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I am interested in knowing if we can place a satellite beyond the geostationary orbit. I know that we can send objects beyond that, but can a normal satellite do all its functionalities in that case?

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Note that the moon, 385000km away, is way beyond geostationary orbit (42164km from the Earth's centre), but still "functions" as a natural satellite, orbiting the Earth regularly every 28 days or so.

There is nothing special about the geostationary orbit as any kind of limit on orbits, it is just convenient for certain applications of satellites that they would "hover" in a fixed location relative to the Earth's surface.

As the linked image from Tomi's comment shows, there are a number of artificial satellites which orbit outside the geostationary be radius.

One upper bound for a sustainable orbit around the Earth would be at the L1 Lagrange point of the Earth-Sun system, 1500000 km from the centre of the earth. At this point an object would technically be orbiting the Sun rather than the Earth, albeit with the Earth's gravitation influencing its path to keep synchronised with the Earth's own orbit.

The area of space around a body in which orbits are dominated by that body, is called the Hill sphere. It is connected with the Lagrange points, and as with the L1 point, the radius of the Earth's Hill sphere is around 1500000km.

(We could get into technicalities regarding whether an object orbiting beyond the moon is technically orbiting the Earth-Moon system rather than just the Earth itself, but this is outside the scope of this question; the point is, orbits much further than the geostationary are certainly possible).

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