Computing Jupiter's Thermal Time Scale

[jkrivda]

1. Jupiter radiates more energy than it receives from the Sun by 8.7x10^-10L₀. Jupiter's radius is 7.0x10⁹cm and its mass is 1.9x10³⁰g. Compute its thermal time scale. Could gravitational collapse power this luminosity for Jupiter's entire lifetime of 4.5 Gyr?



2. Kelvin-Helmholtz (aka thermal) timescale equation is given by: t=ΔE_g/L . ΔE_g=GM²/R ... so, t=GM²/RL



3. Not sure what to sub in for "L" in the timescale equation. I'm guessing I have to use the 8.7x10^-10 to figure that out. Any tips in the right direction would be greatly appreciated!

 

[bossman27]

L for the timescale equation is just the luminosity of Jupiter. 8.7x10^-10L_o is referring to the intrinsic luminosity of Jupiter as a fraction of the solar luminosity. Astronomical units that have that subscript that looks like a dot with a circle around it are solar units.

 

[jkrivda]

so i just convert the solar luminosity fraction to erg/s and then plug and chug?