So, i’m constructing an alien solar system for fun, and while it’s easy to determine how much gravity a planet will have, how much mass, and volume, I am unable to figure out a few things relating to the atmosphere.
What I want to know is, how does one determine what the atmospheric pressure of a hypothetical planet will be?
Also, how does one determine how warm a planet will be (average temp, higest and lowest average temperatures)?
Those are some very complicated questions. What is the chemical composition of the atmosphere, what is its mass, how much energy does it receive from the star, how much energy is reflected and emitted back into space, what is the temperature of the planet, does it have a significant magnetic field, what is its rotation rate?
Maybe I should clarify:
I know that to get exact pressure one needs all of the variables you’ve mentioned. As such, i’m looking to figure out what general pressure might be like. I know, rather imprecise for whipping up a hot batch of extra solar planets, ya?
Here’s what I can tell you:
Since gravity is proportional to mass, I think you’re going to have a problem with a planet of 1.01 Earth masses whose gravity is 0.98 Earth gravities.
For a very very rapidly rotating planet you could have percieved gravity at the equator be materially less, due to centrifugal/centripetal force, but that effect would diminish to zero at the poles and would have no influence on orbiting bodies (artificial satellites, moons, etc).
Naw. The planet’s less dense than earth, so the distance between the surface and the centre of mass is greater. Gravity is inversely proportional to the square of the distance. Easy peasy.
D’oh.
You can get a very rough estimate of the surface temperature of a planet by assuming that the sun and the planet are perfect blackbodies and using the Stefan-Boltzmann law. You need to know the radius of the sun in your solar system; once you have that, you can calculate the temperature the planet will have in thermal equilibrium by equating the energy received from the sun with the energy radiated by the Earth. The result becomes
T[sub]planet[/sub] = sqrt(R[sub][/sub] / 4 d) T[sub][/sub]
where R[sub][/sub] and T[sub][/sub] are the radius and surface temperature of the sun, and d is the radius of the planet’s orbit. (We’re also assuming that the planet is rotating rapidly enough that it doesn’t have a “hot” side and a “cold” side, which would probably be the case for your planet.)
Note that this doesn’t take into account the insulating effects of the atmosphere, radiativity, and surface albedo; and indeed if we apply this formula to the Earth we get that the average surface temperature of the Earth should be a balmy -75 C. Obviously one or more of these factors can’t be easily neglected (I seem to recall from my planetary science courses that the atomsphere’s effects are the biggest), but this calculation gives us a rough calculation of the lower limit on the planet’s temperature.
Based on this calculation, and assuming your star has the same radius as our Sun, I would estimate your planet would be (on average) roughly 5 degrees Celsius colder that the Earth.
D’oh, I forgot to take the square root of the 4 in my equation above. It should read
T[sub]planet[/sub] = sqrt(R[sub][/sub] / 2 d) T[sub][/sub]
and so Earth’s average temperature, according to this, is around 5 C. From this calculation, then, your planet has an average surface temperature of about 3 C before atmospheric effects are taken into account. I wouldn’t take this too literally, though; the best you can probably say is that your planet is a little bit cooler than Earth (but not much.)
Then again, it has nearly 7 times the atmospheric CO[sub]2[/sub], which probably means it’s rather warmer than it would be otherwise.
Frankly, I don’t think there is a ‘correct’ density of the atmosphere given any number of measurements you want to make. For instance, Titan is much smaller than Earth, yet it has an atmospheric pressure about 60 percent greater. Ganymede, on the other hand, is slightly larger than Titan, and has no atmosphere at all.
Then there’s Venus - almost a twin of Earth in size, and yet it has an atmospheric pressure at the surface almost 90 times greater.
I imagine part of the reason is that various processes on earth have sequestered the carbon out of the atmosphere, lowering its density. I don’t have a clue how you would begin to model something like that.
Huge variations are possible, given the parameters you have. I was also going to mention Venus: Not only is it slightly smaller than the Earth, it’s much hotter, also, both of which factors would ordinarily contribute to a thinner atmosphere. And yet it’s many times thicker. Your planet is both cooler and weightier than Venus, so you could certainly justify an atmosphere 100 times thicker than Earth’s, if you wanted. Likewise, you could also justify an arbitrarily low atmospheric pressure, by positing some cataclysm early in the planet’s existance which stripped off most of the volatiles. Since you’re apparently shooting for a planet habitable to Earthling life, I would just pick some random number close to 1.
Incidentally, there’s some speculation that our apparently freakishly large Moon might be related to our low atmospheric pressure, so you might want to put something similar around your world. Of course, given our small sample size for Earthlike worlds, and our even smaller sample of habitable ones, this should be taken with 6.479891 centigrams of NaCl.