How do the size and mass of Jupiter's core compare to the size and mass of Earth?
We are not sure what Jupiter's core contains.
There have been a number of theories about the core of Jupiter. Some suggest a rocky core of heavier elements.
As Jupiter is mainly Hydrogen. There will be a layer of metallic liquid Hydrogen under high pressure at its centre. There are theories that this metallic Hydrogen would have dissolved any solid core.
There is gravitation evidence that Jupiter's core has a mass of between 12 and 45 times the mass of the Earth.
The Juno satellite which is currently orbiting Jupiter is going to take measurements which will determine the structure of Jupiter and reveal what the core actually contains.