View Full Version : mass-radius relationship and atmospheres

2004-Nov-25, 01:01 AM
Is there an easy gauge for how much of an atmosphere a planet can hold?
Let's assume it only has to do with a planet's mass and radius. In that case, the surface acceleration due to gravity would be the measure.

I don't really want to discuss what effect different composition would have. Let's assume an atmosphere that is 75% nitrogen and 25% oxygen.
There's also the fact that our planet's magnetic field deflects a large amount of energy around the atmosphere. What effect that may have, I don't really want to know.

What surface gravity does a planet need to maintain an atmosphere with the same pressure or greater than ours? 1g? Could the moon ever had had an atmosphere(a thick one). Would the sun blow away any atmosphere that is not being replenished?


2004-Nov-25, 01:59 AM
Originally posted by alainprice@Nov 25 2004, 01:01 AM
For starters, that's a pretty good question.

Tempurature is also a factor, as is time since Planet formation. This is why Titan can have an atmosphere thicker than the one that Mars has. I think that major impact events also have an effect.

I have not seen any paper or graph showing the relationship between surface gravity, temperature, and pressure, for given gasses, but I expect that as we start to discover terrestrial planets, such charts will become more common in the literature.

2004-Nov-26, 01:07 AM
You're absolutely right. I forgot about impacts, volcanoes, and of course, temperature.

Ok, let's just say that a group of humans want to find another planet to settle on. It must have the same temperature and atmospheric pressure as earth, give or take 10%. The extra body weight we can deal with.

Something I just realized is that the radius of a planet makes a big difference.
If 2 planets yielded the same acceleration on the surface, but one was twice as large radially, the larger planet could have a thicker(literally) atmosphere. The change in weight(acceleration) as you get further away is less for the larger planet.

Back up 2 paragraphs, and we have a new topic. Partial pressures. The atmosphere of earth is the sum of many parts. Water vapor(ie, cloud formation), oxygen, nitrogen, etc...
I think we can all agree an atmosphere consisting of purely nitrogen and oxygen would be ridiculously similar to our own. Therefore, we can neglect the other pieces. Except maybe humidity.

2004-Nov-27, 02:20 AM
There are a few formulas you should have a look at. The first claculates the velocity of a gas particle.

1. Average speed = "constant" x sqrt(T/m)

Where T equals maximum temperature
m equals mass of the particle
"constant" = ? Someone else will need to tell you that one.

The escape velocity equation is:

2. v = sqrt(2rg)

Where v is the escape velocity
r is the radius of the planet
g is acceleration due to gravity at the surface

Now if you combine these equations you get:

3. sqrt(2rg) > "constant" x sqrt(T/m)

If equation 3 is correct (note the greater than symbol) then the planet can hold an atmosphere. There are other factors that have been stated in this thread but there's a mathematical look.

Ola D.
2004-Nov-28, 05:20 PM
Originally posted by alainprice@Nov 26 2004, 01:07 AM
I think we can all agree an atmosphere consisting of purely nitrogen and oxygen would be ridiculously similar to our own. Therefore, we can neglect the other pieces. Except maybe humidity.
Hey alainprice,
I'm afraid that your previous statement isn't specific enough. The air we breath is made up of Nitrogen (78.1%), Oxygen (20.9%), argon (0.9%), carbon dioxide (0.04%) and ofcourse water vapour (Variable according to the surrounding) with other gases.

Carbon dioxide, although found in traces, is one of the essential gases in our atmosphere. Any slight increase or decrease in these precentages , especially of carbon dioxide gas, would lead to the suffocation of living things.

So the strict ratio of gases in a planet's atmosphere plays a crucial role in the survival of species.

2004-Nov-28, 09:57 PM
In what way is it not specific enough? I thought it was clear that I'm trying to avoid non necessary specifics.

I personally have no interest for the survival of life. I'm merely concerned with the survival of an atmosphere. Therefore, it is fair to consider any theoretical atmosphere. We need not concern ourselves with earth's PRESENT partial pressures.

2004-Nov-29, 04:18 AM
This is a very interesting subject.

I also wonder about comets, is a coma (http://nssdc.gsfc.nasa.gov/planetary/chiron.html) an atmosphere ? Chiron (http://www.vub.ac.be/STER/www.astro/chihp.htm) case in point, demonstrates a distance that a tail forms from a coma on a Comet. Why can comets hold gas?

The density of the solar wind/ distance from the Sun, presence of a magnetosphere would also impact on the structure/presence of an atmosphere.

2004-Nov-29, 03:08 PM
Originally posted by zephyr46@Nov 29 2004, 04:18 AM
Why can comets hold gas?
Comets don't hold gas, they hold ice, which sublimates into gas, and blows away. If you took a comet and somehow got it into an Earth-like orbit, it would be mostly out-gassed in a few centuries [that is, the near surface ices would be gone].

John Wood
2004-Dec-02, 07:58 PM
Re maximum amount of atmosphere an Earth-size planet can hold.

I'm not sure there is any limit. Nitrogen and oxygen atoms are too heavy to be lost at an appreciable rate by thermal escape. If you kept adding N2 and O2 to the Earth's atmosphere it would compress at depth and Earth would grow, becoming increasingly Jupiter-like in its structure. The mass of the atmosphere would come to be larger and larger relative to the mass of the solid planet, and after a while the premise of a system having a total mass equal to that of the present Earth would be violated. So it seems to me the limiting factor in this situation is not how much gas the Earth can hold onto, but simply the rules of the game.

Dr. John A. Wood
Harvard - Smithsonian Centre for Astrophysics

2004-Dec-03, 04:07 PM
Carbon dioxide, although found in traces, is one of the essential gases in our atmosphere. Any slight increase or decrease in these precentages , especially of carbon dioxide gas, would lead to the suffocation of living things.
How slight? Are plants living things?

