A Gasgiant need at the begin a rocky core to gain all the hydrogen and helium in his orbit around his star, so a star, so our sun had a hearth of stone too.
Oh, and a gasgiant is dangerous for space ships at his orbit.
From the wiki about the Juno Probe for 2016:
https://en.wikipedia.org/wiki/Juno_(spacecraft)
Juno's planned polar orbit is highly ellipitical and takes it close to the poles—within 4,300 kilometers (2,672 mi)—but then far beyond even
Callisto's orbit.
[28] Each orbit takes 14 days and the spacecraft is expected to complete 37 orbits until the end of the mission.
This type of orbit helps the spacecraft avoid any long-term contact with Jupiter's radiation belts, which can cause damage to spacecraft electronics and solar panels.
[28][29] The "Juno Radiation Vault", with 1-centimeter-thick
titanium walls, will also aid in protecting and shielding Juno's electronics.
[30] However, the radiation is so destructive that the instruments JunoCam and Jovian Infrared Auroral Mapper (JIRAM) are expected to last only through the eighth orbit. The microwave radiometer is planned to last 11 orbits.
[31] In comparison, Juno will receive much lower levels of radiation than the
Galileo orbiter at its equatorial orbit.