Divine Angel said:
Last night I dreamed that something had a near miss of the Earth but nudged us out of stable orbit. Our end of days was going to be a fiery collision into the sun. In the dream, we only had about 10 days before the demise of the planet. I got to the part where the sun was huge, it was getting pretty warm and water was evaporating quickly. I woke up before anything happened though.
Obviously dream-physics are a bit off, but I was wondering how would we would die in that scenario? I think it’s likely to be due to heat rather than the lack of water first. And in a time span of 10 days before collision, about what day would we die? Day 3?
I used to be good at answering questions like these. Let’s see if I still am. I calculated recently the the solar system’s Oort Cloud was quite unlikely because since the time of the solar system’s formation, the probability of another star passing through the nearer part of the Oort Cloud exceeded 80%, and any such traverse would have had a catastrophic effect on the Oort Cloud.
Now let’s suppose that the destabilisation of the Earth’s orbit was due to an unrelated star passing closer in through the solar system than the above. If such a star was slightly smaller in mass than the Sun then its radiation would be much smaller and we would survive the initial stellar pass. The Earth’s orbit could easily be destabilised to the point where its innermost part is inside that of Venus, but it wouldn’t crash into the Sun itself.
An alternative would be if the solar system passed through a thick cloud of dust and gas. The hydrodynamic drag of the Earth moving in its orbit through this would cause the orbit to decay, causing it to spiral into the Sun, but slowly.
Now let’s set the origin of the loss of orbit aside and postulate as above an Earth travelling in towards the Sun. We can either assume a uniform velocity due to the original kick in the orbital direction or an acceleration of velocity due to the Sun’s gravity. I’m going to assume a uniform velocity.
The amount of energy received from the Sun is proportional to the inverse square of the distance from the Sun. The amount of energy radiated by the Earth is proportional to the surface temperature in Kelvin to the fourth power. Ignoring transient effects such as evaporation for the moment, the balance between energy received and that radiated means that the Earth’s surface temperature increases as the inverse square root of the orbital radius. So to a first approximation the average (day + night, equator to pole) surface temperature of the Earth is:
Day , Temperature(Celcius)
0 , 15
1 , 31
2 , 49
3 , 71
4 , 99
5 , 134
6 , 182
7 , 253
8 , 371
9 , 638
Even after day 9 we’re nowhere near melting the rocks of the Earth’s crust.
Evaporation of the oceans will cool this slightly, Can I determine by how much?
By day 4, 1% of the Earth’s oceans have evaporated, by day 7 that’s 6%, by day 8 that’s 13% and by day 9 it’s 40%.
Evaporation of the Earth’s oceans will tend to keep the surface temperature at 100 Celsius while the evaporation continues, so even by day 9 the average surface temperature on the Earth could still be very close to 100 Celsius.
What about death? Without air conditioning 50 Celsius over a sufficiently long time will cause serious burns. So that’s a death due to high temperature on about day 2. With air conditioning, a typical air conditioning temperature drop is about 12 Celsius which is half way through day 2.