# Could a habitable planet with lower gravity have a thick atmosphere?

I'm designing a habitable earth-like planet that has oceans, forests and life. Now this planet is a bit larger in diameter than earth but its mass and therefore its gravity is a bit lower. This lower gravity has resulted into large lifeforms. Now, one of this lifeforms resembles in appearance a large jellyfish with wings that glides through the air. However, I wasn't sure if a lower gravity is enough to allow such a huge creature to fly though the air, so I figured out a way to solve this by making the atmosphere thicker. But then it hit, " if a planet has lower gravity, how can it have such a thick atmosphere?" I was looking if there were real life planets that have these traits (lower gravity, thick atmosphere) and realized than Venus is a good match. But then again, Venus isn't really the most hospitable planet there is? So, to sum it up, could a planet have lower gravity and yet a thicker atmosphere? And also could such a planet be Earth-like?

• Don't use thickness to refer to density. Thickness is about physical length. – L.Dutch Aug 10 '18 at 11:03
• Titan might be a good source of info. Less surface gravity than our moon, but with a nitrogen rich atmosphere 20% more massive than Earth's; we could literally fly by strapping by strapping big wings to our arms and flapping. It has frozen oceans of water, but the surface temps are 90k/-180c/-300f and is full of liquid methane and ammonia, so it's kind of a mixed bag when it comes to habitability. – Giter Aug 10 '18 at 12:35
• You might be able to achieve the atmospheric density you want, but it probably wont be filled with breathable air. – Tyler S. Loeper Aug 10 '18 at 19:54

Yes. In fact, given your premise of a planet with a larger diameter but lower surface gravity than Earth, I'd expect a thicker atmosphere (both in terms of atmospheric pressure and literal thickness) than Earth.

The relevant variables here are gravitational acceleration and escape velocity. You want a planet with less gravity than Earth at its surface, but a higher escape velocity at its upper atmosphere. Is this plausible? Absolutely!

The relevant variables that you can directly tune here are the mass and radius of the planet. Note that on the scales of planets (other than gas giants), the thickness of the atmosphere is insignificant in comparison to the radius of the planet itself- so, to simplify things here, I'll just ignore the thickness of the atmosphere entirely.

The relevant formulas are gravitational acceleration at the planet's surface:

$$g = {GM\over r^2}$$

and escape velocity:

$$v_e = \sqrt {2GM \over r}$$

where r is the radius of your planet, M is the planet's mass, and G is Newton's gravitational constant.

You want to reduce the surface gravity (as per your premise), while increasing the escape velocity (which will make it easier for the planet to hold on to an atmosphere). Surface gravity decreases rapidly with radius, as indicated by that $r^2$ term, so increasing the planet's radius will very quickly decrease its surface gravity. However, in order to keep the escape velocity from decreasing, the mass must be increased by at least as much.

As an example, let's take a planet with 9 times Earth's mass and 4 times Earth's radius.

$$g = {G (9M_\oplus) \over (4r_\oplus)^2} = {9GM_\oplus\over 16r_\oplus^2} = {9 \over 16} g_\oplus$$

$$v_e = \sqrt {2G (9M_\oplus) \over 4r_\oplus} = \sqrt {9 \over 4} \cdot \sqrt {2GM_\oplus \over r_\oplus} = {3 \over 2} {v_e}_\oplus$$

As you can see, this planet has just over half of Earth's gravity, but 1.5 times Earth's escape velocity. You don't need to use these exact numbers, of course- I chose them mainly to avoid getting irrational numbers. But the point is there: Take Earth, increase the radius a bit, increase the mass a bit more (but not too much more), and you're done.

Now, there is one more complication for you to consider, handwave, or ignore: The material your planet is made of. Density is proportional to $M/r^3$, so it decreases even faster than surface gravity. This example planet's density is about 14% that of Earth. Which means that it must mostly be made of something less dense than water- more like ethanol or kerosene. Making things worse, larger, more massive planets tend to be denser than smaller planets, since gravity compresses the material in the middle of the planet. Earth is (slightly) denser than Mercury, even though Mercury's iron core makes up over half of its volume. Thus, your planet must be made of materials much less dense than those that make up Earth, yet able to withstand even higher pressures. Perhaps instead of silicon, magnesium, and iron, your planet has a lot of lithium?

You have to remember that surface gravity and escape velocity are two different attributes of a planet, and you need one to be as low as possible and the other to be as high as possible.

As far as I remember, the escape velocity from the planet, at the uppermost level of the atmosphere where gases escape from the planet, has to be a certain number of times - 5 or 6 I think - greater than the average velocity of gas molecules at that level in order to retain the atmosphere for billions of years. The average velocity of the gas molecules at the top of the atmosphere depends on their average temperature, which may be different from that at ground level.

If the ratio between escape velocity and average molecular velocity is not that high, the planet will lose it s atmosphere in less than billions of years and needs to replenish its atmosphere from various sources in order to have one long enough to develop multi celled life, intelligent natives, a breathable for humans atmospheric composition, or other stuff necessary for an interesting planet in most types of science fiction stories. It is believed that the atmosphere on Titan is replenished about as fast as it escapes, for example.

Earth seems capable of retaining it's original atmosphere for billions of years. Venus, for example, has a slightly lower escape velocity and a much denser and more massive atmosphere than Earth, so it is hard to imagine that a lot of Venusian atmosphere is constantly being lost and replenished.

