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Nodal period

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[edit]

The oblate figure of the Earth has important effects of the orbits of near-Earth satellites.^[6] 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 the following:^[7]

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

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

See also[edit]

• Lunar nodal period

References[edit]