Editing Orbital mechanics (section)

==Orbital maneuver==
{{Main|Orbital maneuver}}
In [[spaceflight]], an '''orbital maneuver''' is the use of [[spacecraft propulsion|propulsion]] systems to change the [[orbit]] of a [[spacecraft]]. For spacecraft far from Earth—for example those in orbits around the Sun—an orbital maneuver is called a ''deep-space maneuver (DSM)''.{{citation needed lead|date=September 2011}}

===Orbital transfer===
Transfer orbits are usually elliptical orbits that allow spacecraft to move from one (usually substantially circular) orbit to another.  Usually they require a burn at the start, a burn at the end, and sometimes one or more burns in the middle.
*The [[Hohmann transfer orbit]] requires a minimal [[delta-v]].
*A [[bi-elliptic transfer]] can require less energy than the Hohmann transfer, if the ratio of orbits is 11.94 or greater,<ref>{{cite book |last=Vallado |first=David Anthony |title=Fundamentals of Astrodynamics and Applications |page=317 |publisher=Springer |date=2001 |isbn=0-7923-6903-3 |url=https://books.google.com/books?id=PJLlWzMBKjkC}}</ref> but comes at the cost of increased trip time over the Hohmann transfer.
*Faster transfers may use any orbit that intersects both the original and destination orbits, at the cost of higher delta-v.
*Using low thrust engines (such as [[electrical propulsion]]), if the initial orbit is supersynchronous to the final desired circular orbit then the optimal transfer orbit is achieved by thrusting continuously in the direction of the velocity at apogee. This method however takes much longer due to the low thrust.<ref>{{cite book |last=Spitzer |first=Arnon |title=Optimal Transfer Orbit Trajectory using Electric Propulsion |publisher=USPTO |date=1997 |url=https://patents.google.com/patent/US5595360}}</ref>

For the case of orbital transfer between non-coplanar orbits, the [[orbital inclination change|change-of-plane thrust]] must be made at the point where the orbital planes intersect (the "node"). As the objective is to change the direction of the velocity vector by an angle equal to the angle between the planes, almost all of this thrust should be made when the spacecraft is at the node near the apoapse, when the magnitude of the velocity vector is at its lowest. However, a small fraction of the orbital inclination change can be made at the node near the periapse, by slightly angling the transfer orbit injection thrust in the direction of the desired inclination change. This works because the cosine of a small angle is very nearly one, resulting in the small plane change being effectively "free" despite the high velocity of the spacecraft near periapse, as the Oberth Effect due to the increased, slightly angled thrust exceeds the cost of the thrust in the orbit-normal axis.

{{multiple image
|direction = horizontal
|align = center
|width1 = 147
|width2 = 239
|width3 = 190
|width4 = 190
|width5 = 192
|image1=Orbital Hohmann Transfer.svg
|image2=Bi-elliptic transfer.svg
|image3=Orbital Two-Impulse Transfer.svg
|image4=Orbital General Transfer.svg
|image5=Optimal Transfer Orbit using Electric Propulsion.png
|caption1=A [[Hohmann transfer]] from a low circular orbit to a higher circular orbit
|caption2=A [[bi-elliptic transfer]] from a low circular starting orbit (dark blue), to a higher circular orbit (red)
|caption3=Generic two-impulse elliptical transfer between two circular orbits
|caption4=A general transfer from a low circular orbit to a higher circular orbit
|caption5=An optimal sequence for transferring a satellite from a supersynchronous to a geosynchronous orbit using electric propulsion
}}{{clear}}

===Gravity assist and the Oberth effect===
In a [[gravity assist]], a spacecraft swings by a planet and leaves in a different direction, at a different speed.  This is useful to speed or slow a spacecraft instead of carrying more fuel.

This maneuver can be approximated by an [[elastic collision]] at large distances, though the flyby does not involve any physical contact.  Due to Newton's third law (equal and opposite reaction), any momentum gained by a spacecraft must be lost by the planet, or vice versa.  However, because the planet is much, much more massive than the spacecraft, the effect on the planet's orbit is negligible.

The [[Oberth effect]] can be employed, particularly during a gravity assist operation. This effect is that use of a propulsion system works better at high speeds, and hence course changes are best done when close to a gravitating body; this can multiply the effective [[delta-v]].

===Interplanetary Transport Network and fuzzy orbits===
{{Main|Interplanetary Transport Network}}
{{See also|Low energy transfers}}
It is now possible to use computers to search for routes using the nonlinearities in the gravity of the planets and moons of the Solar System. For example, it is possible to plot an orbit from high Earth orbit to Mars, passing close to one of the Earth's [[trojan point]]s.{{citation needed|date=January 2016}} Collectively referred to as the [[Interplanetary Transport Network]], these highly perturbative, even chaotic, orbital trajectories in principle need no fuel beyond that needed to reach the Lagrange point (in practice keeping to the trajectory requires some course corrections). The biggest problem with them is they can be exceedingly slow, taking many years. In addition launch windows can be very far apart.

They have, however, been employed on projects such as [[Genesis (spacecraft)|Genesis]]. This spacecraft visited the Earth-Sun {{L1}} point and returned using very little propellant.