Editing Orbital speed (section)

==Mean orbital speed==

For orbits with small [[eccentricity (orbit)|eccentricity]], the length of the orbit 
is close to that of a circular one, and the mean orbital speed can be approximated either from observations of the [[orbital period]] and the [[semimajor axis]] of its orbit, or from knowledge of the [[mass]]es of the two bodies and the semimajor axis.<ref>{{cite book |editor-last1=Wertz |editor-first1=James R. |editor-last2=Larson |editor-first2=Wiley J. |title=Space mission analysis and design |date=2010 |publisher=Microcosm |location=Hawthorne, CA, US |isbn=978-1881883-10-4 |page=135 |edition=3rd }}</ref>

:<math>v \approx {2 \pi a \over T}  \approx \sqrt{\mu \over a}</math>

where {{math|''v''}} is the orbital velocity, {{math|''a''}} is the [[length]] of the [[semimajor axis]], {{math|''T''}} is the orbital period, and {{math|1=''μ'' = ''GM''}} is the [[standard gravitational parameter]]. This is an approximation that only holds true when the orbiting body is of considerably lesser mass than the central one, and eccentricity is close to zero.

When one of the bodies is not of considerably lesser mass see: [[Gravitational two-body problem]]

So, when one of the masses is almost negligible compared to the other mass, as the case for [[Earth]] and [[Sun]], one can approximate the orbit velocity <math>v_o</math> as:<ref name="lissauer2019" />

:<math>v_o \approx \sqrt{\frac{GM}{r}}</math>

or:

:<math>v_o \approx \frac{v_e}{\sqrt{2}}</math>

Where {{math|''M''}} is the (greater) mass around which this negligible mass or body is orbiting, and {{math|''v<sub>e</sub>''}} is the [[escape velocity]] at a distance from the center of the primary body equal to the radius of the orbit.

For an object in an eccentric orbit orbiting a much larger body, the length of the orbit decreases with [[orbital eccentricity]] {{math|''e''}}, and is an [[ellipse#Circumference|ellipse]]. This can be used to obtain a more accurate estimate of the average orbital speed:<ref>{{cite book |first=Horst |last=Stöcker |first2=John W. |last2=Harris |date=1998 |title=Handbook of Mathematics and Computational Science |pages=[https://archive.org/details/handbookofmathem00harr/page/386 386] |publisher=Springer |isbn=0-387-94746-9 |url-access=registration |url=https://archive.org/details/handbookofmathem00harr/page/386 }}</ref>
 
:<math> v_o = \frac{2\pi a}{T}\left[1-\frac{1}{4}e^2-\frac{3}{64}e^4 -\frac{5}{256}e^6 -\frac{175}{16384}e^8 - \cdots \right] </math>

The mean orbital speed decreases with eccentricity.