Celestia Forums

Ok, I -may- have asked this before and been given a link but its been a while since I even worried about it, so please forgive me if I'm repeating myself.

A) What constraints might I put on the radius of a jovian-style planet. I recall sometime ago being told one of my planets was "too large". Of course there is gravitational contraction to account for, but how many J-masses might I allow for before the Radius starts to stabilize/shrink?

B) Is there an actual reliable limit on the size of a terrestrial planet? I realize that theres the matter of hydrodynamic capture of the solar nebula once a core reaches a certain size, but what rough estimate (of mass) might I make to ensure my rocky planets are not too big.

C) What limits on density for both Jovian and Terrestrial planets might I impose. I'm not entirely sure just how dense is too dense, any data here would be appreciated.

Thanks again.

Apollo7 wrote:A) What constraints might I put on the radius of a jovian-style planet. I recall sometime ago being told one of my planets was "too large". Of course there is gravitational contraction to account for, but how many J-masses might I allow for before the Radius starts to stabilize/shrink?

Not sure exactly, but I do know that gas giants tend to be much bigger when they form, and shrink down to a stable size in a few hundred million years at most.

That said, a 15 Jupiter mass (the smallest example of a brown dwarf) is pretty much the same size as Jupiter after 4 billion years, at 71,340 km radius. A 70 Jupiter mass BD (the biggest they can be) at 4 billion years is
about 57,830 km radius. Generally, the lowest mass BDs have the largest radius.

Not sure about the radius of 'superjovians' with masses less than 15 jupiters - I think they can be bigger than Jupiter, but not by a huge amount (ie maybe a few 10s of % larger, but not like double the size).

B) Is there an actual reliable limit on the size of a terrestrial planet? I realize that theres the matter of hydrodynamic capture of the solar nebula once a core reaches a certain size, but what rough estimate (of mass) might I make to ensure my rocky planets are not too big.

I'd say 2 or 3 earth masses. Though then you're really getting into the range where they're going to be holding on to hydrogen and snowballing into jovians.

C) What limits on density for both Jovian and Terrestrial planets might I impose. I'm not entirely sure just how dense is too dense, any data here would be appreciated.

For Terrestrials I'd say the upper limit (unless you're talking about worlds that are basically exposed iron cores) is about 8000 kg/m3. These worlds would have really big iron-rich/sulphur-poor cores and very thin silicate crusts, so they'd form in unusual circumstances (e.g. like Mercury, but more extreme). But generally I'd say that for normal planetary formation the upper limit is probably nearer 6000 - 6500 kg/m3.

The lower limit for terrestrials depends on what they're made of. A predominantly silicate terrestrial with a small iron core would have a density of about 3000 kg/m3. Ice/rock terrestrials like Callisto, Ganymede, Pluto, or Triton would be 1500-2000 kg/m3. Smaller icy worlds would be more likely to have densities between 1000 and 1500 kg/m3.

For Jovians, it depends. Hydrogen gas giants like Jupiter and Saturn tend to have lower densities than Icy giants like Uranus and Neptune, but all are less than 2,000 kg/m3. But when you start getting into superjovian scale (2 or more jupiters), you're packing much more mass into a sphere not much bigger than jupiter, so the density skyrockets. Most brown dwarfs have densities in the tens of thousands of kg/m3!

We have radius estimates for the planets detected via the transit method. The 'hot Jupiter' HD 209458 b is estimated to have a radius 1.43x Jupiter's, or about 100,000 km. Because it was also detected with the radial velocity method, it was possible to estimate its mass as 0.69 Jupiters. Ordinarily a planet of this mass would be have a smaller radius than Jupiter, but in this case it's inflated by heat, orbiting as it does a mere 0.04 AU from its parent star.

The only other planet observed by both the transit and radial velocity techniques is OGLE-TR-56 b (the star is not in Celestia's database unfortunately.) The mass is estimated at 0.9x Jupiter and the radius at 91000 km. The planet is another hot Jupiter, so inflation due to heating is again a factor

--Chris

That is a good point Chris I had read about the "inflation" of close-in giants due to heating. This would really only be an issue for planets that are very close to their parent stars, I'd presume. 0.04 AU from just about any sun-like star is a scorching orbit, with temperatures over 1000K.

