# I have a question on gravity

Could a planet hold a significant atmopshere of Co2 O2 N and H2O if the gravity was 50% Earths if under the right conditions?

## Answers and Replies

Sure, under the right conditions. Only particles that reach escape velocity will leave the atmosphere, and for that to happen, you need heat. The escape velocity on a planet with weaker gravity will be smaller, but if the temperature of the planet is lower, the particles will be slower. Even if the gravity is weaker, there might still be a smaller portion of gas particles that are able to escape the atmosphere.

One thing to consider though is that with a much lower temperature, you may not see the same chemical processes which form those compounds here on earth.

So if a planet with this gravity was inbetween earths and mars distance do you think it could hold onto the atmosphere? Id imaine if it were at venuses distance there would be no atmoshpere.

So if a planet with this gravity was inbetween earths and mars distance do you think it could hold onto the atmosphere? Id imaine if it were at venuses distance there would be no atmoshpere.

The distance from the star doesn't determine the escape velocity, that's only affected by the planet's gravity. The only thing that will change the strength of gravity on the surface of a planet is a change in density of the planet; it's unaffected by the distance from the star.

Ok so i made up a hypothetical exoplanet that has a mass of .205 earths with a density of 5.20 g/cm3 and a radius of .60 earths and gravity is 57% earths with an orbit of 402 days around a sun like star. The temperature for the planet is around 275 K Could a planet like this retain a thick enough atmosphere for life? Any possibility for life?

Ok so i made up a hypothetical exoplanet that has a mass of .205 earths with a density of 5.20 g/cm3 and a radius of .60 earths and gravity is 57% earths with an orbit of 402 days around a sun like star. The temperature for the planet is around 275 K Could a planet like this retain a thick enough atmosphere for life? Any possibility for life?

The escape velocity of the planet can be found by:
$\Large v_{e}=\sqrt{\frac{2GM}{r}}$

For your planet, it would be about 6.5 km/s, while earth's escape velocity is about 11.2 km/s.

Using the Maxwell-Boltzmann distribution for the speed of gas particles, you could determine the relative amount of gas you'd expect to lose compared to earth. However, just by taking a look at a plot of the Maxwell-Boltzmann distributions for a few gases at 298°K, you can see that even the lighter gases seem to fit well within the range of your escape velocity.
http://upload.wikimedia.org/wikipedia/commons/0/01/MaxwellBoltzmann-en.svg

Without actually going into the math for the Maxwell-Boltzmann probability density, this seems to indicate that a planet of those proportions would be able to sustain an atmosphere similar to earth's. The temperature could even be a bit higher.

So a planet like this could be habitable. Wow and some people tell me that a planet like that cant have life because of its size haha.

What about 290 K or would that be too hot for this planet?

I think it would be fine. The Maxwell-Boltzmann distribution I posted is for 298°K.

Nabeshin
Science Advisor
The escape velocity of the planet can be found by:
$\Large v_{e}=\sqrt{\frac{2GM}{r}}$

For your planet, it would be about 6.5 km/s, while earth's escape velocity is about 11.2 km/s.

Using the Maxwell-Boltzmann distribution for the speed of gas particles, you could determine the relative amount of gas you'd expect to lose compared to earth. However, just by taking a look at a plot of the Maxwell-Boltzmann distributions for a few gases at 298°K, you can see that even the lighter gases seem to fit well within the range of your escape velocity.
http://upload.wikimedia.org/wikipedia/commons/0/01/MaxwellBoltzmann-en.svg

Without actually going into the math for the Maxwell-Boltzmann probability density, this seems to indicate that a planet of those proportions would be able to sustain an atmosphere similar to earth's. The temperature could even be a bit higher.

Indeed, it appears this process only really ever matters for the lightest elements, H and He. Everything else is simply too massive.

(I did some digging and got some numbers. For the hypothetical planet in question, you could probably hold onto any substance with a weight over 6amu for 10Gyr+. Which is basically everything not H and He.)

Apparently though, there are other processes at work which can strip a planet of its atmosphere. Things like stellar wind and ionizing radiation come to mind, but I'm not familiar enough with how these work to state numbers.

The planet would have a global magnetic field.

K^2
Science Advisor
Temperatures in Thermosphere can reach 1,800 K. That's going to throw all of the above computations way off.

For a hypothetical planet, the Thermosphere temperature will depend on parent star's UV output. So a planet orbiting a blue star will have harder time holding on to its atmosphere than one orbiting a red star, provided equal energy flows from both.

And, of course, magnetic field is vital for holding on to the atmosphere. Just look at Mars.

What about a yellow or orange star? Yea i feel bad for mars like if it kept its field we might actually see small patches of liquid water givin the air pressure was enough.

mfb
Mentor
And, of course, magnetic field is vital for holding on to the atmosphere. Just look at Mars.
It is not. Just look at venus. A magnetic field is relevant, but not required for an atmosphere.
We had a similar discussion some days ago in the astronomy forum here, with the same thread starter.

