reactionless thrust

[raaaid]

im in the top of a tower and two cannons are shot underneath me, one to the left and one to te right, im united to the cannonballs by a cable and i give away cable or take it with a spool lests look at the drawing:

the cannonball i shot in trajectory 3, a straight one, i give away as much cable as needed so the tension of the cable is 0

the tension in trajectory 1 the circular one the tension is constant of 10000 N so the tension is the same the one that pulls up that the one that pulls down

but in the trajectory 2 the one that is first an otwards spiral and then and inwards one the tension that pulls down is of 1 N while the one that pulls up is of 10000 N

i would be virtually shot up in trajectory one with almost no reaction

[raaaid]

besides conservation of energy predicts that once the cannonbal is spinning in this spiral shape it will last forever with no friction

so i just would have to keep this spiral trajectory to go as high as wanted by only having used the initial energy of the cannons

i could maybe then use this upwards thust to feed a motor that made the cannonball spin faster what would increase the upwards thrust which would increase again the spin