Fly Me to the Moon by Belbruno Edward Tyson Neil deGrasse

Author:Belbruno, Edward, Tyson, Neil deGrasse
Language: eng
Format: epub
Publisher: Princeton University Press
Published: 2013-08-14T16:00:00+00:00

1 Unlike a Hohmann transfer, based upon modeling the motion of the spacecraft with either the Earth or the Moon in two-body problems, the ballistic capture transfer requires modeling simultaneously the Sun, Earth, Moon, and spacecraft—a four-body problem! Not too much is known about this problem.

2 No vibrations were recorded at the seismic stations when Hiten crashed, likely due to the fact that the impact didn’t have enough force.

Chapter Ten

Significance of Hiten

The route designed for Hiten’s new mission to the Moon represents a turning point in the design of lunar transfers, and transfers in general. A short history of the trajectory design of missions will put the significance of Hiten in perspective.

In the 1960s, missions to the Moon and other destinations were designed based upon Hohmann transfers, based on two-body modeling—between the spacecraft and the Earth, or the spacecraft and Moon, as we saw earlier. The resulting path to the Moon is just one half of a very thin ellipse that looks almost like a straight line (see figure 10.1). A departure from the Hohmann transfer was made in the late 1960s when Apollo went to the Moon. That was a free return trajectory. It looks similar to a Hohmann transfer on the way to the Moon, but when it arrives there it doesn’t fly by as Hohmann’s does if you don’t slow down. It loops around the Moon as shown in figure 10.2, and returns to Earth. This is called a figure-eight trajectory. It was used by Apollo for safety reasons. If the astronauts have to abort the mission due to some catastrophic failure prior to reaching the Moon, as in Apollo 13, they would automatically return to the Earth. To find this route we don’t do the modeling by breaking up the motion as two two-body problems, as with Hohmann, but model it as a three-body problem between the Earth, Moon, and spacecraft. So, the spacecraft feels the gravity of both the Earth and the Moon together at all times. This is more complicated than the Hohmann transfer and enables the free return to the Earth. The three-body problem cannot be solved using explicit formulae as with the two-body problem.1 We have to rely on the computer to model this problem and find the right trajectories.

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