What would the situation be like for an Earth-like planet on either edge of the Goldilocks Zone?
Closer to the sun, could you have livable conditions at the poles, but be unable to travel from one pole to the other?
And what about the opposite, an Earth-like planet at the farthest edge of the Goldilocks Zone?
Let’s leave aside complexities in climate and just shift the damn planet.
Solar incidence at Venus = 2600 W/m[sup]2[/sup]
Solar incidence at Earth= 1360 W/m[sup]2[/sup]
Solar incidence at Mars= 586 W/m[sup]2[/sup]
So following this progression found hereand using Temp[sub]3[/sub]= 253K
Temp[sub]v[/sub] = Temp[sub]e[/sub](SI[sub]v[/sub]/SI[sub]e[/sub])sup[/sup] = 297K
Temp[sub]m[/sub] = Temp[sub]e[/sub](SI[sub]m[/sub]/SI[sub]e[/sub])sup[/sup] = 204K
Now you need to wrap the planet is nice warm atmosphere which gives us about 34 degrees more warm
Temp[sub]v*[/sub] = 58 C
Temp[sub]e*[/sub] = 14 C
Temp[sub]m*[/sub] = -34 C
Still not liking much of this
Nice work, but wouldn’t the “Goldilock’s Zone” fall well within the orbits of Venus and Mars? I suppose you can use these calculations to determine how far +/- from Earth’s orbit would suit one’s comfort level. For already adapted life on Earth, I’m guessing you couldn’t shift the planet much at all without catastrophic consequences.
There is no simple answer to this because the Goldilocks zone is sort of nebulous and dependent on the traits of the planet. Planets with the right masses, magnetic fields, atmospheres, etc. could be habitable in the current positions of Venus and Mars but the planets currently there are of course dead. (I couldn’t begin to do the math myself, but possibly if you moved Venus to the distance of Mars, the temperature would be in a range comfortable for humans, though you’d still choke to death on the air.) Earth itself has been nearly frozen solid at least once. And at the moment our poles are too damn cold for comfort and our equator too damn hot for comfort.
Also, I remember reading years back of research that eccentric orbits are less of a problem to habitability than one might think. Here is an article from 2002, and more modeling from this year.
(tl:dr–give the Earth an orbit that is the same average distance as now, but with an eccentricity that takes it from the orbit of Venus to the orbit of Mars in the course of a year, and the Earth would still be human habitable.)
Thanks. The key in my simplistic model is the solar incidence. Since SI varies as the square of distance.
So I think you could say R[sub]x[/sub]=R[sub]e[/sub]*(Temp[sub]e[/sub]/Temp[sub]x[/sub])[sup]2[/sup]
If we said we wanted a range of +/- 5K
R[sub]min[/sub] = R[sub]e[/sub](253/258)^2 = 0.96 AU
R[sub]max[/sub] = R[sub]e[/sub](253/248)^2 = 1.04 AU
I think. Normally this is where I look back in an hour an notice a glaring mistake.
Just as a quick rule of thumb, since I try to avoid math -
The sun incident on the earth at 60º LAT is about half the sunlight falling on the equator (based on angle of globe).
Life at 60 N Lat (or South) is no piece of cake. In summer it’s tolerable, in winter it is awful. (-40C/F or worse.) That of course includes heat leaking from lower latitudes.
This assumes you have seasons. The earth’s tilt is about 22º so that’s the variation. with no seasons, odds are half the sunlight would be nowhere near enough to maintain life in normal conditions.
(Ignoring those fantasy life forms that have antifreeze for blood. IIRC there are maybe a few species of fish that manage this, but not life in general).
More sunlight? The poles (well, the South Pole) typically run to the -60ºC range. I presume that a small area of the poles would be habitable with double the sunlight.
My gut (for what it’s worth - worth nothing) is that with high sunlight, there would be a balancing effect where the heat would cause massive cloud cover, like we used to think Venus was like. I assume there are life forms that could survive in 50C or higher as a regular temperature, provided the temperature did not stray to boiling point. Shiny white clouds woul reduce the amount of sunlight hitting the earth.
(Keep in mind that during the dinosaur era, the poles were warm enough that they supported large forests and dinosaurs migrated up and down the coast of the ocean that ran from the Gulf of Mexico to the Arctic… I haven’t seen a consensus what the exact cause of that was, but it was definitely a warmer earth.)
This ignores secondary effects, like oxygen levels. Our oxygen supply is constantly refreshed by photosynthesis. Unless there is a sufficient population of plants and algae it’s likely we would not have a breathable atmosphere. OTOH, too much CO2 may make a colder planet less habitable but warmer from greenhouse effect.