Have a look at this website: http://ircamera.as.arizona.edu/NatSci102/NatSci102/lectures/spiralarms.htm
Formation of spiral arms is due, partly at least, to density waves and as such means they are transient phenomena over a galactic lifetime
You know T it is defined in your question...for the Earth T would be 24 hours so what is it for Venus? [Don't forget to change you units to seconds when doing the final calculation]