If an object revolves around the earth in a perfectly circular path, where the center of the circular path is different from that of the earth, (which means the object is close to earth's surface at one of its node - say by a distance X, and away from the earth on the diametrically opposite node, by a distance - say Y, where Y is substantially larger than X), will the path be called as elliptical path w.r.t. earth?
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$\begingroup$ Since you mention both center and surface, consider that the shape of the Earth may also be in play. $\endgroup$– uhohCommented Sep 4, 2021 at 6:02
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3$\begingroup$ Perfectly circular path around Earth, not centered around the gravity of Earth? It will require constant adjustment of the orbit, consuming a lot of fuel even if the offset is only a few hundred meters. Gravity and Orbits simply do not work that way. $\endgroup$– CuteKItty_pleaseStopBArkingCommented Sep 4, 2021 at 6:41
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1 Answer
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Yes, it would be considered an elliptical path, because every circle is an ellipse.
However, the situation you describe requires special circumstances to come about, and not all of your requirements can be fulfilled on an unpowered gravitational orbit around a spherically-symmetric Earth.
Option 1: Object has significant mass relative to Earth, orbits shared barycenter.
To have an unpowered circular orbit, around the Earth that is not centered on the Earth, in a two-body, Keplerian-Newtonian orbit, where both-bodies are circularly symmetric, and the Earth and the Object are the only objects that exist in the universe the object must have a non-negligible mass compared to the Earth, and be sufficiently distant from the Earth that their combined barycenter is separated from the Earth's center, allowing both bodies to orbit it.
In this depicted situation, the Object has a mass equivalent to one-third that of the Earth.
In this two-body situation, the circular orbits of Earth and the object must stay on opposite sides of the barycenter, and have the same orbital period, and the distance between the Earth and the object never changes.
Option 2: Object orbits the shared barycenter between the Earth and Satellite Object of significant mass at a distance.
A situation could be envisioned where the Earth and a significant, massive object orbit each other, and your object orbits them both at a significant distance, but in that situation, your third body's orbit is unlikely to stay perfectly circular or elliptical, and there will not be a consistent point on the orbit where the object remains close to Earth.
An example of such a situation exists in the Solar System with the smaller moons of Pluto; Nix, Hydra, Kerberos, and Styx orbit the barycenter dominated by Pluto and Charon.
Option 3: Second object of significant mass is in circular orbit over Earth, Object of negligible mass is precisely at a Lagrange point
If the object was precisely at one of the five LaGrange points between the Earth, and a second, massive satellite object in a precisely-circular orbit around the Earth, this would allow the object to remain in a 1:1 orbital resonance with the satellite, and in a circular orbit around the Earth-Satellite barycenter. In this hypothetical perfect situation, however, the mutual distances between Earth, the Satellite, and the Object will remain constant.
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1$\begingroup$ In options 1 and 3, the distance between the Earth and the object in question remains constant, so I don't think this satisfies the questioner's intent. $\endgroup$ Commented Sep 5, 2021 at 13:25