A Generalized Study of Two-dimensional Trajectories of a Vehicle in Earth-Moon Space

  • H. Hiller
Conference paper


A Generalized Study of Two-dimensional Trajectories of a Vehicle in Earth-Moon Space. A study has been made of the two-dimensional motion of a vehicle in a simplified Earth-Moon system, using the concept of a “sphere of influence”. The trajectory, starting from the vicinity of the Earth, is considered to be divided into three phases — to, across and away from the Moon’s sphere of influence. Graphical results are presented of the following: the geocentric and selenocentric velocity vectors and location of the vehicle for arrival at and departure from the Moon’s sphere of influence; the periselene distance; the parameters defining the departure conic-section trajectory, so that subsequent motion is determined; and finally, the conditions for grazing and centrally hitting the Moon.

An additional study, using some of the above results, has shown that the tolerance in direction of the initial geocentric velocity, to miss the Moon’s centre by its radius, has a mean value of approximately ± 0.2° about an initial value of 90°.


Elliptic Trajectory Vehicle Arrival Hyperbolic Trajectory Incoming Trajectory Geocentric Velocity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Allgemeine Untersuchungen über zweidimensionale Bahnen im Erde-Mond-Bereich. Die betrachteten Bahnen, die in unmittelbarer Nachbarschaft der Erde beginnen sollen, werden in drei Phasen behandelt, und zwar im Einflußbereich des Mondes, im Übergangsgebiet und in größerer Entfernung. Folgende graphische Resultate werden gezeigt: Die geozentrischen und die selenozentrischen Geschwindigkeitsvektoren sowie die Position des Fahrzeuges bei Ankunft und Verlassen des Einfluß-bereichs des Mondes, die periselenische Distanz und schließlich die Bedingungen für eine Umfahrung sowie für ein zentrales Auftreffen auf dem Mond.

In einer zusätzlichen Untersuchung wird unter Verwendung obiger Resultate gezeigt, daß die Toleranzen in der Richtung der anfänglichen geozentrischen Geschwindigkeit etwa ±0,2° bei einem Anfangswinkel von 90° betragen können, wenn das Zentrum der Mondscheibe maximal um ihren Radius verfehlt werden darf.


Etude généralisée de trajectoires bidimensionnelles dans Pespace Terre-Lune. L’étude est basée sur le concept de la “sphère d’influence”. La trajectoire est divisée dans les phases: vers-intérieure-hors de la sphère d’influence lunaire. Résultats graphiques présentés: vecteurs vitesse géocentriques et sélénocentriques et position du véhicule à l’arrivée et au départ de la sphère d’influence lunaire; distance peri-sélénique; paramètres de la conique de départ; conditions d’effleurement ou d’impact central sur la Lune.

Un prolongement de l’étude montre que la tolérance angulaire sur la vitesse géocentrique initiale est en moyenne de ± 0.2° autour d’une valeur initiale de 90° pour manquer le centre de la Lune d’une distance égale à son rayon.


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Copyright information

© Springer-Verlag Wien 1962

Authors and Affiliations

  • H. Hiller
    • 1
  1. 1.Royal Aircraft EstablishmentFarnborough, HantsEngland

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