Richard Arenstorf
Encyclopedia
Richard F. Arenstorf is an American
mathematician
who discovered a stable orbit between the Earth and the Moon, called an Arenstorf Orbit, which was the basis of the orbit used by the Apollo Program for going to the Moon.
The Arenstorf Orbit
While the orbit of a satellite around the Sun was empirically discovered by Kepler and theoretically proven by Newton to be an ellipse
, at the time when the United States was interested in going to the Moon, there was no such solution known for the shape of a satellite orbiting regularly around two objects, such as a spacecraft going between the Earth and the Moon. This is a special case of the infamous Three Body Problem, for which a general analytical solution is not known because of its complexity of solving the effect of three bodies which all pull on each other while moving, a total of six interactions. However the case of an Earth-Moon satellite can be simplified to four interactions, because although the three objects gravitationally all pull on each other, the effect of the spacecraft's gravity upon the motion of the vastly more massive Earth and Moon is practically non-existent. Arenstorf found a stable orbit for a spacecraft orbiting between the Earth and Moon, shaped like an '8' with the Earth or Moon located inside each loop of the '8'. This orbit is the basis of a path going to the Moon from the Earth, such as the United States Apollo program. For a permanent presence on the Moon, it would be the path of what Arenstorf calls a 'Space Bus', a ferry which could regularly orbit supplies and people between the Earth and Moon without directly expending fuel. By staying on the Arenstorf orbit, lunar astronauts automatically return back to Earth. Before leaving NASA at the first Moon Landing, Arenstorf mapped out an emergency rescue orbit, which was used in the Apollo 13 incident, in which a catastrophic malfunction forced aborting the Moon landing, but the astronauts ultimately returned safely to Earth without a major course adjustment.
Additional Career
After the first Moon Landing, Arenstorf became a professor of mathematics at Vanderbilt University, now retired, where he specialized in celestial mechanics
and analytic number theory
. In number theory, one speciality was the properties of the Riemann zeta function, which allows generalizations to be made about the nature of prime numbers.
Recognition and Awards
Arenstorf's portrait is found among Kepler and Newton in the "Museum" beginning the book, Foundations of Mechanics by Ralph Abraham.
Arenstorf received the NASA Exceptional Achievement Medal
in 1966.
Arenstorf received his Ph.D. from the Johannes Gutenberg University of Mainz
in 1956.
Popular Culture
In the movie Apollo 13 , a sketch of the Arenstorf Orbit is drawn on a chalkboard and referred to throughout the movie to mark the progress and dangers of the imperilled astronauts.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
who discovered a stable orbit between the Earth and the Moon, called an Arenstorf Orbit, which was the basis of the orbit used by the Apollo Program for going to the Moon.
The Arenstorf Orbit
While the orbit of a satellite around the Sun was empirically discovered by Kepler and theoretically proven by Newton to be an ellipse
Ellipse
In geometry, an ellipse is a plane curve that results from the intersection of a cone by a plane in a way that produces a closed curve. Circles are special cases of ellipses, obtained when the cutting plane is orthogonal to the cone's axis...
, at the time when the United States was interested in going to the Moon, there was no such solution known for the shape of a satellite orbiting regularly around two objects, such as a spacecraft going between the Earth and the Moon. This is a special case of the infamous Three Body Problem, for which a general analytical solution is not known because of its complexity of solving the effect of three bodies which all pull on each other while moving, a total of six interactions. However the case of an Earth-Moon satellite can be simplified to four interactions, because although the three objects gravitationally all pull on each other, the effect of the spacecraft's gravity upon the motion of the vastly more massive Earth and Moon is practically non-existent. Arenstorf found a stable orbit for a spacecraft orbiting between the Earth and Moon, shaped like an '8' with the Earth or Moon located inside each loop of the '8'. This orbit is the basis of a path going to the Moon from the Earth, such as the United States Apollo program. For a permanent presence on the Moon, it would be the path of what Arenstorf calls a 'Space Bus', a ferry which could regularly orbit supplies and people between the Earth and Moon without directly expending fuel. By staying on the Arenstorf orbit, lunar astronauts automatically return back to Earth. Before leaving NASA at the first Moon Landing, Arenstorf mapped out an emergency rescue orbit, which was used in the Apollo 13 incident, in which a catastrophic malfunction forced aborting the Moon landing, but the astronauts ultimately returned safely to Earth without a major course adjustment.
Additional Career
After the first Moon Landing, Arenstorf became a professor of mathematics at Vanderbilt University, now retired, where he specialized in celestial mechanics
Celestial mechanics
Celestial mechanics is the branch of astronomy that deals with the motions of celestial objects. The field applies principles of physics, historically classical mechanics, to astronomical objects such as stars and planets to produce ephemeris data. Orbital mechanics is a subfield which focuses on...
and analytic number theory
Analytic number theory
In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Dirichlet's introduction of Dirichlet L-functions to give the first proof of Dirichlet's theorem on arithmetic...
. In number theory, one speciality was the properties of the Riemann zeta function, which allows generalizations to be made about the nature of prime numbers.
Recognition and Awards
Arenstorf's portrait is found among Kepler and Newton in the "Museum" beginning the book, Foundations of Mechanics by Ralph Abraham.
Arenstorf received the NASA Exceptional Achievement Medal
NASA Exceptional Achievement Medal
The NASA Exceptional Achievement Medal is an award of the National Aeronautics and Space Administration that was established in 1991. The medal is awarded to both civilian members of NASA and military astronauts....
in 1966.
Arenstorf received his Ph.D. from the Johannes Gutenberg University of Mainz
Johannes Gutenberg University of Mainz
The Johannes Gutenberg University of Mainz is a university in Mainz, Rhineland Palatinate, Germany, named after the printer Johannes Gutenberg. With approximately 36,000 students in about 150 schools and clinics, it is among the ten largest universities in Germany...
in 1956.
Popular Culture
In the movie Apollo 13 , a sketch of the Arenstorf Orbit is drawn on a chalkboard and referred to throughout the movie to mark the progress and dangers of the imperilled astronauts.