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I am just wondering whether any man-made satellites are currently orbiting our Moon. If there is one, would I be able to see it using my telescope?

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The Lunar Reconnaissance Orbiter is still up there. At a compact 2000kg, it's likely too small to see via earth based telescope. Mission Page

I think the Chinese orbiter is back on earth now, but there may be others.

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    $\begingroup$ At a compact 2000kg, it's likely too small to see via earth based telescope. That's an understatement. The Hubble wouldn't be able to see it, let alone a backyard telescope. See hubblesite.org/reference_desk/faq/… . $\endgroup$ – David Hammen Feb 25 '15 at 22:18
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    $\begingroup$ @David Hammen your link only deals with he ability of Hubble to resolve small objects, which is relevant for artefacts on the Lunar surface, but a satellite orbiting the Moon will at least at times be a bright spot against a dark background (albietly close to a bright object) sperated from the lunar surface by many times the resolution limit of Hubble. $\endgroup$ – Conrad Turner Feb 26 '15 at 7:50
  • $\begingroup$ The upper stage of Chang'e 5T is still maneuvering in cis-lunar space, but has left Lunar orbit. $\endgroup$ – LocalFluff Feb 26 '15 at 11:17
  • $\begingroup$ Hubble on XKCD What if? $\endgroup$ – Mithoron Feb 26 '15 at 11:39
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Except for LRO, an upper stage of a payload destined to lunar orbit, might stay in lunar orbit for a while, and be much larger than the payload itself. But according to this answer it would be short lived without station keeping.

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