Does Jupiter's high rotation speed affect its gravitational strength at the surface?

Question

Jupiter's outer, equatorial atmosphere rotates at 12,517.12 meters/second, once every 9.5 hours, at a radius of 71,492 km. Geostationary orbital speeds for earth are around 3,000 meters/second, at a radius of 42,164 km. From what I understand, the gravitational acceleration in the upper atmosphere of Jupiter is around 2.4g.

Would a stationary probe (relative to the atmosphere) that maintained its altitude with something like a hot hydrogen air balloon or vacuum-filled sphere experience noticeably less gravity than 2.4g from the extremely fast rotation of Jupiter at the equator? Or to ask in another way, is there noticeably less gravity at the equator than the poles, due to the high rotation rate of the gas giant?

Answer 1

The felt centripetal acceleration is about 0.22gs, quite high compared to the gravity of the planet, 2.53gs at the equator.

Net acceleration is calculated by

$$\frac{m}{r^2}-w^2r$$

or, using velocity instead of angular velocity, $$\frac{m}{r^2}-\frac{v^2}{r}$$

The only thing lighter than hydrogen is hot hydrogen (except for vacuum, which is difficult to confine with a lightweight structure), so it is the only possibility to make an airship. For the buoyancy, that is just an issue about sinking low enough in the atmosphere to get a good density gradient between the hot hydrogen and the surrounding gas.

A possible durable heat source may be an RHU.