Nodal period explained

The nodal period (or draconic period) of a satellite is the time interval between successive passages of the satellite through either of its orbital nodes,^{[1] [2]} typically the ascending node. This type of orbital period applies to artificial satellites, like those that monitor weather on Earth, and natural satellites like the Moon.

It is distinct from the sidereal period, which measures the period with respect to reference stars seemingly fixed onto a spherical background, since the location of a satellite's nodes precess over time.^[3] For example, the nodal period of the Moon is 27.2122 days^[4] (one draconic month), while its sidereal period is 27.3217 days^[5] (one sidereal month).

Near-Earth satellites

The oblate figure of the Earth has important effects of the orbits of near-Earth satellites.^[6] An expression for the nodal period of a near circular orbit, such that the eccentricity is almost but not equal to zero, is the following:^[7]

T _{n} = (2 \pi a ^{(32)/()})/(\mu ^{(12)/()}) \left( 1 - (3 J _{2} \left( 4-5 \sin ^{2} i\right))/(4 \left( (a)/(\right) ^{2} \sqrt{ 1- \varepsilon ^{2} R)) \left( 1+ \varepsilon \cos\omega\right) ^{2}} - (3 J _{2} \left( 1+ \varepsilon\cos\omega\right) ^{3})/(2 \left( (a)/(\right) ^{2} \left( 1- \varepsilon ^{2\right)} ^{3} R)) \right)

where

a is the semi-major axis, \mu is the gravitational constant, J _{2} is a perturbation factor due to the oblateness of the earth, i is the inclination, R is the radius of the earth and \omega is the argument of the perigee.

See also

• Lunar nodal period

Notes and References

1. Web site: Glossary of Meteorology . American Meteorological Society.
2. Web site: Nerd . Dr. R. Steven . ASEN5050 Spaceflight Dynamics course slides . . 2013-02-18 . 2016-03-04 . https://web.archive.org/web/20160304070006/http://ccar.colorado.edu/asen5050/ASEN5050/Lectures_files/lecture18.pdf . dead .
3. Book: Satellite Orbits: Models, Methods, and Applications. Oliver Montenbruck, Eberhard Gill . 50. 2000. Springer Science & Business Media. 978-3-540-67280-7.
4. Book: Thompson, Richard . Vedic Cosmography and Astronomy . 2003 . Motilal UK Books of India . 978-8120819542 . 12.
5. Web site: Moon Fact Sheet . NASA . David R. . Williams . 3 July 2017 . 1 June 2018.
6. King-Here . D.G. . 1958 . The Effect of the Earth's Oblateness on the Orbit of a Near Satellite . Proceedings of the Royal Society of London A . 247 . 1248 . 49–72. 1958RSPSA.247...49K . 10.1098/rspa.1958.0169 . 122560890 .
7. Blitzed . L. . 1964 . Nodal period of an earth satellite . AIAA Journal . 2 . 8 . 1459 - 60 . 1964AIAAJ...2.1459B . 10.2514/3.2579 .