Vedic Rta... one last time

Ooops, thought I was done with looking into various IE linguistics
but....

I know that the Snaskrit Rta, Sanskrit Ritu, and Avestan Asha all
ultimately derive from the PIE root *Ar- "to fit together" but what I
am unsure about are the intermediate stages between *Ar- and the
finished terms.

Could anyone clarify whether the terms Rta/Ritu/Asha stem from the
suffixed form *ar-ti- from which we get artisan and the Greek
artios 'fitting'?
Or do they stem from the variant form *re- (which gives rate, ratio,
rede) or possibly the variant form *rei (from which come rite and
arithmos)??

Sincerely,
Aydan