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"I went [to the top of] Vehicle Assembly Building and looked down, and tears burst from my eyes. The size of this cathedral where the Rockets take off to go to the moon is so amazing."
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These "manoeuvres" were an essential part of the earliest visits to the outer solar system.
In the book, an Earth spaceship by Martian brigands who are determined to get their hands on the Moon's one key resource, radiactum. Radiactum was "the catalyst mineral which was revolutionising industry."
The mathematics of the manner in which the orbits of comets were altered by close approaches to planets was known in the late eighteenth century. However, this idea was not applied to space craft until much later.
In the early nineteen-twenties, Walter Hohmann demonstrated that the lowest energy path between any two planets is an ellipse that is tangential to the orbits of both the planets. However, no rockets existed until the 1960's that were powerful enough to generate the initial thrust, and a minimum energy orbit would take thirty years from Earth to Neptune - and forty years to Pluto.
In the volume published in 1932, Nikolai Alexyevich Rynin introduced the reader to the mysterious Yuri Vasilievich Kondratyuk. In a volume of Interplanetary Flight published in Russian in 1932, this description of gravity assisted flight was included:
A historical review of the theory of gravity‑assists
in the pre‑spacefight era
It's not clear whether or not this published work was related to earlier, unpublished work by the author dating back as far as 1920.
To the best of my knowledge, the concept of "gravity assist" as a means of altering the speed or course of a spacecraft was apparently not discovered by the scientific world (in English, anyway) until some 20 years after the publication of Cummings' novel. In a footnote A C Clarke indicates the first ref he's aware of was the paper "Perturbation Manoeuvres" by Derek Lawden (Journal of the British Interplanetary Society, vol 13, no 5, Sept 1954). Lawden is a mathematician, and in the early fifties worked on the optimization of rocket trajectories. It is also reported that a summer intern at JPL in 1961, Michael A. Minovitch, showed that the gravity field of a planet could provide thrust to a spacecraft. He demonstrated that careful design of the trajectory to a target planet could provide a gravity assist to move from that planet to a second planet.
Historians of science still differ on this issue.
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