Chapter 1

Energy

In terms of orbital mechanics, energy refers to the total mechanical energy associated with an object in orbit around another celestial body, such as a planet or a star. This energy consists of two components:

  1. Kinetic Energy (KE): This is the energy associated with the object's motion. In the context of orbital mechanics, it's the energy due to the object's velocity as it moves in its orbit.
  2. Potential Energy (PE): This is the energy associated with the object's position relative to the gravitational field of the celestial body it's orbiting. It's the energy an object has because of its altitude or distance from the celestial body.

The sum of kinetic energy and potential energy gives the total mechanical energy (E) of the object:

E = KE + PE

In an orbit, these two forms of energy change as the object moves. According to the law of conservation of energy, the total mechanical energy of an object in orbit remains constant unless acted upon by external forces.

  1. Circular Orbit: The total mechanical energy is negative. This means that the object is in a bound orbit and will continue orbiting the central body indefinitely without escaping. The negative energy indicates that the object is gravitationally bound.
  2. Elliptical Orbit: Similar to a circular orbit, the total mechanical energy of an object in an elliptical orbit is also negative. The object is bound to the central body's gravitational field.
  3. Parabolic Orbit: The total mechanical energy for a parabolic orbit is zero. A parabolic orbit represents the boundary between a bound (negative energy) and unbound (positive energy) orbit. An object in a parabolic orbit will follow a trajectory that just grazes the central body and then continues on an escape trajectory. Its energy is precisely at the point where it's neither bound nor unbound.
  4. Hyperbolic Orbit: The total mechanical energy for a hyperbolic orbit is positive. This indicates that the object is unbound and will not remain in a closed orbit around the central body. Instead, it will follow a hyperbolic trajectory and eventually escape the central body's gravitational influence