Ola D.
2004-Dec-03, 07:09 PM
Thanks Dr. John for your time

What kind of factors found on planet Jupitar contribute to the formation of such a massive atmosphere; moreover, is there any possibility that our Earth's atmosphere would evolute to form a denser one?

Ola D.
2004-Dec-03, 07:18 PM

An increase in the carbon dioxide level, up to 5-6%, accompanied by an antagonistic decrease in the oxygen level is relatively enough to induce excessive heart beat, very rapid breathing rate and suffocation. By living things I meant animals and humans. However, an increase in CO2 level would correspond an increase in the plant's photosynthetic rate, and consequently their growth rate.

2004-Dec-04, 05:21 AM
Originally posted by Ola D.@Dec 3 2004, 07:18 PM
By living things I meant animals and humans. However, an increase in CO2 level would correspond an increase in the plant's photosynthetic rate, and consequently their growth rate.
And, would not their growth increase not also increase the O2 output, enabling "living things" to prosper (Earth based entities)?

So, Venus is slightly smaller than Earth and has a dense "atmosphere". Mars is smaller than Venus and has a minimal atmosphere. Just looking at the relative size of the planets, a 6,000 km diameter appears to be the minimal size for a minimal gasious atmosphere, at least in this planetary system.

Check this out:

http://www.nationalgeographic.com/solarsys.../ax/low.html?2d (http://www.nationalgeographic.com/solarsystem/ax/low.html?2d)
Venus's atmosphere is 92 times more dense than Earth's!

2004-Dec-04, 05:50 AM
But plants absorb O2 at night, though not as much as they produce. As such the increased photosynthesis would not do much. It would take hundreds of thousands of years for all the plants on landmasses of earth to reduce the CO2 levels back to their current levels.

2004-Dec-04, 02:57 PM
Atmospheric density is unfortunately a very complex subject; it depends most of all on the mass of the planet or moon, and on the temperature; the temperature is also quite complex, as it depends on the distance from the Sun or from the local star, amd on the composition of the atmosphere. The two most important greenhouse gases are water vapour and carbon dioxide.

Incidentally the lower limit you suggested of 6000 km is not correct, as Titan is only 5,150 km and its atmosphere is denser than Earth's.
If not for the stripping action of Jupiter's magnetic field Ganymede and Callisto would also probably have thick atmospheres too.

There are some interesting equations on this page which give an idea about the loss of various gases from planets; the lightest ones are lost from small planets, but this varies with temperature as well.

Bridh Hancock
2004-Dec-06, 01:28 AM
"What is atmosphere? how to get it? how to keep it? and who & what gets to use it?": what a set of questions!, and well worth our considering in every detail. 'It is simply'.../ No!, it is a complexity among compexities, and is astounding.

Earth's atmosphere was thus for us, and is thus to spite us.

Thank you, Dr John, and every other contributor to this.

You can now buy bottled water; and I am sure many of you do. Air-conditioners are a part of many a first-worlder's life-style. How long before we can and must
buy bottled air? By then, we should know that we have poisoned our global life-support system, and are successfully ecopoiesizing one for beings other than ourselves. Were our media so honest! How clever we are!

:) Bright.

2004-Dec-06, 01:53 AM
Exactly Bright! We haven't found anything quite like our atmosphere, and yet we give it away to cars to consume for free!

How is your rocket going by the way?

Antoniseb, but what about cometary comas? They seem to mimic a small atmosphere. There is also two distinct tails with comets, a gas tail and a dust tail, the dust tail being responisible for meteor showers as the Earth passes through it presumably.

I believe Mercury has a small atmosphere, as does Io.

2004-Dec-06, 04:30 AM
Mercury has a very thin atmosphere, from ememory its 1/1000th the size of earth's. It is made up of potassium and sodium that slowly escape from the planets crust. Besides is small size, mercury cannot hold a think atmosphere due to the high temperature it can reach.

Ola D.
2004-Dec-06, 09:51 AM
Originally posted by Bright@Dec 6 2004, 01:28 AM
Were our media so honest! How clever we are!

Very bad that the majority can't realise that they are unintentionally contributing to the damage of our atmosphere, not only our atmosphere as you mentioned, but also the whole planet's resources and habitats. There should be some kind of campaigns and efforts to educate the biggest number of people about such issues and problems. If we, as humans, weren't the ones to speak on behalf of our planet, who would instead?

2004-Dec-06, 03:55 PM
Now we have air purifiers for those with breathing problems and sensitivites. Soon for everybody? Sheesh, its crazy, but not hard to imagine. I like our atmosphere, and I do what I can to keep it just the way it is. I hope the masses learn to appreciate it soon enough, before it gets too difficult to reverse.

2004-Dec-10, 01:23 AM
shameless bump

2004-Dec-10, 04:39 PM
Long ago in days of yore, Stephen Dole made a somewhat simplistic computer model of the formation of solar systems, called Accrete. It is showing its age now, but is still interesting. You can find various version of the program here (http://www.accesscom.com/~iburrell/create/accrete.html).

Here is the output of a sample solar system (http://www.projectrho.com/accrete.txt). Note the planetary figures labeled Smallest molecular weight retained.

Here is a list of molecular weights (http://www.projectrho.com/accgas.txt). For each planet, note the smallest molecular weight retained, look it up in the table, and figure that chances are the planet will have an atmosphere composed of all the molecules with a higher weight.

If you want to go into more detail, a good readable book is World Building (http://search.barnesandnoble.com/booksearch/isbnInquiry.asp?isbn=158297134X): A writer's guide to constructing star systems and life-supporting planets by Stephen L. Gillett.

2004-Dec-10, 06:41 PM
Nice links Nyrath, thank you!