chance of surviving a planet killer explosion

Question

Our main characters have just arrived at the brand new SpaceStation2™ (now with geostationary orbit!) soon they get settled in with the other characters already there, then the planet explodes, no particular reason why, just blows up with the average velocity of a chunk being 9km per second (deviating up to 5kmps more or less) in the general direction of away from where earth used to be. Obviously a chunk hitting the station would be bad, and so would some other things, but could it survive?

important stuff:

• 3x the size of the ISS currently
• the station can have whatever modules or supplies is necessary for its survival within reason
• the crew is 16 people
• assume crew can be specialized in whatever is needed
• there are 2 crew dragons docked and 1 cargo dragon
• assume they can grow enough food to survive using SuperPlantX™
• take into account survival for 1st month
• survival requires at least 14 people remaining at the end of the month
• survival requires at least 90% of ship to be intact and no major issues

So, can they survive?

Answer 1

Your death star blast is so weak that they wont notice it.

9km/s is below the 11.1km/s you need to break out of Earths gravity well. All those chunks are going up, slowing down, and coalescing back and reforming a new planet from the same parts.

They're in geostationary orbit (35,786 kilometres above equator)

Earth explodes at 9km/s in all directions. Those chunks travel "upwards", reaching a maximum height of about 4,200km above the old surface, before reforming.

They'll wake up one morning, notice the internet is down, scratch their heads, look out the window, and notice Earth has become a ball of fire and lava and steam and ash clouds. When the ash settles and lava cools, they'll notice the continents have been shuffled.

---

Edit: After I posted this you added the 5kmps standard deviation. Meaning back or envelope about 40% of the mass escapes (but I suspect it will be much lower I'll explain below). it's reasonable to assume that the mass that escapes will be the smaller end of the chunk size spectrum, and overrepresents the crust and atmosphere. These chunks will be decelerated significantly by the climb, friction with the former atmosphere, and collisions with other chunks.

The pull of gravity will decay over the few hours it takes for the chunks to reach the space station (as less mass is below each chunk), this will cause the outer chunks to be decelerated more than the inner chunks, creating secondary collisions, reducing the chunk size further, and turning kinetic energy into heat.

This slows down the chunks significantly. With zero play between them you're looking at 0 - 3kmps impact speed for particles within 1 stddev. With secondary impacts, I'm guessing those parts of the crust that reach geostationary will be ground to dust / pebbles and moving 0-2kmps.

Under these modified conditions, your space station will probably get hit with hot gasses travelling at hypersonic speeds (remains of atmosphere, greatly reduced in density - the 2-3 stddev cases), then covered in dust on the underside with small particles (remains of fastest moving crust chunks), then hit with small pebbles travelling at about 1-2kmps. These will ding the hull, may be enough to breach weak sections and damage solar and radiators, but if crew quarters are not against the bottom wall, and no breaches or critical damage occurs, they still may not notice it immediately.

This does add a heat problem however, those hot gasses heated the ship. If the system is automatic and radiates heat into space automatically and has sufficient capacity they'll be alright. The iss has excess capacity to allow experiments and heat producing tasks.

When they look out of the window in the morning they will know what has happened - airborne chunks of planet will still be airborne, chunks of rock below them are slowly starting to fall back towards the planet.

But what if we add more power?

If you add a zero to the velocity of the chunks - big chunks go very high. If big chunks miss them, they'll transition into a solar orbit along with some of the debris - which could be very nice stable orbit or chaotic elliptical depending on exact time of day the planet blew. If they're self sufficient for food, water, and power, they could survive until they run out of spare parts for critical systems and their jerry-rigs fail. If stocked with enough spare parts or decent 3D printers, they might die of old age, perhaps even raise a second generation. The rest of their life will be spent avoiding orbital debris of Earth in adjacent solar orbits.

Answer 2

My answer to this question:

https://worldbuilding.stackexchange.com/questions/151398/aliens-blew-up-pluto-so-we-would-stop-debating-whether-or-not-to-call-it-a-plane[1]

Discusses whether Earth life would survive if Pluto was exploded.

As you can see, I tend to believe in the Endor Holocaust.

I may note that Pluto has a mass of 0.00218 Earth, so Earth is 458.7155963 times as massive as Pluto. Geostationary orbit is 35,786 kilometers above the equator. One Astronomical Unit or AU is 149,597,870.7 kilometers. Earth is 1 AU from the Sun, and Pluto is between 29.658 and 49.305 AU from the Sun, so the distance between Earth and Pluto varies between 28.658 and 50.305 AU. Taking the closest distance between Earth and Pluto for comparison, that would be about 4,287,175,779 kilometers, which is about 119,800.3627 times geostationary orbit at 35,786 kilometers.

The density of an expanding debris field should decrease with the cube of the distance, so when the debris from Earth reaches geostationary orbit it should be about 119,800 cubed times as dense as the degris from Pluto in my answer. So the debris from Earth reaching geostationary orbit should be about 1,719,374,300,000,000 times as dense as the debris from Pluto in my answer to: https://worldbuilding.stackexchange.com/questions/151398/aliens-blew-up-pluto-so-we-would-stop-debating-whether-or-not-to-call-it-a-plane[1]

And thus it should be much more likely to damage the space station in geostationary orbit.

