This term "senators" is Roman. More accurate to classical Greece would be Boule (i.e. a council). Council members were appointed to carry out the daily operations of the state in conjunction with the magistrates. Thus, they were responsible for preparing measures and putting them into effect.
In Athens council members numbered five hundred and were elected by lot in such a manner that fifty served from each of the ten various tribes. To facilitate action each tribe served one tenth of a year as the Presiding Committee. Except for festivals, council members met daily, received compensation for their service, and served for one year. A second term in a nonsuccessive year was possible but no more after that (no career politicians here)! The council ordinarily met in public though it had the authority to go into closed session. Council senators conducted their official civic business in the Bouleuterion.
Map of Athens (207K)