Small Transport; Low Wing; 2 Turbojet Eng
ATC Issue All Types; Conflict Airborne Conflict; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter CFTT / CFIT
Flight Crew Requested ATC Assistance / Clarification; Flight Crew FLC Overrode Automation
Airspace Structure; Company Policy; Human Factors; Procedure
As we were cleared to line up and wait; we heard another aircraft instructed to continue for landing 10 miles out. We stayed in position on the runway for what seems longer than usual; possibly for separation from the aircraft that just departed. After takeoff on a heading of 343 at about 8;300 ft. we got a traffic alert immediately followed by a RA with a command to 'descend; descend'. We had reached approximately 8;700 ft. I cautiously began to follow the TCAS command bars on the PFD while slowing the aircraft and maintaining visual contact with the mountains. The red command bars disappeared and ATC issued a low altitude warning. At that point I saw an aircraft descending to the front left of our aircraft that appeared to be within 500 ft. of us horizontally. The TCAS issued another RA with another descend; descend warning. With what I believe to be the conflict aircraft insight; I chose to climb as we were getting close to the mountain in front of us and that seemed to be the safest alternative with a rapidly evolving situation. Once we were clear of the conflict and in the climb with Denver Center; we were given a number to call by the controller stating a possible pilot deviation. Once we landed and completed our post flight duties I called the facility to discuss what happened.Aspen is a very busy airport. While trying to get aircraft in and out on opposing runways; it seems that the tolerances between aircraft departing and arriving have gotten tighter. We sat on the runway for a while before being cleared for takeoff. At that point the conflicting aircraft was on a 10 mile final or so before we were cleared for takeoff. I don't know what the separation standard is supposed to be between arriving and departing aircraft; but I believe in this case the separation between us was too close.
Pilot departing a mountain airport reported a traffic conflict with opposing traffic and climbed even though TCAS told them to descend due to the nearby mountainous terrain.