In the hypothetical universe where gravity follows an inverse cube law, the force of gravity between two objects is proportional to \( \frac{1}{r^3} \), where \( r \) is the distance between the objects.

Initially, let's consider the gravitational force at the original distance \( r \) to be \( F \). When the planet is pushed into an orbit that is twice as far away, the new distance is \( 2r \). According to the inverse cube law, the new gravitational force \( F' \) at the distance \( 2r \) would be:

\[ F' = \frac{F}{(2)^3} = \frac{F}{8}. \]

This indicates that the gravitational force at twice the distance is one-eighth of the original force.

Now, considering the planet's orbit, originally it was in a perfectly circular orbit, which means the gravitational centripetal force was balanced with the planet's inertial forces to maintain that orbit. If the planet is pushed into a new orbit at twice the distance, the reduced gravitational force alone may not be enough to sustain a circular orbit unless the planet's velocity is specifically adjusted.

In a typical gravitational scenario governed by the inverse square law, increasing the distance would usually result in the planet transitioning to a more elliptical orbit if not properly adjusted. In this universe governed by an inverse cube law:

1. **Velocity Adjustment Concerns:** If the planet's velocity remains unchanged when it is pushed to the new orbit, the reduced gravitational pull would likely make it unable to remain in a stable orbit at the new distance. The gravitational force is significantly reduced (to one-eighth), which might not provide the necessary centripetal acceleration required for a stable orbit at that speed.

2. **Likely Outcome:** Without the right velocity to match a stable orbit at the new distance, the planet may initially enter an elliptical orbit, potentially escaping the star's gravitational pull entirely if the velocity is not diminished appropriately. Alternatively, if the velocity were reduced to match the weakened gravitational pull (providing the appropriate centripetal force), a new stable orbit could theoretically be achieved.

In summary, the gravitational force is reduced by a factor of eight at twice the distance, leading to the necessity for a significant orbit and velocity adjustment. Without such adjustments, the planet would likely move to an elliptical orbit or escape, depending on its initial velocity upon relocation.