To be a burlesque / pole dancer or whatever , one needs to be supple.I can't see any suppleness in jade.Meanwhile weren't the ancient Greeks and Romans to which the Europeans have named their space craft and constellations in their memory, Pagans?
In that case I think the Chinese have got it right and picked a symbol which also appears in pagan culture as I'm pretty sure the rabbit/ hare is their fertility symbol.
No, rabbits have nothing to do with fertility. The whole jade rabbit thing came from an ancient Chinese legend. In the legend, we used to have ten suns in the sky. Nothing can survive in the scorching heat. So an amazing archer, Ho Yi, shot down nine suns and left only one in the sky. To reward him, the gods gave the archer some kind of magic pill that would allow him to become god and live in the heaven. He decided to postpone this because he loved his wife and wanted to spend more time with her. His wife, Chang E, who had a lovely little rabbit with her at all times because she loved rabbits, was a lot more eager to become a god. So one day, she decided to try the pill and see what happens. After eating the pill, she began to rise into the sky while holding her,lovely little rabbit in her arms. At that point, she couldn't do anything to stop it even though she regretted t already. So she went to the heaven without her husband. To punish her for her selfishness, the gods sent her to live on the moon in a cold palace. Yes,, the name of the palace is called "the palace of wide and cold" (please forgive me for the poor translation). The only companion is her lovely rabbit. So the most commonly seen image of her is a sad and beautiful lady holding a jade rabbit standing on the moon.
That is why the Chinese moon satellite is named Chang E. All from the Chinese legend. The only god associated with the moon in Chinese legends would be Chang E and her jade rabbit. Nothing erotic about it at all.