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The study of gases that are not in motion is called aerostatics.
Aerodynamics comes from Aero (Air), and Dynamics (Moving).
For aircraft, lift (force) is the force pushing up. Gravity is the force pushing down. If lift is stronger than gravity the plane goes up. If gravity is stronger than lift, the plane goes down. In planes, lift is caused by airflow. Airplane wings are designed in such a way that, the air molecules prefer moving under the wing rather than above it, so as a result there is more air flowing underneath the wing compared to above it. This motion of the air gives upward lift to the aircraft. See Bernoulli's principle.
Thrust and drag govern forward motion. Thrust is the force pushing forward, and drag is the force pushing backward. Thrust is usually made by either propellers or jets. Drag is the force pushing backward. Most drag is caused by air friction.