Gravitational Pressure

Classical Mechanics Level 5

Determine the pressure in Pascals caused by gravitational compression at the center of Jupiter. Hint: Compute the pressure \(p(r)\) as a function of the distance \(r\) to the center of the planet and evaluate it at \(r=0\). You may assume that Jupiter's density is constant.

Details and assumptions

  • Jupiter's mass is \( M_{J}=1.9 \times 10^{27}~\mbox{kg}\)
  • Jupiter's radius is \(R_{J}=70,000~\mbox{km}\)
  • The gravitational constant is \( G=6.67\times 10^{-11}~\mbox{N m}^{2}/\mbox{kg}^{2}\)

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