Mystery Orbit

Man-made orbits are generally circular, best exemplified by the equatorial geostationary orbit (GEO), with its hundreds of satellites, some with 'transponders' delivering, say, television broadcasts to rooftop 'dishes' relayed from satellite trucks at news and sporting events.

The puzzle describes the invention of the most radically eccentric geosynchronous orbit eGEO.  No necessity has been identified for mothering the invention, making it a Mystery Orbit.  The question, is...

What would be an application for a satellite in an eGEO?

Figure 1 -- Man-Made Earth Satellites + Mystery Orbit (eGEO)

The graph in Figure 1 summarizes the numerical information in Table 1 -- Parameters for Man-Made Earth Satellite Orbits. Superimposed is eGEO, the Geosynchronous Satellite orbit discovered in the Mystery Orbit puzzle.  For proposing new satellites in an eGEO, ten existing applications were provided for solvers to take into consideration...

{1} Astronomical Observations are conducted by Hubble in near-circular orbit above the atmosphere.
are supported by hundreds of circular geostationary earth orbits.

{3} Communication Services use constellations of satellites in polar orbits.
{4} Debris Remediation in the future will require specialized satellites in various circular orbits.
{5} Intelligence Gathering must operate at low orbital elevations for close-up imaging.
{6} Mapping Services are operated from elevations by governments and businesses worldwide.
{7} Meteorological Imaging satellites operate in either asynchronous or geostationary earth orbits.
{8} Navigation Services use upwards of a hundred satellites in three constellations.
{9} Scientific Experiments are conducted in a wide range of satellites at various orbital elevations.
{10} Space Station, most prominently the ISS, is deployed in a near-circular low-earth orbits.

At first glance we see in Figure 1 a devastating reality: Twice every day, a satellite in an eGEO orbit slices across nearly all earth orbits, threatening to collide with hundreds of satellites.  Clearly, all the applications in the list must be dismissed out of hand, which is hardly encouraging news for our eGEO satellite.  If ever an exclamation point might be warranted, it is for the solution to the Mystery Orbit puzzle...

 There seems to be no application for a satellite in an eGEO!

Meanwhile, space scientists have concluded that there are over 500,000 debris fragments in earth orbits in sizes ranging from one-centimeter fragment to discarded orbital launch stages and derelict satellites!
In the list above, application {4} Debris Remediation reminds us of an immense need -- dare we say the mother of all necessities for invention
Solvers are invited to view alarming worldwide realities and formidable challenges as described by NASA's: Orbital Debris Program Office.

 In looking for a solution to the Mystery Orbit, your puzzler became acutely aware of the immense necessity to be addressed in {4} Debris Remediation, which did indeed play the r ôle of Mother-of-Invention: see Trampoline Deorbiting System.

Moreover, our analytic efforts in studying eccentric orbits may become quite relevant.
ESA’s double-satellite Proba-3 mission will be flying where no previous member of the Proba minisatellite family has gone before – up to 60 Mm away, a seventh of the way to the Moon
.

Figure 2. European Space Agency PROBA-3
In 2019, the two satellites will be launched together into a highly eccentric orbit with a period of 19.7 hours, which will allow continuous contact with the two satellites using a single ground station.  Near apogee, the satellites spend six hours making solar observations in close formation.
Paired satellites will maneuver relative to each other with millimeter precision, intended to serve as the equivalent of a giant structure in space and thereby open up a whole new way of conducting space missions.  An occulter satellite will blot out the Sun’s fiery disc as viewed by a coronagraph satellite, revealing mysterious regions of the sun’s ghostly ‘corona’.

 Table 1--  Parameters for Man-Made Earth Satellite Orbits Elevation MSL Radial Distance Period Velocity Quantity Notes Zone Range km mi km mi hr km/h mph HE0 High Earth Orbit $\bigwedge$ 384,000 238,540 390,378 242,502 {1} GEO & GSO | 35,786 22,230 42,164 26,192 24.000 11,038 6,900 300+ {2} High Earth Orbit $\bigvee$ 35,786 22,230 42,164 26,192 MEO Medium Orbit ⋀ 35,786 22,230 42,164 26,192 Galileo | 23,222 14,425 29,600 18,387 14.000 13,284 8,300 30 GPS | 20,180 12,536 26,558 16,498 12.000 13,906 8,690 31 GLONASS | 19,130 11,884 25,508 15,846 11.000 14,570 9,100 29 Medium Orbit ⋁ 2,000 1,242 8,378 5,204 LEO Low Earth Orbit ⋀ 2,000 1,242 8,378 5,204 Polar Orbiting | 700 435 7,078 4,397 {3} | 435 270 6,813 4,232 Iridium & SSO | 620 385 6,998 4,347 1.670 26,329 16,455 72 Hubble | 595 370 6,973 4,332 1.593 27,503 17,190 1 ISS | 412 256 6,790 4,218 1.545 27,602 17,251 1 Deorbit  < 1year | 250 155 6,628 4,117 ~1.445 ~28,820 ~18,000 {4} Low Earth Orbit ⋁ 0 0 6,378 3,962 HEO, Molniya - Apogee 38,552 24,100 44,930 12.000 3 {5} MEO, - Perigee 1,626 1,020 8,004 & Tundra - Apogee 38,552 24,100 44,930 12.000 3 {5} LEO - Perigee 1,626 1,020 8,004