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:
- 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?
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.
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.
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.
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!
Looking forward to reading your responses, <3 R