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How about a probe or ship that was orbiting around the planet and made a soft entry in the atmosphere (in a similar way space shuttles do re-entry) and then it went flying spirals around the planet upper atmosphere, going deeper and deeper with each pass...
How long would the ship survive as it enters more dense layers of gas?
Could it go deep enough into the gas planet (even if it can’t reach too close to the core) as to collect data about the composition of the gas and other environmental conditions?
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Think of a submarine. As you go down into the Jovian atmosphere pressure gets higher and higher, until you finally get crunched. You wouldn´t go very far down deep. An object solid enough to withstand the pressures of the Jovian atmosphere to significant depths would probably be too massive to be sent there from Earth.
Writers as Arthur Clarke have proposed balloon-like vehicles to get samples from the top layers of the Jovian atmosphere.