Computing Jupiter's Thermal Time Scale

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SUMMARY

Jupiter's thermal time scale can be computed using the Kelvin-Helmholtz timescale equation, t=GM²/RL, where G is the gravitational constant, M is Jupiter's mass (1.9x1030g), R is its radius (7.0x109cm), and L is its luminosity (8.7x10-10L0). The luminosity L must be converted from solar units to erg/s for accurate calculations. This analysis confirms that gravitational collapse can sustain Jupiter's luminosity over its lifetime of 4.5 billion years.

PREREQUISITES
  • Understanding of the Kelvin-Helmholtz timescale equation
  • Familiarity with gravitational constants and astronomical units
  • Knowledge of luminosity in solar and erg/s units
  • Basic astrophysics concepts related to planetary formation and energy output
NEXT STEPS
  • Learn how to convert solar luminosity to erg/s for astrophysical calculations
  • Explore the implications of gravitational collapse on planetary bodies
  • Study the relationship between mass, radius, and luminosity in celestial mechanics
  • Investigate the thermal evolution of gas giants in astrophysics
USEFUL FOR

Astronomers, astrophysicists, and students studying planetary science or celestial mechanics will benefit from this discussion, particularly those interested in the thermal dynamics of gas giants like Jupiter.

jkrivda
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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=ΔEg/L . ΔEg=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!
 
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L for the timescale equation is just the luminosity of Jupiter. 8.7x10-10Lo 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.
 
so i just convert the solar luminosity fraction to erg/s and then plug and chug?
 

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