Prograde orbits

Originally it was thought that SP comets were Oort cloud comets that had been captured into short-period orbits following a close encounter with Jupiter. This process can occur and even explain why SP comets usually have prograde orbits with relatively low inchnations. However, Fernandez (1980) pointed out that this source could not produce the number of SP comets that are observed, and suggested that the SP comets were derived from a disk-hke distribution of bodies beyond Neptune. It was shown by numerical simulations that this trans-Neptunian distribution of comets could quantitatively supply the SP flux and explain their inclinations (Duncan et ok, 1988). 

Substituting dt/dr from here, do/dt = fi as given for prograde orbits by Eq. (31), and the metric elements (23-27), we get after some labor... 

Geostationary satellites are positioned in a circular orbit in the Earth s equator plan. More technically, a geostationary orbit is a circular prograde orbit in the equatorial plane with an orbital period equal to 24 h (Figure 14.1). Positioning the satellite at an... 

Figure 1. The ISCO. The solid (broken) curve gives the radius of the ISCO of a Kerr BH as function of a = ca/GM for prograde (retrograde) orbits, while the dotted line is the radius of the horizon. All radii are expressed in units of GMc 2.

Figure 2. The azimuthal frequency. The azimuthal frequency va in kHz multiplied by M/Mq for prograde circular orbits outside ISCO in the equatorial plane of a Schwarzschild BH (dashed) and extreme (a = 1) Kerr BH (solid curve) as function of rc 2/GM.

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