The planet would no longer
be bound in a gravitational orbit and would just travel freely through
space.

We would still be influenced by the gravitational forces of other planets in
the Solar System.

I wonder if Jupiter's gravity would be sufficient to keep all the planets
together. Maybe the Planet Earth will eventually enter into an orbit around
Jupiter.

It may not be all doom and gloom. For instance, Jupiter's moon, Io, is very
very hot indeed. Its heat does not originate from the sun but from the
friction caused by constant squishing and squashing (tidal effects) by being
in orbit around Jupiter.

Brendan