I'll analyze this step-by-step, considering both the force change and orbital stability implications.

## Change in Gravitational Force

In this universe, gravity follows an inverse cube law:
$$F = \frac{Gm_1m_2}{r^3}$$

When the planet moves from distance $r$ to distance $2r$:
- Original force: $F_1 = \frac{Gm_1m_2}{r^3}$
- New force: $F_2 = \frac{Gm_1m_2}{(2r)^3} = \frac{Gm_1m_2}{8r^3}$

Therefore: **The gravitational force would become 1/8 of its original value.**

## Orbital Stability Analysis

For a circular orbit to be stable, the gravitational force must equal the centripetal force:
$$\frac{Gm_1m_2}{r^3} = \frac{m_2v^2}{r}$$

This gives us the orbital velocity:
$$v = \sqrt{\frac{Gm_1}{r^2}}$$

Notice that with an inverse cube law, orbital velocity decreases with distance (∝ 1/r), unlike Kepler's laws where v ∝ 1/√r.

## The Planet's Fate

When suddenly pushed to twice the distance, the planet would likely:

1. **Have excess velocity**: The planet retains its original velocity momentarily, but the required circular orbital velocity at 2r would be only 1/4 of the original. This massive excess velocity means the planet has far too much kinetic energy for a bound orbit.

2. **Escape the system**: With such extreme excess velocity, the planet would almost certainly escape the star's gravitational influence entirely, following a hyperbolic trajectory into interstellar space.

3. **No stable orbits exist at arbitrary distances**: Inverse cube gravity creates a peculiar situation where circular orbits are *neutrally stable* at best. Small perturbations don't self-correct like they do with inverse square gravity. The system is extremely sensitive to initial conditions.

## Key Insight

Inverse cube gravity makes planetary systems fundamentally unstable. Unlike our universe where planets can migrate between orbits and remain bound, in this universe, any significant perturbation would likely destroy the orbital system entirely. This is one reason why inverse square gravity is so special—it's the unique power law that allows for stable, closed orbits (Bertrand's theorem).