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According to earthsky.org the Earth gets 3 million miles closer to the Sun than its usual distance of about 93 million miles on average.

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My question is, how close would the earth have to be to the sun for there to be problems with our survival?

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  • $\begingroup$ That happens every year. There's nothing unusual about it. $\endgroup$ – gerrit Mar 1 '18 at 23:36
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    $\begingroup$ Sure, but thats not my question $\endgroup$ – K Split X Mar 1 '18 at 23:38
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    $\begingroup$ The Earth is currently inside the Goldicks Zone. If the Earth goesanywhere outside the Goldilocks Zone then there will be severe circunstances be it near the Sun or away from it. $\endgroup$ – Sushant Gurjar Mar 4 '18 at 7:16
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I'm going to use Gm (1 gigameter = $1\times10^9$m) and degrees Celsius for this answer.

By getting closer to the Sun, probably the most major problem would be the increase in temperature.

A while ago I wrote a program that calculates the effective surface temperature of a planet. Having dug it back out, I've played around with the values a bit. It's important to note that the effective temperature is not the same as the actual surface temperature, since it doesn't account for Earth's atmosphere. If Earth had no atmosphere, it would be the correct actual temperature.

At our current distance of (avg.) 149.6Gm, the effective temperature is 257K, or -16°C (some websites cite other values ±2°C). NASA cites an actual average temperature of 15°C. Assuming a linear relationship between effective temperature and actual temperature, we can assume that $T_{actual} = T_{eff}+31 \pm 2$.

So, what would happen if we moved, say, 10Gm closer?

Well, the effective surface temp is now -7°C, and I'm guessing the actual temperature would be about 24°C. This is an increase of 9°C. We would probably still be able to survive, but with difficulties. For starters, the sea level would rise by over 40m, leading the world to look (at the best) like this. Not an easy situation, but nevertheless survivable. Of course, there would be other effects like an increase in extreme weather, the mass extinction of species, and probably a whole load of things that are hard to foresee, but I'm not going to try to predict them.

So, what about a move towards the Sun of 20Gm?

The effective temperature is now ~3°C, and the surface temperature is about 34°C. Things start to get bad now. All of the ice caps have melted. Once fertile areas are now barren deserts. Surviving is hard, but possible, although famine is now a major problem across much of the world (especially around the equator). The Gulf Stream may have stopped, oddly enough cooling down some of western Europe and all of Britain. It's not looking good.

What about 50Gm?

The effective temperature is 42°C; the actual one is around 73°C. Where the Sun's habitable zone begins and ends is disputed, but now, at 0.65AU away from the sun, it's quite likely that we're not in it. It's very hard to predict what happens now. Humans would likely have to stay underground to remain alive, and food would be a major issue. The ecosystem would be pretty much destroyed, having not had a chance to adapt to the new temperature.

For fun, if we moved 100Gm closer, we'd be at about 205°C. Ouch. We're closer than Mercury now, and look how that planet's coping. Mercury ranges from -173°C to 427°C depending on various factors. Survival without massive life support is not possible.

Any closer, and things just get worse.

Hope this is a suitable answer for your question!

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    $\begingroup$ When you consider feedback mechanisms, change in albedo and greenhouse gas both CO2 and Watervapor, you should increase your T'actual and T'effective upwards. Look at Venus' T'actual and effective or Earth's during the last ice age. You need to adjust your 31 degree estimate upwards significantly as Earth moves that much closer to the sun. (accurate estimates are obviously impossible, but your estimates are clearly too low). $\endgroup$ – userLTK Mar 2 '18 at 9:20
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    $\begingroup$ @userLTK Yeah, I'm guessing most things in this answer: "Assuming a linear relationship between effective temperature and actual temperature" was what I was doing with calculating the $T_{actual}$ because it's extremely hard to accurately work out how they are related. My temperature estimates, if anything, are minimum bounds. $\endgroup$ – JThistle Mar 2 '18 at 9:21
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    $\begingroup$ Excellent what-if style answer. $\endgroup$ – Carl Witthoft Mar 2 '18 at 18:17
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The Earth passes within 91.4 million miles for just a brief time, then it moves back further out and 6 months later it's 94.5. That 3.4% and change closer works out to 7% more solar energy, but that's just for closest and furthest points. Over the closest and furthest month, the variation is smaller and (perhaps obviously), it averages out over the entire year.

There's two ways to address to this question - how eccentric the Earth's orbit can get which would make the perihelion closer and aphelion further, or, the 2nd way, how much closer can you make the semi-major axis, which defines orbital period.

Earth's present eccentricity is 0.017 and decreasing (Wikipedia article above). For simple approximation and low eccentricity orbits, the eccentricity 0.017 translates into (doubling it) a 0.034 (or 3.4%) variation perihelion to aphelion, which works out to a (1.034^2), about a 7% variation in solar energy.

