Gravitational Pressure

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

Details and assumptions

  • Jupiter's mass is MJ=1.9×1027 kg M_{J}=1.9 \times 10^{27}~\mbox{kg}
  • Jupiter's radius is RJ=70,000 kmR_{J}=70,000~\mbox{km}
  • The gravitational constant is G=6.67×1011 N m2/kg2 G=6.67\times 10^{-11}~\mbox{N m}^{2}/\mbox{kg}^{2}

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