The goals of this class are
- to show that building models of gas giant planets is not so hard
- to show the basic observable constraints of such models
- to show what the giant planet interiors really are like - when you build up a more complex model using all pieces of information and fold in all the physics.
Starting with the SIMPLEST possible model for a gas planet..... (also given on P194 of Hartmann)
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This means that the pressure at the center of a gas giant Po can simply be calculated from the bulk density and radius - both easily measured.
What happens when we calculate the central pressures of JSUN? Plugging in G, rho and R we get...
| R (km) | density (kg/m3) | Po - model | Po ("real") | |
| EARTH | 6400 | 5520 | 1.7 Mbar | 3.7 Mbar |
| JUPITER | 71400 | 1326 | 12 Mbar | 40-70 Mbar |
105 N m-2 = 1 bar ~average pressure of the atmosphere on the Earth
So - the simplest possible model is not so bad! In reality, the pressures are greater because the density is not constant throughout the planet and material is denser towards the center of the planet, increasing the central pressure.
What does a "megabar" of pressure feel like? The central pressure inside Jupiter is about the pressure under the foot of 100 elephants standing on top of each other with the bottom elephant standing on one foot in a high-heel shoe! Alot - but not enough to trigger nuclear fusion.
Needless to say, we do not have lab experience of hydrogen at 40 Mbars pressure and 30,000K - so we have to guess about the behavior of materials - e.g. hydrogen - at these conditions.
BUT - we can make a first guess at the compressibility of hydrogen - how does density vary as the pressure is increase?
A plot of sin
x / x function.
THIS IS REMARKABLE!!
We can say that to first approximation, ALL objects made out of hydrogen have
a mass between 0.001 and 0.1 Msun.
Gas giant planets that are not big enough for nuclear fusion are ALL THE SAME
SIZE - ~80,000 km
Physically, this means that if you keep adding hydrogen, the radius does not
get bigger - the central density just increases. (The central density is "rho
zero" in the equation above). Think of pillows......
In reality? Jupiter and Saturn do not have radii of 79,700 km
