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Why a rocket in space need to use its engine keep moving?

A spacecraft does not need to use its engine continuously to keep moving. By Newton's First Law, Inertia, an object at rest will stay at rest and a body in motion will remain in uniform motion, if there is no net external force acting on the object. Spacecraft in orbit around Earth (like satellites and Space Stations) continue to move and do not need to "fire their engines" to maintain the orbit. The orbital motion of such objects is due to the balance of gravitational forces between the spacecraft and the central planet.

As long as the spacecraft is in a vacuum environment, like free space, once the required speed and direction is achieved, it will continue moving by inertia without firing its engine until an external force is applied to change its motion, like coming near a celestial body and interacting gravitationally.

However, in most practical scenarios spacecraft does need to use their engines to make changes to their trajectory or to navigate through space. Here are a few reasons:

- Gravity and drag: Even though the vacuum of space is nearly frictionless, there are still some external forces that can affect a spacecraft's motion. Gravity from other celestial bodies, such as the planets and moons, can pull on a spacecraft and alter its course. Additionally, there is a small amount of drag caused by the interstellar medium, which can gradually slow down a spacecraft over time. To counteract these external forces, spacecraft may use their engines to make occasional course corrections or to maintain their desired speed.

- Maneuvers: Spacecraft often need to change their position, orientation, or velocity to achieve their mission objectives. This could involve moving from one orbit to another, changing the inclination of their orbit, or rendezvousing with another spacecraft. To perform these maneuvers, spacecraft use their engines to apply thrust in specific directions.

- Deorbiting: When a spacecraft's mission is complete, it may need to deorbit and return to Earth or another celestial body. This process involves using the spacecraft's engines to slow down and enter a trajectory that will bring it back to the desired destination.

In summary, while spacecraft can coast through space without continuously firing their engines, they do need to use them strategically to overcome the effects of external forces, perform maneuvers, and change their trajectories as needed.