Editing Escape velocity (section)

=== From an orbiting body ===
The escape velocity at a given height is <math>\sqrt 2</math> times the speed in a circular orbit at the same height, (compare this with the velocity equation in [[circular orbit]]). This corresponds to the fact that the potential energy with respect to infinity of an object in such an orbit is minus two times its kinetic energy, while to escape the sum of potential and kinetic energy needs to be at least zero. The velocity corresponding to the circular orbit is sometimes called the '''first cosmic velocity''', whereas in this context the escape velocity is referred to as the '''second cosmic velocity'''.<ref>{{Cite book |last=Teodorescu |first=P. P. |url=https://books.google.com/books?id=k4H2AjWh9qQC&pg=PA580 |title=Mechanical systems, classical models |publisher=Springer, Japan |year=2007 |isbn=978-1-4020-5441-9 |page=580}}, [https://books.google.com/books?id=k4H2AjWh9qQC&pg=PA580 Section 2.2.2, p. 580]</ref><ref>{{cite book |title=Physics of Planetary Ionospheres |author1=S. J. Bauer |edition=illustrated |publisher=Springer Science & Business Media |year=2012 |isbn=978-3-642-65555-5 |page=28 |url=https://books.google.com/books?id=ssPyCAAAQBAJ}} [https://books.google.com/books?id=ssPyCAAAQBAJ&pg=PA28 Extract of page 28]</ref><ref>{{cite book |title=Classical Mechanics in Geophysical Fluid Dynamics |author1=Osamu Morita |edition=2nd, illustrated |publisher=CRC Press |year=2022 |isbn=978-1-000-80250-4 |page=195 |url=https://books.google.com/books?id=cqAIEQAAQBAJ}} [https://books.google.com/books?id=cqAIEQAAQBAJ&pg=PA195 Extract of page 195]</ref>

For a body in an elliptical orbit wishing to accelerate to an escape orbit the required speed will vary, and will be greatest at [[periapsis]] when the body is closest to the central body. However, the orbital speed of the body will also be at its highest at this point, and the change in velocity required will be at its lowest, as explained by the [[Oberth effect]].