Nodal period

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 ($T_{n}$) 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.