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Interesting question!

I can come somewhat close because the inner core of Jupiter is about 20,000 km in diameter and the atmosphere is 87% hydrogen. Assuming a mass of core some what like earths, an equality will do here.

12,756 km/6 X 1024 kg = 20,000 km/X core mass Jupiter

12,756X = 1.2 X 1029

X = 9.4 X 1024 kg core Jupiter mass

============================================A rough estimate!!

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