Couple of questions.

Why does the earth keep moving?

The engine of a rocket applies a continual force to push the rocket along. When the engine stops what will happen?

I think the rocket will stop acceleration

You need to be aware of the concept of inertia. Inertia is the tendency of a body to stay at rest or in linear motion, unless influenced by some other force.

If it was not for the gravity pull of the sun, the earth would fly off into space.

If the rocket is in the atmosphere or within the gravity pull of the earth, either the friction of the atmosphere or the pull of the earth's gravity will cause it to change course. These are some "other forces."

Acceleration is an increase in speed, which will stop once the engine stops. However, if there are no other forces acting on it, it will continue to travel at the same speed in a straight line.

I hope this helps. Thanks for asking.

The Earth keeps moving because of its inertia and the gravitational force acting on it. Inertia is the tendency of an object to continue moving in a straight line at a constant speed unless acted upon by an external force. The Earth's initial motion was set in motion billions of years ago when it accreted from the rotating disk of gas and dust around the young Sun. Since then, it has been continuously moving in its orbit around the Sun due to its inertia.

The engine of a rocket applies a force that propels it forward. When the engine stops, there is no longer an external force acting on the rocket, so it will cease to accelerate. However, according to Newton's first law of motion, the rocket will continue to move at a constant speed in a straight line due to its inertia, unless acted upon by another force.

In space, where there is no atmosphere or significant gravitational forces, the rocket will indeed continue to move at a constant speed in a straight line. However, if the rocket is within the atmosphere or influenced by gravitational forces (such as Earth's gravity), other forces will come into play. The atmosphere can cause air resistance or drag, which can slow down the rocket and eventually bring it to a stop. Similarly, gravitational forces can alter the rocket's trajectory and cause it to change course.

It's important to understand the concept of inertia and the role it plays in motion. In the absence of external forces, objects will maintain their state of motion, whether that's staying at rest or continuing in motion at a constant speed in a straight line.