Space stations in low Earth orbit are slowed by the extremely thin atmosphere hundreds of kilometers above the surface of Earth and slowly descend from their orbits, and so have to sometimes uses thrusters to boost themselves to higher orbits.

And it seems very, very, very probable to me that the explosion of Earth will move gases up to geostationary orbit which will be at least as dense as Earth's atmopshere in low Earth orbit. Thus the space station will slowly descend into regions were the gas is denser and will slow and descend faster and faster until it eventually crashes into the red hot surface of Earth.

And it seems quite possible to me that the exploding Earth will produce a gas layer at geostationary orbit which will be at least as dense as the atomsophere at the surface of the Earth. Ignoring whatever velocity that gas will have, a space station in geostationary orbit would have an orbital speed of 3.0746 kilometers per second. Running into gas with a density similar to sea level atmospheric pressure would be the equivalent of encountering sea level winds with a speed of 3.0746 kilometers per second, or 11,068.56 kilometers per hour.

And the space station would quickly heat up and vaporize like space junk reentering Earth's atmopshere.

Ash's answer says that the specified average velocity of Earth chunks of 9 kilometers per second would be less than the necessary escape velocity of 11.186 kilometers per second, and so the Earth maderial would mostly fall back to Earth. But there should be a wide range of velocities of Earth pieces, so that a significant percentage of them would be travelling at least 11.186 kilometers per second and thus eventually reach and pass geostatioary orbit. So the space station at geostationary orbit should encounter a significant density of gas and plasma particles.

Topcode said in a comment to his question that the material should deviate by 5 kilometers per second from the average speed of 9 kilometers per second. Thus the speed range would be between 4 kilometers per second and 14 kilometers per second and some of Earth's mass would definitately reach and pass geostationary orbit.

I note that at geostationary orbit the Earth should have an angular diameter of about about 33.80 degress, about 67.6 times the angular diameter of the Sun, and thus its surface would cover about 4,569.76 times the amount of the sky that the Sun did.

So if the space station received only 1/4569.76 as much energy from every square arc second of the Earth's surface as it received from each square arc second of the Sun's surface, it would receive as much energy from the Earth as it received from the Sun. Which would eventually overload the space station's cooling systems and everyone would die from the heat.

And the Earth would have just been exploded and many of the chunks would have eventually fallen back onto the Earth, and Earth would be red hot lava radiating a lot of energy into space, possibly for millennia.

Answer 3

in a short term, I think so.

in a long term... no.

here is my view of your scenario. if the space station is very modern, areas should be able to be closed off and hereby saving the crew.

but there will die slowly for what I can see. because;

1. they have lost their planet. meaning no place to go and no new way of getting oxygen, food, or fuel to the spaceship.
2. the food will only let them live for so long. even if only half of the crew survives.
3. I am pretty sure they will lose oxygen before food, but I am no expert so that this with a gram of salt.

if they are going somehow survive. they either need to find another spaceship or get back to the planet of hope for the best there. those are the only scenes I can possibly see them survive in the long run.

Answer 4

Most likely.

I don't see why they shouldn't. Resupply runs for the ISS are less frequent then every month (see here). Given that ISS doesn't have this revolutionary SuperPlantX™, your SS (not the best abbreviation) would last quite a while.

The other thing is being hit by Earth chunks. In that case, it all really depends on where the chunks hit and how big they are.

Answer 5

With speed of 9km/s, and deviation of +-5km/s on top of that, only about 2%-5% will get as high as your GEO station. And it will be moving at only about 1km/s when it passes the orbit.

Your station is 3x the size of the current ISS. So about 300m diameter. Surface area about 70000m2 Total 'surface' of GEO sphere = 7.44×10^17m2 So only about 1 part in 10^13 of the ejecta that passes GEO, hits you.

Total mass that passes by GEO distance =
5% of Earth mass 5,972 × 10^24 kg = 2.986 x 10^23kg

1 part in 10^13 of this is 2.986e+10

Your spacestation is HIT BY 29.86 MILLION TONS of debris, moving at about the speed of an anti-tank cannon projectile.

NO, you would not survive that!

Answer 6

I'll take a look at it from after the survival of the initial explosion (by whatever means). The biggest question here is how much of the earth's mass is intact? It is the earth's mass that kept the station in orbit. Even if the earth didn't lose all its mass, the station would be set adrift (not even considering any forces like expanding gasses pushing it away). Not tied to the earth, the station would also not be tied to the sun. The station will eventually exit the solar system. Based on trajectory, it could be out of the solar disc quite quickly. The station could be exiting at speeds exceeding 1,000 mph an estimate based on earth's rotation. The current space station is not in geostationary orbit and moves at 17,500 mph (28,000 km/h).

Alternatively, it could be headed into the sun! To my knowledge, stations are better at being stationary than stellar propulsion.