Editing Characteristic energy (section)

==History of the notation==
According to Chauncey Uphoff, the ultimate source of the notation ''C<sub>3</sub>'' is [[Forest Ray Moulton]]'s textbook ''An Introduction to Celestial Mechanics''.  In the second edition (1914) of this book, Moulton solves the problem of the motion of two bodies under an attractive gravitational force in chapter 5.  After reducing the problem to the relative motion of the bodies in the plane, he defines the [[constant of the motion]] ''c<sub>3</sub>'' by the equation 
::''ẋ<sup>2</sup> + ẏ<sup>2</sup> = 2k<sup>2</sup> M/r + c<sub>3</sub>'', 
where ''M'' is the total mass of the two bodies and ''k<sup>2</sup>'' is Moulton's notation for the [[gravitational constant]].  He defines ''c<sub>1</sub>'', ''c<sub>2</sub>'', and ''c<sub>4</sub>'' to be other constants of the motion.  The notation ''C<sub>3</sub>'' probably became popularized via the [[Jet Propulsion Laboratory|JPL]] technical report TR-32-30 ("Design of Lunar and Interplanetary Ascent Trajectories", Victor C. Clarke, Jr., March 15, 1962), which used Moulton's terminology.<ref>[https://cbboff.org/UCBoulderCourse/documents/history_c3.pdf "The History of the Term C3"], Chauncey Uphoff, Fortune Eight Aerospace Industries, Inc., December 19, 2001.  Accessed December 21, 2024.  [https://web.archive.org/web/20241220054625id_/https://cbboff.org/UCBoulderCourse/documents/history_c3.pdf Archived on December 20, 2024] by the [[Wayback Machine]].</ref><ref>{{Internet Archive|introcelestial00moulrich|''An Introduction to Celestial Mechanics''|page=162|at=no}}, Forest Ray Moulton, New York: The Macmillan Company, 2nd revised edition, 1914, Chapter 5, §83-88.</ref><ref>"Design of Lunar and Interplanetary Ascent Trajectories", Victor C. Clarke Jr., Technical Report 32-30, JPL, March 15, 1962.</ref>