Orbital Mechanics is the study of the motion of artificial and natural bodies under gravitational influence and is closely related to celestial mechanics and astrodynamics. It describes how spacecraft, satellites, planets, moons, asteroids and other objects move through space under gravity and additional forces. The classical foundation is the two body problem, in which two masses interact gravitationally while other influences are neglected. Under idealised conditions, gravitational motion produces conic section trajectories including circles, ellipses, parabolas and hyperbolas.
Real spacecraft operate in environments where additional effects matter, including the gravitational influence of multiple bodies, atmospheric drag, solar radiation pressure, nonspherical gravity fields, third body perturbations and thrust from propulsion systems. Orbital Mechanics therefore ranges from analytical equations that provide rapid approximations to numerical propagation methods that model highly complex trajectories. It is essential for satellite operations, launch trajectory design, interplanetary exploration, rendezvous, docking, navigation, mission planning and collision avoidance.
The central concept in Orbital Mechanics is orbital energy. For an ideal two body orbit, specific orbital energy determines the general class of trajectory and is related to the semimajor axis of an elliptical orbit. Specific angular momentum determines important geometric characteristics, while eccentricity describes how far an orbit departs from circularity. Orbital velocity is not simply determined by altitude because it also depends on the shape and energy of the orbit.
A spacecraft in a low circular Earth orbit moves much faster than a spacecraft in a high geostationary orbit because gravitational orbital dynamics require different velocities at different orbital radii. Keplers laws provide an important historical and mathematical description of orbital motion. The first law states that bound planetary orbits are ellipses with the central body at one focus, the second describes equal areas swept in equal times, and the third relates orbital period to the size of the orbit. Newtonian gravitation subsequently provided the physical explanation for these laws.
Orbital Mechanics uses orbital elements to describe the size, shape and orientation of an orbit. Common classical orbital elements include semimajor axis, eccentricity, inclination, right ascension of the ascending node, argument of periapsis and true anomaly. These elements separate the geometry of an orbit from the instantaneous position of an object along that orbit. Inclination describes the tilt of the orbital plane relative to a reference plane, while eccentricity describes the degree of elongation.
The ascending node identifies where the spacecraft crosses the reference plane in a specified direction. Argument of periapsis describes the orientation of the closest orbital point within the orbital plane. True anomaly describes the spacecraft position relative to periapsis. Alternative state representations use position and velocity vectors directly. Engineers transform between these representations depending on whether they are analysing orbital geometry, propagating trajectories, estimating spacecraft states or planning manoeuvres.
Orbital manoeuvres alter spacecraft energy, momentum, orientation or orbital geometry. A prograde burn generally increases orbital energy and changes the orbit, while a retrograde burn generally decreases orbital energy. The practical effect depends strongly on where the burn occurs. A velocity increase at periapsis raises apoapsis, whereas a velocity increase at apoapsis raises periapsis. The Hohmann transfer is a classic two impulse manoeuvre between coplanar circular orbits and is important because it provides an efficient idealised transfer under simplified assumptions.
Bi elliptical transfers can sometimes reduce propellant requirements for sufficiently large changes in orbital radius. Plane changes can be expensive because they require substantial velocity change, which is why launch site latitude and the timing of orbital manoeuvres are important. Real mission planning combines these principles with launch vehicle performance, operational constraints, communications requirements, lighting conditions, thermal constraints and the gravitational environment.
Orbital Mechanics becomes more complicated when perturbations are included. Earth is not a perfect sphere, so its gravity field contains harmonics that cause orbital elements to evolve over time. The equatorial bulge produces important effects on orbital plane orientation and the orientation of the orbital ellipse. Atmospheric drag affects low Earth orbit spacecraft by removing orbital energy and gradually lowering their altitude, with the effect varying according to atmospheric density, spacecraft area, mass and solar activity.
Solar radiation pressure produces small but cumulative accelerations, particularly for spacecraft with large reflective surfaces relative to their mass. The gravitational fields of the Moon and Sun can significantly affect long duration missions. These perturbations are essential for precise orbit determination and long term mission planning because small accelerations accumulated over months or years can produce large positional differences compared with an ideal two body prediction.
Orbital Mechanics is fundamental to rendezvous and formation flying. Two spacecraft cannot simply travel toward one another in space in the same way that vehicles approach each other on Earth because their relative motion is governed by orbital dynamics. A spacecraft seeking to rendezvous with a target must manipulate its orbit so that their positions and velocities converge at the correct time.
Relative motion models such as the Clohessy Wiltshire equations can approximate motion near a circular reference orbit under particular assumptions. Operational missions also require precise navigation, estimation and guidance because even small state errors can lead to significant separation over time. Docking operations add strict requirements because relative position, velocity, attitude and approach geometry must all remain within safe limits. Formation flying extends these principles to multiple spacecraft that maintain carefully controlled relative configurations for scientific observations, interferometry or distributed sensing.
Orbital Mechanics has applications throughout spaceflight, from Earth observation and communications to planetary exploration and space traffic management. Different orbit classes serve different purposes. Low Earth orbits support many imaging, scientific and crewed missions because they provide relatively low latency and high spatial resolution for many applications. Geostationary orbits allow a spacecraft to remain approximately fixed above a longitude on Earth, making them valuable for many communications and meteorological applications.
Highly elliptical orbits can provide long dwell times over selected high latitude regions. Sun synchronous orbits exploit orbital precession to pass over locations at approximately consistent local solar times, supporting comparable illumination for Earth observation. Interplanetary trajectories use heliocentric orbital dynamics, gravity assists and carefully timed departures to reach other planets while managing propellant consumption.
A major misconception is that astronauts in orbit experience weightlessness because there is no gravity. Earths gravity remains substantial in low Earth orbit, but spacecraft and occupants are continuously falling around Earth, producing the condition commonly described as microgravity. Another misconception is that an orbit is simply a path that requires continuous engine thrust. A spacecraft in an ideal orbit does not need continuous propulsion to maintain its trajectory, although real spacecraft require occasional corrections because of perturbations.
Orbital Mechanics also differs from general navigation because it deals with trajectories governed by gravitational dynamics and often requires consideration of orbital energy, angular momentum and timing. Its practical importance is that spacecraft missions are fundamentally constrained by what trajectories are physically achievable, how much delta v is available, when manoeuvres can occur and how accurately the resulting motion can be predicted.
