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In the Norse prophesy of Ragnarok, Fenrir eats the sun. Considering the Earth is not immediately consumed by a supernova, it must be assumed that he swallows it whole and it just ceases to exist on the material plane. (Taking its gravity and solar energy with it)

From the Wikipedia page:

In stanza 46, Odin asks what sun will come into the sky after Fenrir has consumed the sun that exists. Vafþrúðnir responds that Sól will bear a daughter before Fenrir assails her, and that after Ragnarök this daughter will continue her mother's path.

Assuming that, for dramatic tension, the gap between having a sun and a new identical sun is 3 days, what would be the effects on the other bodies in the solar system? (Lets forget about the inhabitants. What few remain are covered by the Ragnarok narrative.)

Also assume that the new sun takes the exact position of where the sun should be at that moment. (Taking into account the sun's movement through the galaxy.)

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  • $\begingroup$ that is going to depend a bit on when in the planetary cycle, as the other bodies will then get greater say in the orbit of the planets $\endgroup$ – ratchet freak Oct 15 '14 at 13:34
  • $\begingroup$ I do not know enough about the planetary cycle to define that. But by all means assume the worst-case-scenario. $\endgroup$ – Danny Reagan Oct 15 '14 at 13:39
  • $\begingroup$ This may be easier to answer if you just focus on earth. $\endgroup$ – James Oct 15 '14 at 13:44
  • $\begingroup$ But everything will happen in concert. Possibly effecting each other. I don't need a planet by planet breakdown of the effects, just the general effects on the solar system as a whole. $\endgroup$ – Danny Reagan Oct 15 '14 at 13:46
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    $\begingroup$ Fun fact: Gravity propagates at the speed of light. Since Earth is 8 light-minutes away from the Sun, we'd continue to orbit (and see) the sun for 8 more minutes after it's disappearance. Not that it really matters though. The moment we stop seeing it, we stop being affected by it's gravity. $\endgroup$ – Corey Ogburn Oct 15 '14 at 17:58
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I'll start with Earth

Earth is hurling through space at a speed of approximately $29.78 km/s$ If the sun were to disappear, the Earth would move in a straight line until the sun reappears. Since there are $259,200 seconds$ in three days that gives Earth the time to travel $29.78 km/s \times 259,200 s = 7,718,976 km$ That's quite a distance.

Since the distance between the Earth and the sun varies between $147,098,290 km$ and $152,098,232 km$, I'll average that down to about 150 million kilometers for calculations.

Using Pythagoras, we can get the distance form the sun when it comes back after 3 days: $\sqrt{150,000,000^{2} + 7,700,000^{2}} = 150,1632,44.504$. This puts us about $160,000 km$ out of orbit, peanuts compared to the difference between the Earths aphelion and its perhelion which is about 5 million kilometer.

What about the influence of other planets?

Good point, Jupiter is huge and can get reasonably close to Earth [citation needed]. We'll assume a worst case scenario and place Jupiter at a distance of 600,000,000 km from earth. Jupiter is significantly slower than earth, but in the span of three days, this is not going to make a huge difference considering the distance between them.

You can calculate the acceleration of a body under gravitaional influence by another body as: $G\frac{m}{r^{2}}$ Where G is the gravitational constant, m is the mass of the body attracting (Jupiter in our case) and r is the distance between the two bodies. Filling this in gives us: $6.673\times10^{−11}\frac{1.8986\times10^{27}}{600,000,000,000^{2}} = 3.51926606\times10^{-7} m/s^{2}$ Which means that the earth will accelerate towards Jupiter at a rate of 3.51926606*10^-7 m/s every second. After 3 days we will have traveled $\frac{3.51926606\times10^{-7}\times259200^{2}}{2} = 11822.0311653 m$ towards Jupiter, not even $12 km$!

Mars is closer though.

I see your point, but assuming Mars is as close as 50 million km, we get an shift towards Mars of about $56 km$. Not really significant.

How will other planets fare?

