An artificial satellite fired it's rocket engine and produces a force exactly equal and opposite.. ?

Question

to that exerted by the Earth's gravitational field. the satellite would then start to move..

and the answer is.."along a tangent to the orbit"

can you please explain why? because i tought the forces are equal.and the object will only fly off tangentially when the force is larger then the centripetal force?

Answer 1

Here is a simplified version as requested.  I hope it helps.

Although a satellite in orbit looks like it is circling the Earth, it is actually moving in a straight line with gravity pulling it towards the Earth, while the shape of the Earth is such that the satellite never reaches the ground.

When the rocket engine is fired, as long as satellite achieves a speed that is known as ‘escape velocity’, it will overcome the pull of gravity and continue in a straight line which will be "along a tangent to the orbit".  Also, Newton's third law says that “every action has an equal and opposite reaction” so this means that the satellite will move forward in a straight line opposite to the thrust coming out of the rocket engine, which again will be "along a tangent to the orbit".

Answer 2

Worded another way, the only thing preventing straight line movement is the earth's gravitational field.  If you negate that with the rocket motor, a straight line is the only way the satellite can go........