Outer Solar System

Jupiter

voyager path the grand tour — Voyager's Grand Tour

By Voyager_Path.jpg: created by NASAderivative work: Hazmat2 (talk) - Original from http://solarsystem.nasa.gov/multimedia/display.cfm?IM_ID=2143This file was derived fromVoyager Path.jpg:, Public Domain, https://commons.wikimedia.org/w/index.php?curid=18049439

jupiter-voyager-approach — Voyager 1 approaching Jupiter in 1979

Pressure & Density & size

Let's start with Hydrostatic equilibrium $$\begin{equation} \frac{dP}{dr} = -\frac{G M_r \rho}{r^2} \end{equation}$$ where $M_r$ is the mass contained within a radius $r$.

We can find the total mass within a radius $r$ by integrating the density times the volume of a single shell:

$$\begin{equation} M_r = 4 \pi \int_0^r \rho(r) r^2 dr \end{equation}$$ To a first approximation, let us take the average density which makes is a constant: $\rho(r) = \bar{\rho}$ Thus we can do the integral above and get $$\begin{equation} M_r = \frac{4 \pi}{3}\bar{\rho}r^3 \end{equation}$$ allowing us to rewrite hydrostatic equilibrium as: $$\begin{equation} dP = -\frac{4 \pi}{3}\bar{\rho}^2 G r dr \end{equation}$$

We can integrate both sides of this, going from the center out to $R$: $$\begin{equation} \int_{P_c}^0 dP = -\frac{4 \pi}{3 }\bar{\rho}^2 G \int_0^R r dr \end{equation}$$ and then obtain an expression for the pressure at the center $$\begin{equation} P_c = \frac{2 \pi}{3}\bar{\rho}^2 G R^2 \end{equation}$$

The center of Jupiter based on this comes out to be 11.2 times that of the earth's core, or 10⁷ atm

hydrogen-phase-diagram — The Phase Diagram of Hydrogen

Based on Figure 10.11 - Ryden & Peterson

Jupiter's Magnetosphere

jupiter-magnetic-field — Artistic Impression of Jupiter's Magnetic Field lines

NASA's Goddard Space Flight Center, Images courtesy of NASA/JPL/SwRI

jupiter-magnetic-field-extent — Jupiter's magnetic field extends up to nearly 2 million miles from the planet. Its influence likely reaches beyond the orbit of Saturn.

NASA's Goddard Space Flight Center Images courtesy of NASA/JPL/SwRI

Juno Mission

Juno spacecraft — By National Aeronautics and Space Administration (NASA) - Juno Mission to Jupiter (2010 Artist's Concept) at the official NASA website., Public Domain, https://commons.wikimedia.org/w/index.php?curid=41408653

juno-instruments — The instruments onboard Juno.

Credit: NASA/JPL

juno-vault — The cube in between the dish and the main hexagonal region is the Juno Radiation Vault.

Juno Gallery →

Jovian Satellites

First four discovered by Galileo in 1610

For a long time, there were only 4... Now we have found 69 79 80 95.

Amalthea

Dimensions: 250 × 146 × 128 km
Mean radius: 83.5±2.0 km

Not very big...

The pressure a the center of the moon will be given by: $$\begin{equation} P_c = \frac{2 \pi}{3}\bar{\rho}^2 G R^2 \end{equation}$$ Whatever the moon is made out of will have a compression strength, $S$. If the pressure is comparable to this value, then the object will begin to become spherical: $$\begin{equation} \frac{2 \pi}{3}\bar{\rho}^2 G R^2 \approx S \end{equation}$$ solving for $R_\textrm{sph}$ $$\begin{equation} R_\textrm{sph} = \left( \frac{3S}{2 \pi G} \right)^{1/2}\frac{1}{\bar{\rho}} \end{equation}$$