Why is aleinu said twice: once at the end of Maariv, and then again at the end of Kiddush Levanah?
First Because we say:
שֶׁהֵם מִשְׁתַּחֲוִים לְהֶבֶל וָרִיק וּמִתְפַּלְּלִים אֶל אֵל לֹא יושיע
- That is we are illustrating the Idol worshipers pray to heavenly bodies but we do not. (Likutie Maharich,Chelek Beis,Daf Kuf)
- Aleinu, was written by Yeshouah Ben Nun he was compared to moon. That is the Gemara in Baba Basra 75a says:
The face of Moshe was Like the sun,Yeshouah was like the Moon.
Therfore the comparison compels us to say Aleinu at Kiddush Levanah.