Trajectory of a projectile
In physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

, the ballistic trajectory of a projectile is the path that a thrown or launched projectile
A projectile is any object projected into space by the exertion of a force. Although a thrown baseball is technically a projectile too, the term more commonly refers to a weapon....

 will take under the action of gravity, neglecting all other forces, such as friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and/or material elements sliding against each other. There are several types of friction:...

 from air resistance, without propulsion
Vehicle propulsion
Vehicle propulsion refers to the act of moving an artificial carrier of people or goods over any distance. The power plant used to drive the vehicles can vary widely. Originally, humans or animals would have provided the propulsion system, later being supplemented by wind power...


The United States Department of Defense
United States Department of Defense
The United States Department of Defense is the U.S...

 and NATO define a ballistic
Ballistics is the science of mechanics that deals with the flight, behavior, and effects of projectiles, especially bullets, gravity bombs, rockets, or the like; the science or art of designing and accelerating projectiles so as to achieve a desired performance.A ballistic body is a body which is...

A trajectory is the path that a moving object follows through space as a function of time. The object might be a projectile or a satellite, for example. It thus includes the meaning of orbit—the path of a planet, an asteroid or a comet as it travels around a central mass...

 as a trajectory traced after the propulsive force is terminated and the body is acted upon only by gravity and aerodynamic drag.

The following applies for ranges which are small compared to the size of the Earth.