Well, Mercury will be off the worst. If there's no significant change there, there won't be a significant change anywhere. As it is traveling at about $47.362 km/s$ It could travel a distance of more than 12 million km in 3 days. Taking into account its smaller orbit, this would take it about 1.2 million km out of orbit, not bad. But still not much compared to the variance in its orbit which is almost 14 million km.

Conclusion:

If Fernir eats the sun, there are more important things to worry about than where the planets will be in 3 days, when Fernir needs to go to the bathroom.

Edit:

But wait, the Earth is now going too fast for its distance from the sun

You're right. And it's slightly turned away from the sun too. And I must admit, I underestimated the effect of this. As some intelligent people in the comments pointed out, this would change the eccentricity of the earths orbit from 0.016 to 0.06. Using this calculator we can then figure out that Earths orbit will now vary between 141 million km and 159 million km. The difference has nearly quadrupled! In the grand scheme of things, our orbit will still be relatively similar, this might be enough to seriously influence weather pattern though.

Another possible effect.

Since gravity can not travel faster than the speed of light, the effect of the sun disappearing can only propagate with the speed of light. Gravity needs about 4 seconds to traverse the diameter of the sun, so gravity will drop from 100% to 0 over the course of 4 seconds. Additionally, there will be about a 0.04 second lag between the part of the Earth facing the sun and the most distance part. The acceleration due to the suns gravity is $\frac{6.67\times10^{-11}\times1.9891\times10^{30}}{(1.496\times10^{11})^{2}} = 5.928151\times10^{-3}m/s^{2}$. Dropping from this value down to 0 over the course of 4 seconds with a maximum lag of 0.04 seconds doesn't seems bad enough to cause anything major, but maybe it is enough to cause some earthquakes? I'll leave that to geologists to decide.

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    $\begingroup$ Excellent. Thanks. Surprisingly, for this SE, not as apocalyptic as I'd expect. $\endgroup$ – Danny Reagan Oct 15 '14 at 14:25
  • $\begingroup$ Actually, it's a bit worse than this...I'm putting together an answer now $\endgroup$ – guildsbounty Oct 15 '14 at 14:29
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    $\begingroup$ A thought. This process (in addition to moving the planet to a higher orbit by giving it energy) is going to increase the elipticallity of the orbit, possibly by more than it travels in those 3 days (since its heading "uphill" when the sun comes back it's going to keep going uphill for a while) $\endgroup$ – Richard Tingle Oct 15 '14 at 16:58
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    $\begingroup$ @RichardTingle is correct. There will be a rather drastic change to the eccentricity of the orbit, above and beyond the distance that the planet traveled in that period. The planet's velocity will be too great for a circular orbit at it's new distance, and will be angled about 3 degrees away from the Sun. Both of these factors will increase the eccentricity. $\endgroup$ – Caleb Hines Oct 15 '14 at 17:15
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    $\begingroup$ This assumes that Earth is in its current state when the Ragnarok begins. If a hypothetical pre-Ragnarok Earth was travelling a different orbit, then couldn't three days without the Sun's influence result in our current orbit? $\endgroup$ – Kelly Thomas Oct 16 '14 at 12:44
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72 hours of total darkness will lead to a significant drop of temperature. The difference in temperature between day and night can be anywhere between 10 and 30 degrees Celsius. It depends on cloud cover (clouds keep the warm temperature in) and distance to the sea (water is very good at storing warmth, while land isn't); 72 hours darkness should have about six times that effect; that would be between 60 and 180 degrees Celsius. So this could be fatal in some points of the earth, say in the middle of Asia, and much less fatal say in Hawaii, surrounded by water.

It may take some time for the temperature to get back to normal as well. The darkness itself should be not such a big deal, from experience plants survived being stuck in a storage container for days. You would find out how well the insulation of your house works, if it's -50 Celsius outside.

