The governing body of any county shall have power to make and enforce such resolutions, rules, and regulations as shall lawfully be made for the control and supervision of any airport, landing field, or airdrome acquired, established, or operated by it, and for the control of aircraft and airmen, but such resolutions, rules, and regulations shall not conflict with the rules and regulations for the navigation of aircraft promulgated by the United States Government. This power shall extend to the space above the lands and waters included within the limits of such county, and to the space above any airport, landing field, or airdrome outside its limits.