# Nodal period

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The nodal period of a satellite is the time between successive passages of a satellite through successive orbital nodes.[1][2] This applies to artificial, such as weather satellites, and natural satellites the moon. The nodal period of Earth's moon is 27.2122 days.[3]

## Near Earth-Satellites

The oblateness of the Earth has important effects of the orbits of near Earth-satellites.[4] An expression for the nodal period (${\displaystyle T_{n}}$) of a near circular orbit, such that the eccentricity (ε) is almost but not equal to zero, is:

${\displaystyle T_{n}={\frac {2\pi a^{\frac {3}{2}}}{\mu ^{\frac {1}{2}}}}\left[1-{\frac {3J_{2}(4-5\sin ^{2}i)}{4({\frac {a}{R}})^{2}{\sqrt {(1-\epsilon ^{2}}}(1+\epsilon \cos \omega )^{2}}}-{\frac {3J_{2}(1-\epsilon \cos \omega )^{3}}{2({\frac {a}{R}})^{2}(1-\epsilon ^{2})^{3}}}\right]}$ [5]

## References

1. ^ "Glossary of Meteorology". American Meteorological Society.
2. ^ Nerem, Dr. R. Steven. "ASEN5050 Spaceflight Dynamics course slides" (PDF). University of Colorado.
3. ^ Thompson, Richard (2003). Vedic Cosmography and Astronomy. Motilal UK Books of India. p. 12. ISBN 978-8120819542.
4. ^ King-Hele, D.G. (1958). "The Effect of the Earth's Oblateness on the Orbit of a Near Satellite". Proceedings of the Royal Society of London. Series A, Mathematical and Physical. 247 (1248). pp. 49–72.
5. ^ Blitzer, L. (1964). "Nodal period of an earth satellite". AIAA Journal. 2 (8). pp. 1459–60.