How Would a Halved Earth Mass Affect the Moon's Rotation Period?

[nmsurobert]

Someone texted me and asked me if the Earth was half as massive what impact would that have on the rotation period of the moon?

I'd think that the moon would rotate slower as it's gravity would more influence on the earth. But I am not sure if that makes sense or not haha

 

[Bystander]

https://www.google.com/?gws_rd=ssl#q="orbital+mechanics"

 

[Philosophaie]

\mu would be greater then the velocity would be greater at the present position therefore the Period would decrease but the moon would eventually correct for the change is speed and mass changing the whole orbit.