Another thing that can remove a planetary atmosphere is the solar or stellar wind of particles that knock molecules out of the upper atmosphere and into space. A strong planetary magnetosphere deflects most of those particles and protects the atmosphere.

What you desire is for a planet that has as low a surface gravity as possible, in order to make flying easier, and as dense an atmosphere as possible in order to make flying easier, and having a denser atmosphere is made easier if the escape velocity is as high as possible.

Mercury has a surface gravity of 3.7 meters per second per second, 0.3772 of Earth's, and an escape velocity of 4.25 kilometers per second, which is 0.3799 of Earth's escape velocity. The ratio of the escape velocity compared to the ratio of the surface gravity is 1.0071.

Venus has a surface gravity of 8.87 meters per second per second, 0.9044 of Earth's and an escape velocity of 10.36 kilometers per second, which is 0.92615 of Earth's escape velocity. The ratio of the escape velocity compared to the ratio of the surface gravity is 1.0240.

Earth has a surface gravity of 9.807 meters per second per second, and an escape velocity of 11.186 kilometers per second, and of course both are exactly 1.000 of Earth's.The ratio of the escape velocity compared to the ratio of the surface gravity is 1.0000.

The Moon has a surface gravity of 1.62 meters per second per second, 0.1651 of Earth's, and an escape velocity of 2.38 kilometers per second, which is 0.2127 of Earth's escape velocity. The ratio of the escape velocity compared to the ratio of the surface gravity is 1.2883.

Mars has a surface gravity of 3.711 meters per second per second, 0.3784 of Earth's, and an escape velocity of 5.027 kilometers per second, which is 0.4494 of Earth's escape velocity. The ratio of the escape velocity compared to the ratio of the surface gravity is 1.1876.

Io has a surface gravity of 1.796 meters per second per second, 0.1831 of Earth's, and an escape velocity of 2.558 kilometers per second, which is 0.2286 of Earth's escape velocity. The ratio of the escape velocity compared to the ratio of the surface gravity is 1.2484.

Europa has a surface gravity of 1.314 meters per second per second, 0.1339 of Earth's, and an escape velocity of 2.025 kilometers per second, which is 0.1810 of Earth's escape velocity. The ratio of the escape velocity compared to the ratio of the surface gravity is 1.3517.

Ganymede has a surface gravity of 1.428 meters per second per second, 0.1456 of Earth's, and an escape velocity of 2.741 kilometers per second, which is 0.2450 of Earth's escape velocity. The ratio of the escape velocity compared to the ratio of the surface gravity is 1.6826.

Callisto has a surface gravity of 1.235 meters per second per second, 0.1259 of Earth's, and an escape velocity of 2.440 kilometers per second, which is 0.2181 of Earth's escape velocity. The ratio of the escape velocity compared to the ratio of the surface gravity is 1.7323.

Titan has a surface gravity of 1.352 meters per second per second, 0.1378 of Earth's, and an escape velocity of 2.639 kilometers per second, which is 0.2359 of Earth's escape velocity. The ratio of the escape velocity compared to the ratio of the surface gravity is 1.7119.

Triton has a surface gravity of 0.779 meters per second per second, 0.0794 of Earth's, and an escape velocity of 1.455 kilometers per second, which is 0.1300 of Earth's escape velocity. The ratio of the escape velocity compared to the ratio of the surface gravity is 1.6372.

All of these planets and moons have lower diameters, masses, densities, surface gravity, and escape velocities than Earth. And the ratio of their escape velocity to that of Earth is greater than the ratio of their surface gravity to that of Earth, in ratios varying from 1.0071 to 1.7323.

So a smaller planet than Earth is likely to have an escape velocity that is not as much lower than Earth's as its surface gravity is lower than Earth's. And that is what you want, a surface gravity as low as possible to help with flying, and an escape velocity as high as possible to help retain as dense an atmosphere as possible.

And your planet will have a much denser atmosphere than many other planets with similar escape velocities, because of various factors that created a much denser original atmosphere and helped it retain and/or replenish it much more than other similar planets did.

Note that Venus is slightly less able to retain an atmosphere than Earth is, and yet has an atmosphere many times as dense as Earth's. Titan is less able to retain an atmosphere than Ganymede or Callisto but has a much denser atmosphere than they do. Titan is much less able to retain an atmosphere than Earth, but has an atmosphere comparable in density to Earth's.

There will be an upper limit to the density of your planet's atmosphere if you want Earth humans to breath it, and a somewhat higher upper limit if you want the lifeforms on the planet to breath it.

All of the gases in Earth's atmosphere, nitrogen, carbon dioxide, water vapor, even oxygen, have safe upper pressure limits. Beyond those limits all of them, even oxygen, become toxic. So you will have to add up the safe pressure limits of every gas likely to be found in a planetary atmosphere and the total pressure will be the total limit of atmospheric pressure for humans to breath. Life forms native to the planet may have evolved to tolerate higher pressures.

• FYI: Venus's atmosphere is mostly carbon dioxide, which is denser than oxygen or nitrogen, and therefore much easier for a planet to hang on to. That's no small part of why Venus's atmosphere is so much thicker than Earth's, despite Venus's lower escape velocity and higher surface temperature. – Someone Else 37 Aug 12 '18 at 7:29