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Moving is a relative fact: an object moving in a reference system (for example a train as observed from the station by a still observer) can be still in another reference system (for example the same train as seen by a car moving with the same velocity).

What is relevant is to accelerate (for example to start a movement in a reference where the object was still or to stop it). To accelerate a force is needed.

In empty space accelerating is essentially possible due to the so called momentum conservation law.

It states that the product of mass by velocity of an insulated system (no relation with other systems) cannot change in absence of forces.

Let us consider a car on a road: the force rotating the wheels comes from the car: it cannot directly change the car velocity. However, the contact between the wheels and the road causes a reaction from the road due to attrition. This is an external force: the car is not an insulated system and it can accelerate or stop.

In empty space this kind of propulsion is not possible.

Let us consider a rocket. Due to the action of the engine it trows out a mass (for example m1) in unit time from the jet at a speed v1.

The system before expulsion has a momentum (m+m1) v, where m is the rocket mass after the expulsion and v the rocket speed before the expulsion.

It has to be equal after the expulsion, thus, calling v2 the speed after the expulsion and considering that the mass m1 have a speed -v1 (opposite to the rocket direction) it is

(m+m1) v = m v2 -m1 v1

thus the velocity after the expulsion is v2=( (m+m1) v+m1 v1)/m > v. An acceleration has been obtained and the rocket increases its velocity :-))

The expulsion can be due to different causes, it depends on the used engine. Generally it is caused by a liquid fuel used in a turbine.

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