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Regarding the proposed duplicate: Thought the proposed duplicate has a similar titIe, I have read those answers and this question requires a different answer.

We know satellites orbit around Earth, Moon or, any other celestial body. Is the orbital motion of a satellite (relative to earth), translational or rotational, when initially they are not given any additional spin? Further, do satellites need to use their Reaction Wheels in order to maintain a proper orientation (for example, the same side (communication arrays, cameras, etc.) facing Earth, Moon, or any other celestial body), if they had proper orientation at the time of satellite separation from the rocket after launch and they were not given any additional spin (also please neglect additional torques due to atmospheric drag, solar pressure, etc.)?

If we consider a satellite without active station-keeping system and assume that it was not given any additional spin after satellite separation from the launch vehicle, and neglecting any other torques (atmospheric drag, solar pressure, collision with orbital debris, etc.), will their same side face the earth?

Simply my doubt is, Which of the following a satellite with no active orientation-maintaining system undergoes, under the constraint no other torques act on it, and initially, it was not given any additional spin?

Translational Motion:

enter image description here

OR

Rotational Motion:

enter image description here

Image source: My own work :) (Hope you like it)

Image Description: The yellow coloured thing is a satellite bus. Blue ones are solar arrays. Grey one is a communication array (Sorry for not drawing the receiver, it might look like a rocket nozzle!).

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    $\begingroup$ Possible duplicate of Does a satellite naturally turn in phase with its orbit, always facing Earth? $\endgroup$ – Oscar Smith Oct 19 at 5:37
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    $\begingroup$ Pure translation. $\endgroup$ – Oscar Smith Oct 19 at 6:40
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    $\begingroup$ not a duplicate (this question is not well-answered there) but I'd say it could use some clarification. "Inactive" is ambiguous, it could mean several different things, and "losing contact with the ground station" will in most cases have no effect at all on an Earth satellite's ADCS. If you want to ask about satellites that have lost control of their ability to orient themselves, then I'd recommend that you say that explicitly. Loss of ADCS can come from many different reasons, so it may unnecessarily complicate if you pre-specify. $\endgroup$ – uhoh Oct 19 at 7:02
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    $\begingroup$ Also it might be better to ask what typically happens rather than what might happens; questions shouldn't be overly hypothetical. Also, "translational OR rotational" probably over-constrains the answers. Some people view an orbit as a static configuration and may not think of how "translational" motion relates to "orbital" motion the same way you do. $\endgroup$ – uhoh Oct 19 at 7:04
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    $\begingroup$ "under the constraint no other torques act on it" your hypothetical satellite would have to be a sphere of uniform density to satisfy that requirement. No solar panels or other bits that stick out. $\endgroup$ – Hobbes Oct 19 at 9:00
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Taken purerly in ideal terms, a satellite that has no additional forces acting on it will keep doing whatever it was previously doing rotation wise, but that may in fact be a carefully set slow rotation that keeps an antenna or camera facing earth for comunications or earth science, or fixed if it was a telescope watching a distant star. So either of your examples could happened depending on mission/starting state.

In practice atmospheric drag, tidal effects, radiation pressure and YORP will all causes changes orientation.

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To expand on @gremlinWrangler's mention of

let's not forget

So near the end of life, as the altitude of the orbit drops, aerodynamic forces and torques will increase in strength. However I am not sure if they are ever strong enough to slow random tumbling down and produce a stable attitude with respect to the nadir (down, earth-facing, what you are calling "rotational" or not.

Hopefully some additional, more authoritative answers about what actually happens to dead satellites (do they tumble or do some, through either drag or gravity gradients (see How does gravity-gradient stabilization work? as well as Rotating in orbit? and also this one), passively reach some kind of stable attitude configuration.

To help make that happen I'll add a bounty if necessary and when the question hits 48 hours.

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    $\begingroup$ for extra fun when drag starts to build on something already rotating, many satellites have geometry that will be precessing the spin axis sciencealert.com/… so some objects will not be randomly tumbling but also not in a stable attitude. $\endgroup$ – GremlinWranger Oct 19 at 23:04

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