversely, as the object moves farther away, its gravitational potential energy increases, and its kinetic energy decreases. This balance between the two forms of energy results in a stable, repeating trajectory, or closed orbit, around the central body.
• Describe how the shape of a closed orbit is determined by the object's initial velocity and distance from the central body.
  • The shape of a closed orbit, whether circular or elliptical, is determined by the object's initial velocity and its distance from the central body. If the object's initial velocity is just right to balance the gravitational force, it will follow a circular orbit. However, if the initial velocity is higher or lower, the object will follow an elliptical orbit, with the central body located at one of the foci of the ellipse. The eccentricity of the ellipse is determined by the ratio of the object's kinetic energy to its gravitational potential energy at the start of the orbit.
• Analyze the relationship between the total energy of an object in a closed orbit and its stability.
  • The total energy of an object in a closed orbit, which is the sum of its kinetic energy and gravitational potential energy, remains constant throughout the orbit. This constant total energy is a key feature of closed orbits and is essential for their stability. If the total energy were to change, the object would either escape the central body's gravitational influence or crash into it. The constancy of total energy ensures that the object follows a predictable, repeating trajectory, maintaining the stability of the closed orbit.

Related terms

Gravitational Potential Energy: The potential energy an object possesses due to its position in a gravitational field, determined by its mass and distance from the central body.

Total Energy: The sum of an object's kinetic energy and gravitational potential energy, which remains constant for a closed orbit.

Elliptical Orbit: A closed orbit in the shape of an ellipse, with the central body at one of the foci.