Mean longitude: Difference between revisions
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In [[celestial mechanics]] '''true longitude''' is the [[Ecliptic_coordinate_system#Spherical_coordinates|ecliptic longitude]] at which an orbiting body could actually be found if its [[inclination]] were zero. Together with the inclination and the [[ascending node]], the true longitude can tell us the precise direction from the central object at which the body would be located at a particular time. | |||
==Calculation== | |||
The true longitude <math>l\,</math> can be calculated as follows:<ref name=Moulton_1970> | |||
Multon, F. R. (1970). | |||
''An Introduction to Celestial Mechanics'', 2nd ed., | |||
p. 182–183. | |||
New York, NY: Dover. | |||
</ref> | |||
<ref name=Roy_1978> | |||
Roy, A. E. (1978). | |||
''Orbital Motion'', | |||
p. 174, (ISBN 0-470-99251-4). | |||
New York, NY: John Wiley & Sons. | |||
</ref> | |||
<ref name=Brouwer_Clemence_1961> | |||
Brouwer, D., & Clemence, G. M. (1961). | |||
''Methods of Celestial Mechanics'', | |||
p. 45. | |||
New York, NY: Academic Press. | |||
</ref> | |||
<math>l=\nu + \varpi\,</math> | |||
where: | |||
*<math>\nu\,</math> is orbit's [[true anomaly]], | |||
*<math>\varpi \equiv \omega + \Omega\,</math> is the [[longitude of the periapsis|longitude of orbit's periapsis]], | |||
*<math>\omega\,</math> is the [[argument of periapsis]], and | |||
*<math>\Omega\,</math> is the [[longitude of the ascending node|longitude of the orbit's ascending node]], | |||
==References== | |||
<references /> | |||
{{Orbits}} | |||
{{DEFAULTSORT:True Longitude}} | |||
[[Category:Orbits]] | |||
{{Astronomy-stub}} | |||
Latest revision as of 21:22, 12 December 2013
In celestial mechanics true longitude is the ecliptic longitude at which an orbiting body could actually be found if its inclination were zero. Together with the inclination and the ascending node, the true longitude can tell us the precise direction from the central object at which the body would be located at a particular time.
Calculation
The true longitude can be calculated as follows:[1] [2] [3]
where:
- is orbit's true anomaly,
- is the longitude of orbit's periapsis,
- is the argument of periapsis, and
- is the longitude of the orbit's ascending node,
References
- ↑ Multon, F. R. (1970). An Introduction to Celestial Mechanics, 2nd ed., p. 182–183. New York, NY: Dover.
- ↑ Roy, A. E. (1978). Orbital Motion, p. 174, (ISBN 0-470-99251-4). New York, NY: John Wiley & Sons.
- ↑ Brouwer, D., & Clemence, G. M. (1961). Methods of Celestial Mechanics, p. 45. New York, NY: Academic Press.
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