Nodal period

Near-Earth satellites

The oblate figure of the Earth has important effects of the orbits of near-Earth satellites. An expression for the nodal period (Tn) of a near circular orbit, such that the eccentricity (ε) is almost but not equal to zero, is the following:

: T_n = \frac{2\pi a^\frac32} {\mu^\frac12} \left( 1 - \frac{3 J_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{3 J_2 \left(1 + \varepsilon\cos\omega\right)^3}{2\left(\frac{a}{R}\right)^2 \left(1-\varepsilon^2\right)^3} \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.

References

References

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