I understand atmospheric stripping in the thermosphere because of the much higher temperatures spacing between particals. But doesnt the maxwell boltzmann thing explain gases closer to the ground? Cause that would make sense earths temp is 288k and as stated above the chart describes gases at 298 k and the higher up you go the lower the temp is untill you et to the mesosphere and thermosphere.

mfb
Mentor
The Maxwell-Bolzmann-distribution is valid for all gases in equilibrium - to a good approximation, this is true for all gases everywhere in the atmosphere. The temperature is not the same everywhere, therefore the distribution depends on the height.

makes sense.

The thing is, how long a time period do you want the atmosphere to hang around? It has been calculated if we were to terraform Mars to equal our atmosphere, it would hang around for some time, about 100,000 years which would certainly give us enough time to compensate in other ways, make up a planetary magnetic shield and so forth. So in the short term, geologically speaking, yes, we can have an atmosphere hang around a long time on a small planet. The smaller the planet, obviously the shorter time the atmosphere hangs around and whether it has a magnetic shield or not.

No such thing as an earth like atmosphere else where as they come in various differences. A earth size planet could have a mars like atmosphere and a mars sized planet could have a venus like atmosphere. I think there are a number of processes that determine what type of atmosphere occours on a planet or moon other than size. Look at titan thick atmosphere then Ganymede no atmosphere despite similar sized. We also have to consider the what the planet or moon is made of and a number of other processes. Mars has 38% Earths gravity yes but the volcanoes are barley active. The planet i created was 57% earths gravity and has active volcanoes.

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No such thing as an earth like atmosphere else where as they come in various differences. A earth size planet could have a mars like atmosphere and a mars sized planet could have a venus like atmosphere. I think there are a number of processes that determine what type of atmosphere occours on a planet or moon other than size. Look at titan thick atmosphere then Ganymede no atmosphere despite similar sized. We also have to consider the what the planet or moon is made of and a number of other processes. Mars has 38% Earths gravity yes but the volcanoes are barley active. The planet i created was 57% earths gravity and has active volcanoes.
I guess conditions have to be right for an atmosphere, there are certainly a lot of styles of atmospheres in the solar system. But as for active volcanoes, look at Io. There are active volcanoes going on daily, yet it has an atmosphere of 1 billionth of Earth's. So volcanic activity alone is not the whole answer.

In fiction, however, you can assign what you want as far as planetary attributes go, just be as close to scientifically sound as possible. For instance you wouldn't want to make an atmosphere on an asteroid 100 miles across that you could land on and breathe, that would stretch things a bit.

My idea for Io is yes it is small but its also very hot and that heat causes molecules to escape the atmosphere easier. In honesty would give maybe 0.1 Earth masses the minimal size to produce a thick atmosphere for an extented amount of time. We cant forget density also if mars were denser than it is now say by Earths density its gravity would be larger and its internal structure hotter. Another posibilty for Io is maybe Jupiter is eating away its atmosphere but thats a theory, its simply to close to that giant beast.

I wonder if a planet like Mercury could have at one time possessed an atmosphere but then was forced too close to the sun it got boiled off? It has a very rocky core but still with a small gravity, it could have perhaps held on to an atmosphere if it was say 4 AU from the sun, getting 1/16th of the energy we get at Earth, where we get 1355 watts per square meter, at 4 AU it would get barely 80 so being cold could help it maintain an atmosphere also.

Thats what i was thinking maybe even a little closer. I was also wondering what would happen if mars was a mercury type planet huge core much denser. I wish there was a website or something where i could toy with planets masses densities and basically creat a new planet haha.

A rule-of-thumb lower bound to atmosphere retention (derived here) is given by

rm ~ (3/2) (k/G) (1/m_proton) (R/M) T ~ 2*10^14 (R in m / M in kg) (T in K)

where R, M and T are the planet's radius, mass and surface temperature in SI units. The resultant number is the molecular mass, in atomic mass units, below which the thermal kinetic energy exceeds the gravitational binding energy.

Plugging in values for Earth, that yields rm ~ 0.06. Gases with a molecular mass below this value cannot be retained at all (which is meaningless here, since molecular masses are by definition integers). Gases between this value and ten times this value are lost quickly, i.e. within a year or so (still meaningless here). Gases between ten times and a hundred times this value are lost slowly, i.e. within a billion years or so. That means everything with a molecular mass below 6, which covers diatomic hydrogen and helium. Gases above a hundred times this value are retained almost indefinitely.

To get a long-lived Earth-like atmosphere, the lightest gas that has to be retained is diatomic nitrogen, I think, which means a molecular mass of 28 and thus rm ~ 0.3. In other words, you need a planet for which the quantity (R/M)*T is no more than five times higher than it is for Earth. If a shorter-lived atmosphere is sufficient, the quantity may be ten or twenty times higher (for reference, "twenty times higher" corresponds to the Moon, roughly).

As mentioned initially, this is a lower bound. It doesn't stop the atmosphere from, say, being chemically absorbed into the crust or being stripped away by solar wind or any number of other relevant processes which have already been discussed above.

mfb
Mentor
If the planet has water, those molecules (atomic weight of 18) should stay in the atmosphere, too.

Some similar relations:
With the average density ρ, M scales with ρR^3, and the ratio becomes $\frac{T}{\rho R^2}$.

The surface gravity scales with g~M/R^2, and an equivalent ratio is T/(gR).