Earth's peak eccentricity of 0.0679, (this time I'll do the math), closest point (1-0.0679) = 0.9321 and farthest (1+0.0679)= 1.0679. The ratio 1.0679/0.9321 = about 14.5% which works into a 31.3% variation in solar energy closest to farthest. 14.5% and 31% energy variation may sound like a lot, but consider that the winter/summer solar energy variation in latitudes away from the equator can be considerably over 100%. So, 31% isn't world ending, in fact, the Earth handles those 31% days without too much trouble, though they can trigger or end ice ages depending on how it lines up with other Milankovich cycles. We should also remember that it's 31% hottest to coldest, it's about 14.5% hottest to average, and again, just for one day then that number begins to drop.

14.5% size change isn't as much as it sounds either, that's about the variation between the largest full moon or supermoon and the smallest (micromoon), though the average full moon variation is between perigee and apogee 11% and 12% in diameter. How often do you look at a full moon and say "that's bigger than the full moon 4 months ago". That's not to say nobody notices, but many of us wouldn't recognize a supermoon without being told when to look for it, though it's fairly obvious if we could see them side to side.

enter image description here

So what effect does Earth's periodic 0.0679 eccentricity have? Apart from triggering or perhaps ending an ice age, not that much.. You could push Earth's eccentricity pretty far without much danger to Earth, though past a certain point, crashing into Venus might become a concern.

Lets have some fun and push Earth's eccentricity up to 0.15 (that's about half way between Mars' and Mercury's eccentricity.

enter image description here

Perihelion 0.85% of the semi-major axis, Aphelion 1.15%. At perihelion the solar intensity would be (1/.85)^2 = 38% stronger than normal. That might cause scorching heat in some places where the Perihelion lined up with summer, and you might get some bitter cold weather when the Aphelion lines up with winter (note, this doesn't always happen, perihelion slowly cycles around the calendar every 26,000 years or so). But when it lines up you might see some seasonal-weather extreemes, but Earth could (I think) survive even a 0.15 eccentricity. The views of Venus at Perihelion would be impressive too, Venus would stay in the sky longer and be larger and brighter.

Push Earth's eccentricity to about .26 and Earth and Venus would get uncomfortabaly/scary close and might crash into each other. Fun to think about, but a potential planet killer.

But apart from creating potentially greater variation in seasons, some very wild weather and perhaps triggering an ice age (perhaps the biggest ice age since snow-ball Earth) or accelerating climate change (it all depends on how the 3 Milankovich cycles line up with each other), You could push Earth's orbit surprisingly close to the Sun, half way to Venus or even closer at perihelion, without ending life on the planet.

Now, if you adjust Earth's semi-major axis, which makes the orbit faster or slower, and changes the length of the year - with that, there's much less variation. @JThistle covered this. If you push Earth's semi-major axis just a few percentage points closer to the sun, Earth would heat up and it would get bad quickly. In fact, I think his estimates are conservative. There are already some pretty good estimates out there on this, just google "what will the Earth be like in 500 million years or a billion years" for a few articles. Here's one. The sun is growing slowly larger and more luminous, about 1% every 100 million years. That will be a significant problem as soon as 500-600 million years from now, perhaps less. Likewise, just a 2.5%-3% push closer to the sun would have a similar effect. You can't reduce Earth's semi-major axis by much without causing serious problems. Just 1% might be enough to melt Greenland over time, raise sea levels and prevent future ice ages.

Similarly if you push Earth just 1-2% further away, Earth could enter permanent ice ages (fortunately we can fix that by burning oil and coal), but sans man made greenhouse gas, just 1%-2% further away would trigger perhaps a permanent ice age for the next several million years and perhaps, dangerously low CO2 levels, at least until Antarctica drifts north enough for it's ice to melt. It would be nice to be told to burn oil for the "good of the planet" though. :-)

This is all very ballpark, but the Earth is, surprisingly, at a very good distance from the sun and just a few % one way or the other could be very bad, though in 15-25 million years when Antarctica is brushing up against South America and is no longer covered in ice, when that happens, Earth will have greater wiggle room away from the sun, but not closer to the sun.

Precise mathematical answers to this question are obviously impossible. I'm just giving approximations.

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Without any significant change in orbital distance, there have been a variety of long-term (millions of years) tropic or ice ages, and transitions from one to another led to rather a lot of extinctions.
In the same vein, a nice big solar eruption could wreak havoc independent of orbital distance changes.

I"m not arguing with the other answers; just pointing out that time scale matters.

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    $\begingroup$ I feel like this is more of a comment. It doesn't actually answer the question at all. $\endgroup$ – zephyr Mar 2 '18 at 19:15

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