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I've noticed that maneuvers to leave a body's sphere of influence on the way to another body are invariably referred to as injection maneuvers, for instance, translunar injection, while maneuvers to achieve a closed orbit around a body from either a hyperbolic or a suborbital trajectory are referred to as insertion maneuvers, such as lunar orbit insertion.

The etymology makes reasonable sense: insert means "place into", and inject means "throw into", suggesting a more energetic action.

When and how did these terms become standardized in the spaceflight business?

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    $\begingroup$ related information: books.google.com/ngrams/… $\endgroup$ – Polygnome Sep 7 '17 at 12:08
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    $\begingroup$ From the above link, hey seemed to have been established around 60-63, which makes sense, as that is the time of the Apollo Program. $\endgroup$ – Polygnome Sep 7 '17 at 12:10
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    $\begingroup$ Good thinking. Via ngrams I also see "orbital insertion" in an astronautics (rather than medical) sense in 1958. $\endgroup$ – Russell Borogove Sep 7 '17 at 14:07
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When and how did these terms (injection and insertion) become standardized in the spaceflight business?

There are different types of insertions and injections, they were developed as the need arose and refined by practice and advances in orbital mechanics. See also a more advanced explanation of the subject, or "The Book On Rocket Science" by Addison Lilholt. Basic orbital mechanics were fairly well understood by Carl Friedrich Gauss whom wrote a publication about it in 1801.

  • Orbit insertion is the spaceflight operation of adjusting a spacecraft’s momentum, in particular to allow for entry into a stable orbit around a planet, moon, or other celestial body. The result may also be a transfer orbit. There is e.g., the term descent orbit insertion. Often this is called orbit injection.

  • Transfer orbits are performed by several methods. Orbit insertion is a general term for a maneuver that is more than a small correction. It may be used for a maneuver to change a transfer orbit or an ascent orbit into a stable one, but also to change a stable orbit into a descent: descent orbit insertion. Also the term orbit injection is used, especially for changing a stable orbit into a transfer orbit, e.g. trans-lunar injection (TLI), trans-Mars injection (TMI) and trans-Earth injection (TEI).

    The first space probe to successfully perform TLI was the Soviet Union's Luna 1 on January 2, 1959. The first human-crewed mission to successfully perform this procedure, and thus becoming the first humans to leave the Earth's influence, was Apollo 8 on December 21, 1968. Details of the Russian space program remain secret but on the American side Victor Szebehely wrote a book including orbital injection titled: "The Theory of Orbits", a definitive text on the restricted three-body problem as applicable to an Earth-Moon spacecraft system.

    Here are a few of the types of insertions:

    • The Hohmann maneuver was named after Walter Hohmann, the German scientist who published a description of it in his 1925 book Die Erreichbarkeit der Himmelskörper (The Attainability of Celestial Bodies). Hohmann was influenced in part by the German science fiction author Kurd Lasswitz and his 1897 book Two Planets.

    • The bi-elliptical transfer trajectory was first published by Ary Sternfeld in 1934.

    • Low energy transfer, or low energy trajectory, is a route in space which allows spacecraft to change orbits using very little fuel. It is described in the book: "Capture Dynamics and Chaotic Motions in Celestial Mechanics With Applications to the Construction of Low Energy Transfers" by Edward Belbruno.

    • Orbital inclination change is an orbital maneuver aimed at changing the inclination of an orbiting body's orbit. This maneuver is also known as an orbital plane change as the plane of the orbit is tipped. This maneuver is described on Robert A. Braeunig's webpage: "Basics of Space Flight: Orbital Mechanics".

    • In the constant-thrust trajectory the vehicle's acceleration increases during thrusting period, since the fuel use means the vehicle mass decreases. If, instead of constant thrust, the vehicle has constant acceleration, the engine thrust must decrease during the trajectory. This is described in "Trajectories with Constant Tangential Thrust in Central Gravitational Fields" (1960), by W. E. Moeckel, the archive.org link is all that was available as searching NASA's technical report server turned up nothing.

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