What is the force that holds the solar system to a stable revolutions and rotations without crashing the planet's orbit to one another?

The Sun is 99.86% of the Solar system's total mass, the planet's gravity isn't that powerful to bring chaos to each other's orbit (at least for 100 million years).

The combination of

a - the force of gravity

which is balanced by

b - centripetal force

If there were no gravity, the moons and the planets would streak off in straight lines into outer space, the moons leaving their planets and the planets leaving the vicinity of the Sun (leaving the Solar System).

If there were no centripetal force

a - the moons of each planet would gravitate toward the planet (and vice-versa) and they would crash into each other

b - the planets and the Sun would gravitate toward the center of mass of the Solar System, and there they would likewise crash into each other.

There is no "force" preventing planets from colliding. They have all swept their own orbits clear of other objects in the distant past when collisions were common compared to today.

Gravity holds the objects in orbit.

Momentum keeps them moving.

Gravity.

Simple one word Answer: GRAVITY

G r a v i t y (haven't you heard of it like all others here ?)

It's this weird magical phenomenon we call G-R-A-V-I-T-Y.