What is the maximum mass a planet can reach?

[tanzanos]

My son asked me "what is the maximum size a planet can reach". I told him that it depends on its constituents; If it is a gas planet or a solid planet.

Can someone answer this question for me?

 

[phyzguy]

The simple answer to your question is that if a planet has more mass than about .05 times the mass of the sun (which is about 50 times the mass of Jupiter), then it is massive enough to ignite nuclear fusion in its core. In this case, it radiates its own light, and we call it a star and not a planet.

 

[tanzanos]

Thank you for the answer. However does this take into account rock planets as opposed to gas planets? Nuclear fusion of heavier elements such as iron (core of planets) might require much higher pressures and temperature than light elements such as Hydrogen!

 

[phyzguy]

Based on our solar system, once a planet gets to be the size of Jupiter or so, then it has enough gravity to hold on to hydrogen and helium, so it is mostly composed of hydrogen and helium, since they make up the bulk of the material in the collapsing pre-solar cloud. So I think that any planet larger than Jupiter will be mostly hydrogen and helium. I just don't think there is enough of the heavier elements to build a Jupiter-sized rocky planet. However, we're learning rapidly about exoplanets, so maybe I'm wrong.

 

[Astronuc]

Thank you for the answer. However does this take into account rock planets as opposed to gas planets? Nuclear fusion of heavier elements such as iron (core of planets) might require much higher pressures and temperature than light elements such as Hydrogen!

Yes - it would depend on it's composition. One would have to determine the conditions for fusion (pressure or nuclear density and temperature) to determine at what point fusion might initiate.

Jupiter's Core

Down deep, it's hot in there! The temperature at the core of Jupiter is estimated to be 30,000 degrees Celsius (~K) (about 55,000 degrees Fahrenheit). This heat makes its way up through Jupiter and shines through cloud-free holes in the clouds, which are appropriately named "hot spots". Possibly solid, Jupiter's core is estimated to be about one-and-a-half times Earth's diameter, yet ten to thirty times more massive. If there is a solid surface, one could not stand on it without being crushed by the incredible weight of the atmosphere above.

Ref: http://www2.jpl.nasa.gov/galileo/jupiter/interior.html

30,000 K is pretty hot for us, but for fusion it's cold. 1 ev is equivalent to 11605 K, so 30,000K is less than 3 eV and fusion usually requires temperatures (or equivalent kinetic energies) on the order of a few keV, or 10's of millions K.

Here's a slightly different model for Jupiter's core - http://news.wustl.edu/news/Pages/4376.aspx

See this rather dated page on Brown Dwarf Stars
http://astro.berkeley.edu/~stars/bdwarfs/

Stellar models had suggested that a true star must have a m *** at least 80 times that of Jupiter to kindle the stable fusion of hydrogen.

But then this article - http://en.wikipedia.org/wiki/Brown_dwarf - indicates a slightly lower mass threshold for fusion [1]. The threshold would depend on composition since it would be possible to initiate d+d fusion at lower temperature than p+p fusion.

[1] http://www.carnegieinstitution.org/News4-3,2001.html