[vhffm]

If Earth was travelling a bit slower, it would just be on different orbit. Either more eccentric or just further away from the sun. This is encapsulated in Kepler's laws [1], which describe the motion of a single planet around a single star.

If you have other planets in the system (like our solar system does), things are more complicated. Orbital stability then depends on the arrangement of other planets. You are right in pointing out that the Earth's orbit is (possibly) unstable [2] over a timescale of billions of years.

[1] http://www.physicsclassroom.com/class/circles/Lesson-4/Keple...

[2] Unstable in the sense that Earth's orbit may become eccentric enough to smash into another planet, get ejected from the solar system, or dive into the sun.