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  • $\begingroup$ The question asks for the major effects on the planets in teh solar system, I'm also not 100% sure you can linearly extrapolate the temperature decrease like that. I feel like the oceans will hold a substantial amount of heat long enough to prevent strong sub-zero temperatures at any appreciable distance from the poles. $\endgroup$ – overactor Oct 16 '14 at 10:26
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    $\begingroup$ @overactor You're correct, temperature drop is not linear, it will not be six times the same effect. $\endgroup$ – Samuel Dec 16 '14 at 22:47
  • $\begingroup$ I experienced an annular eclipse in 1984. At the moment of totality, the air temperature had dropped 15%. So I imagine that if there's no sun for 3 day's it's going to get awful cold. If Fenrir swallows the sun, that doesn't necessarily mean that the sun's gravity would go away. It would just be in its belly until it was pooped out. $\endgroup$ – Howard Miller Oct 21 '15 at 1:58
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Looking at effects of the absence of the sun's gravity
Since the sun's gravity is gone, all planets will go out of their orbit. But in 3 days they wont get too far, and will regain their position after sun comes back

Look at the effects of the absence of the suns heat
The whole earth will be in instant winter (it will just get colder, not more snowy), and Mercury's surface will be totally frozen.

Looking at General Effects
there will be global chaos, lots of people will commit suicide (just like people commit suicide a day before 9.9.1999), mass robbery, people will panic (like they always do -_- ).

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  • $\begingroup$ Regain their positions? Instant winter? How so? $\endgroup$ – Samuel Dec 16 '14 at 22:48
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There will be one mother of a tidal wave.

How badly this affects anyone will depend on where they are. In the open ocean, the tidal range due to the sun is about 2 feet. That translates to a pretty big mass of water that will suddenly be dropped. This will be accentuated by tidal movement of the Earth's crust. All the normal tidal phenomena will try to happen at once and everywhere. Large sections of coastline will be washed away and water will invade the land disastrously elsewhere.

Sorry no calculations here. The land/sea boundary is so irregular and the depth of the seas likewise, so a realistic simulation would require a huge amount of real-world oceanographic knowledge and some powerful computation.

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In terms of the solar energy, it would depend on how long the sun was missing. However, the rough estimate of the energy available by combustion of the Earth's entire biomass is on the order of about 10 days' worth of illumination by the sun. So, if the sun were gone 10 days, the energy lost would represent all the chemical energy stored up by the chemical processes of the entire biosphere, 99.99% of which is ultimately from photosynthesis. What that means for the biosphere is pretty obvious; the food web would collapse and practically everything on the planet would be frozen solid by the time the sun reappeared.

Second, if the Sun's gravity were lost too (instead of it becoming a black dwarf, it just was removed from existence for 10 days), the orbital dynamics of the solar system would get interesting. At the instant the sun disappears, the planets will be moving in a direction tangential to their roughly circular but in reality somewhat elliptical orbits. Without the Sun's gravity pulling them back, those masses will continue in that straight line. Some of the lighter ones might be drawn toward each other, but for the most part anything outside the "lane" of each planet's orbit exerts too small a force to see much difference over 10 days.

... Until the Sun comes back. Because everything has been moving in a straight tangent line to their original orbit, the biggest observable effect of the Sun's temporary absence is that all the planets' orbits would be re-established further out, and because their velocity didn't change, the orbits would also be more elliptical. That means our deep-frozen Earth will likely get a few more months of a hard winter, but then a few months after that, things will start to get uncomfortably hot as Earth "falls" back toward the Sun. Its orbit is no longer wholly within the "Goldilocks zone" of the habitable temperature range for a planet its size with its atmosphere, and that's a big problem. At a worldwide average air temperature of about 45*C, the evaporation component of the water cycle will begin to increase dramatically, forming an insulating cloud layer, and there's little we could do at that point to reverse the effects. Anything that might have survived the deep freeze will be scoured from the face of the earth if the ambient temperature climbs too far beyond about 70*C.

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I think disappearing of Sun can be a long eclipse (but how does the celestial body, that concealed the Sun, can appear?) or a nuclear winter. Any other cases are too unrealistic or they simply destroy the solar system, because the gravitational force of Sun keeps planets together

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