I believe the Evil Doctor was helpful here, though I'm curious I usually get density in grams/centimeter^3, would that simply be 1000 times less than kg/m^3?

So I'm seeing 1.5 Jupiter Radii might be a handy upper limit on the overall dimensions of a Jovian planet, couple that with the proposed lower-limit on mass for a brown dwarf which I've read as being as little as 13J-masses. Then I might constrain my planets to have Radii < 1.5xJupiter and Masses < 13xJupiter. At least for the gas giants that is.

I think the Evil Doctor had some pretty good thoughts on smaller-rocky worlds. Including those of the Mostly-core-of-Iron types like Mercury. I still find the idea of super terrestrials intriguing. As I recall there was some early speculation that 51 Pegasi B would be such a planet, though in recent times it has been determined (I think) that it would have no problem retaining its H/He atmosphere. I suppose if there was a way to strip the gasious shell off a gas giant or to arrest the condensation/capture of the H/He envelope at an early stage you could have a quite bizzare pseudo-terrestrial world with a thick H/He atmosphere, hey that would be a neat place wouldn't it? heh.

Anyway enough of my blathering, thanks for the further input Chris.

Tristan Guillot provides a couple of handy (theoretical) graphs of mass versus radius and mass versus temperature for some jovians, which I found useful for setting up some generally consistent radii for extrasolar.ssc - his paper is here.
For a cool jovian he shows a steady rise in radius from R~0.9J at M~0.3J to a plateau at R~1.1J at M~4J, and then a descent to R~0.8J in brown dwarf territory at M~80J. At M~13J the radius is approximately that of Jupiter, so the maximum density for a jovian seems to be around 17000kg/m^3 (17 times the density of water), but this is only achieved with the aid of high mass and low temperature.
The same graphs suggest that hot jovians of mass <1J can blow up to 1.4-1.5 jupiter radii if their temperature is over 1000K, but if they're more massive or less hot, they inflate less.

Another paper here posits very large "terrestrial" (ie, rocky) planets, with radii ranging from 0.31J at M~0.5J to 0.35J at M~2J. An object at the top end of this scale would have a density of 60000kg/m^3, and a surface gravity of 40g.

Grant

This article has several insights into the possible relationships between terrestial planets and jovians. This is all from simulations, but some of the findings are not surprising. In particular, eccentric jovians lead to dry terrestials. In their simulations, terrestials were forming up to 4x Earth mass, and sometimes with up to 10x the amount of water.

cheers,
Walton

wcomer wrote:This article has several insights into the possible relationships between terrestial planets and jovians.

The original scientific article underlying this space.com report is cited (with link) by eburacum45 on this thread.

Grant

granthutchison wrote:Another paper here posits very large "terrestrial" (ie, rocky) planets, with radii ranging from 0.31J at M~0.5J to 0.35J at M~2J. An object at the top end of this scale would have a density of 60000kg/m^3, and a surface gravity of 40g.

This is way beyond any hypothetical planet I have heard of before-
it strikes me that such a large planet would retain hydrogen and helium, no matter how close to the central star it was- in fact it would end up as a brown dwarf or even a star.
Yes- surely such a large body forming in a solar system would attract almost as much hydrogen as the primary, and all you would end up with would be a double star...

If such a planet did exist without a massive hydrogen envelope, any other atmosphere would have a very sharp pressure gradient- it could be extemely dense at the planetary surface, but very thin at 1km altitude...

but I still doubt that such ultra-high gravity planets exist outside of simulations.

Just wondering, how do you do those radius calculations (i.e. I have a gas giant of certain mass and surface temperature, how do I predict its radius, assuming the bulk of its mass to be H/He, as in Jupiter/Saturn).

chaos syndrome wrote:Just wondering, how do you do those radius calculations (i.e. I have a gas giant of certain mass and surface temperature, how do I predict its radius, assuming the bulk of its mass to be H/He, as in Jupiter/Saturn).

For extrasolar.ssc I took a very simplistic approach, assigning four "bins" for radius according to just mass and temperature. Wasn't much point in doing anything else, since we have so many uncertainties of true mass, composition, albedo, age.
If you're making an imaginary planet then you have control over the variables, though: Adam Burrows gives a set of equations relating various properties of gas giants, which are fun to play with, but I found they didn't really produce Jupiter or Saturn when the appropriate parameters were supplied.

Grant