# 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 \( G=6.67\times 10^{-11}~\mbox{N m}^{2}/\mbox{kg}^{2}\)