# What atmospheric composition do I need to sustain Earth-like temperatures at my planet's orbital distance; how close should my asteroid belt be?

I need to heat my planet and I've decided that the two most plausible and controllable ways to do so are by increasing the amount of bombardment by meteoroids from a nearby asteroid belt, and by tinkering with the atmospheric composition. My planet is located 2.14 AU from a 1.71 LSol star, giving the star 37.3% the apparent brightness of Sol from Earth.

$$Apparent Brightness = Luminosity/Distance^2$$

$$AB = 1.71*Sol/2.14 AU^2 = 0.37340$$

Therefore I need to make up the remaining 62.66% (or maybe slightly less, if I want a chilly planet) of incoming energy with a combination of:

1. Meteoroids entering the atmosphere: According to this previous question, I need about 200x the average yearly mass of meteoroids that enter Earth's atmosphere to make up the loss of solar radiation. The numbers are slightly different in the linked article, but just to prove that this is still approximately correct:

6371 km Earth radius * 1.5 to include atmosphere approximately = 10,000 km. 10,000 km2 * 4π = 1256000 km2

/2 for amount exposed to sunlight at any given time and converted to m2 = 628000000000 m2

Annual irradiance of Earth's daylight side = 21.6 MJ / m2 / year * 628000000000 m2 = 1.35648(1013) MJ / year

0.6266 * Ans = 8.4997037(1012) MJ / year necessary to replenish to achieve Earth-like temperature ranges

$$KE = mv^2/2$$

According to the aforementioned answer to my prior question, the average velocity of an incoming meteoroid is assumed to be 50 km/s.

Now we just solve for the necessary mass to bombard my planet's atmosphere with to achieve the desired kinetic energy.

8.4997(1012) MJ / year = 8.4997(1018) J = (m * 500002 m2/s2)/2

1.700(1019) MJ / year / 500002 m2/s2 = m = 6.800 billion kg / year

Earth's atmosphere is hit by approximately 100 tons of meteoroids per day

100 tons * 365 days = 36500 tons / year, converted to kg = 33112243 kg / year

6.80 billion / 33.1 million = 205

How densely populated with asteroids would my planet's orbit need to be to supply this amount of meteoroids? Is it plausible for a planet of 0.6 Earth masses to have an orbit so cluttered with debris?

1. A powerful greenhouse effect: My atmospheric composition needs to be similar enough to Earth's to sustain carbon-based humanoid life. I'm building this world for a few possible storylines and I don't want the readers to think of my planet's inhabitants as alien necessarily.

2. Tidal heating from my planet's large moon: My moon is 5.7 Lunar masses. According to this question's best answer, even this wouldn't heat my world significantly.

3. Higher content of radioactive material in the mantle, namely thorium and uranium: According to this question's other most popular answer, I can use the heat generated from the thorium and uranium decay chains to increase the heat conducted to and radiated from the surface of my planet. However, according to the comments on this answer, it would be implausible for me to have a much higher percentage of these materials than Earth does in its mantle, because heavier elements tend to accrete in closer orbits to stars and my planet is high in water content and other volatiles. More likely, Jasmi would have formed past the frost line and may have been towed into the habitable zone by the Great Tack of my system's major gas giant.

4. Finally, and this is a last resort, I could brighten my star. As far as I can remember, the only way to increase the luminosity of a white main-sequence star is to increase its mass, and I can't really do that without changing the orbital periods of every other object in my system. I've already written the basics of a calendar, so I'd really prefer not to do this.

Please let me know if there's anything I'm missing, and thank you all so much for the help you've given me to get to this point!

• What actually stops you from changing the star's luminosity? Altering the calendar shouldn't be that hard in principle; calculate the new orbital period, then shorten the day/month/year as appropriate (cut a few days out of each month, cut the final month, make each day an hour shorter, whatever suits your purpose). Failing that, I would recommend the greenhouse effect; tidal heating and radioactive material won't scale up effectively, and over astronomical time scales you won't get the necessary meteorite bombardment consistently (you'd run out of material, if nothing else). – Palarran Feb 18 '18 at 15:41
• I guess you're right. I shouldn't be so attached to my calendar system, I just think a 44 month year with six day weeks is pretty cool and I already baked in some cultural significance to the vernal equinox and the amount of days per "month" in the solar calendar societies anyway. but it's not a terrible change, i was just too attached to it. – Rúnatál Davino Feb 18 '18 at 16:03
• Why are you calculating apparent brightness? Wouldn't black body temperature be more relevant? – Ville Niemi Feb 19 '18 at 15:11

Methane is purportedly 13 times or more stronger than CO2 as a greenhouse gas, it's colourless, odorless, and non-toxic at even the highest concentrations, although one can still asphyxiate due to lack of oxygen. Methane only readily converts in the presence of Ozone and Halogenic oxidisers which nedd not be present in quantity in the lower atmosphere and indeed if you make the atmosphere thicker to retain heat you don't need as much ozone anywhere in the air column.

As a thought you could put your planet in orbit of a hot gas giant, Jupiter pumps out nearly twice as much heat as it receives from the Sun, in theory a different composition and/or a larger giant would have an even greater output. Have the "moon" also in orbit of said giant in 2:1 resonance with the planet it will supply much more tidal heating, the gas giant will supply some of the energy budget and an orbiting debris cloud the meteoric material needed for direct atmospheric heating.

On a related note think about the composition of the meteors that are raining down on this world of yours, certain materials, like if you had methane rich comets skimming the upper atmosphere, could have interesting secondary effects. At that high a rate of bombardment you'd have an almost constant rain of re-condensed vapour from the chunks of rock and metal that burn up in the atmosphere, some of the meteors that have been found on Earth have been surprisingly stratified in their chemistry.

• These are some top-tier suggestions. I'm not going to add a hot Jupiter to my system because that would probably mess up the rest of the system that I've designed, but I will certainly start focusing more on methane than ozone and carbon dioxide! That is very helpful to know. Thank you! – Rúnatál Davino Feb 19 '18 at 14:33
• Ozone is an important thing to keep in mind, or more to the point blocking "excessive" UV radiation from reaching the surface is important if you want to have "life as we know it" operating on this world. – Ash Feb 19 '18 at 14:36

You could probably do it by loading up the atmosphere with carbon dioxide. I have no idea how much would be required, but Earth gets a substantial greenhouse effect from the 0.04% CO2 in its atmosphere. Although adding more CO2 does have diminishing returns on the greenhouse effect due to a process called band saturation- each gas can only absorb infrared radiation of certain wavelengths, and once there's enough of the gas to scatter most of the light of those wavelengths, adding more of that gas won't make as much of a difference. So you may be better off throwing in a bunch of different greenhouse gases.

However, there is a way to increase the luminosity of a star without changing its mass: let it age. You're right that the mass and luminosity of main-sequence stars are very tightly correlated, but once a star burns up all the hydrogen in its core, it expands into a red giant, increasing its radius by a factor of 200 or so and its luminosity a thousandfold. A bit more than the 3x luminosity increase you're looking for, but your planet would briefly be habitable as the star transitions into a red giant. I have no idea how long this habitable period might last.

Following the red giant phase, when the star's core becomes hot enough to fuse helium into carbon and oxygen, it drops down into the horizontal branch, with only 50-100 times the luminosity of the Sun. Closer to what you're looking for, but not all the way there.

• I was worried about ocean acidity, but now that I think about it, that wouldn't be as much a problem as on Earth because I have waaaay more ocean on Jasmi. Thanks! CO2 will definitely do it, and where that fails, I'll start in on CH4 and water vapor. – Rúnatál Davino Feb 18 '18 at 23:27