# Gravitational Pressure

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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