Geocentric Rankine Vortex – Orbital Decay

In the earlier Geocentric Rankine Vortex posting the trajectory of an object released from 129,530 kilometres above the Earth surface was examined:

The implication of a theoretical [unrestrained] Geocentric Rankine Vortex is that the vortex has a distinct “boundary” at about 130,000 kilometres [above Earth’s surface] above which the Earth’s “gravitational” force becomes [primarily] a circular vector with only a very slight gradient that slowly spirals inwards towards Earth.

Geocentric Rankine Vortex - Outer Ring

https://malagabay.wordpress.com/2013/01/15/geocentric-rankine-vortex/

The overall shape of the Rankine Vortex trajectory has three major elements;

1) An outer spiral where the Gravity vector is primarily circular.
The inverse square law means that the spiral becomes tighter as distance increases.

2) A middle stage descent where the Gravity vector slowly curls towards Earth.

3) A final short [and almost vertical] plunge towards Earth.

Overall, the outlined Rankine Vortex trajectory varies very significantly from the standard model which envisages Gravity as a straight line force.

However, there is evidence to support the Rankine Vortex trajectory in a document published by the Australian Government Bureau of Meteorology: Satellite Orbital Decay Calculations.

http://www.ips.gov.au/Category/Educational/Space%20Weather/Space%20Weather%20Effects/SatelliteOrbitalDecayCalculations.pdf

The initial Summary attributes low earth orbit decay [below an altitude of 500 kilometres] to “the few air molecules” and “space weather”.

The decay of a satellite from low earth orbit is of interest to many people.
The drag force that such a satellite experiences is due to its interaction with the few air molecules that are present at these altitudes. The density of the atmosphere at LEO heights is controlled by solar X-ray flux and particle precipitation from the magnetosphere and so varies with the current space weather conditions.

This view is further reinforced in the Introduction:

Low Earth orbiting satellites experience orbital decay and have physical lifetimes determined almost entirely by their interaction with the atmosphere.

Therefore, the document precedes to details an “Atmospheric Model” that is used to calculate atmospheric density [which causes drag and results in orbital decay].

The constants [in their model] were “empirically derived” but surprisingly the “intermediate variables” generally “do not correspond to true atmospheric values”.

All constants were empirically derived to give an appropriate fit to the standard models.
It should be noted that the only really valid output of this model is the density.
The intermediate variables used in deriving this density in general do not correspond to true atmospheric values at any height within the considered range.
The temperature may be regarded as the mean asymptotic value for the exosphere at large altitudes.
The molecular mass might be regarded as an integrated mean value from the base of the thermosphere up to the specified height.

From my perspective this is a polite way of saying: it works but we don’t know why!

However, looking at their diagrams it is clear that “orbital decay” simply reflects the gravitational [centripetal] trajectory of a Geocentric Rankine Vortex.

Figure 1 clearly illustrates the outer spiral [which becomes tighter with distance] where the Gravity vector is primarily circular.

Orbital_Decay_Spiral

Figure 2 clearly illustrates the middle stage descent before the final [almost vertical] plunge towards Earth.

Orbital_Decay

In conclusion it appears that the orbital decay trajectory could be caused by a “few air molecules” or by the centripetal trajectory generated by a Rankine Vortex.

However, because the atmospheric drag variables “do not correspond to true atmospheric values” it appears more likely that a Rankine Vortex is actually responsible for orbital decay.

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