Orbital mechanics, also known as Astrodynamics, is the study of the motion of objects in space under the influence of gravitational forces. It is a fundamental branch of physics and astronomy that explains how celestial bodies, such as planets, moons, asteroids, and artificial satellites, move and interact with one another.

Key principles of orbital mechanics include:

1. Newton's Laws of Motion
   • First Law: An object in motion will stay in motion unless acted upon by an external force.
   • Second Law: The force on an object is equal to its mass times its acceleration (F=m⋅a).
   • Third Law: For every action, there is an equal and opposite reaction.
2. Newton's Law of Universal Gravitation
   • The force of gravity between two masses is proportional to the product of their masses and inversely proportional to the square of the distance between them: `F = G*(m_1*m_2)/r^2`
3. Kepler's Laws of Planetary Motion
   • First Law (Elliptical Orbits): Planets orbit the Sun in elliptical paths, with the Sun at one focus of the ellipse.
   • Second Law (Equal Areas): A line drawn from a planet to the Sun sweeps out equal areas in equal times.
   • Third Law (Harmonic Law): The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.
4. Two-Body Problem
   • Simplifies orbital mechanics by considering only two objects (e.g., Earth and the Moon) interacting gravitationally, ignoring other influences.
5. Orbital Elements
   • These are parameters that define the size, shape, and orientation of an orbit, as well as the position of an object within it. Examples include:
     • Semi-major axis (size)
     • Eccentricity (shape)
     • Inclination (tilt)

Applications of Orbital Mechanics

• Space Exploration: Planning trajectories for spacecraft to reach other planets or moons.
• Satellite Deployment: Determining stable orbits for communication, GPS, and scientific observation satellites.
• Space Debris Management: Predicting and avoiding collisions in Earth's orbit.
• Interplanetary Travel: Calculating efficient transfer orbits, such as the Hohmann transfer, for missions between planets.

Orbital mechanics combines mathematics, physics, and engineering to solve complex problems related to motion in space.