[thedoc (OP)]

Luke asked the Naked Scientists:
   My question is about a scenario of the Earth suddenly being alone in space with only the moon orbiting it, no sun no galaxy and no other planets. It's actually a couple questions. My first question about the scenario is how long would it take for the surface of the planet to freeze, and how long for the core to freeze, I know that in a vacuum it would have to cool by radiation, but on the scale of an entire planet. My second question would be about orbital and gravitational shifts, since there is no longer a sun or galaxy to apply gravitational force to the Earth and moon I assume it would just continue in its current orbital trajectory until it reaches its next apsis when I think it would go off in a straight line. But what would happen to the earths rotation after that? How would that disrupt the Earth's gravity and the moons orbit of the Earth? I know it's a lot but I'm really curious as to what would happen to the Earth and the moon if suddenly it was alone in space. Thank you - Luke
What do you think?

[chiralSPO]

First, the easy part, Earth's trajectory:

The Earth and moon would continue to orbit their shared center of mass, as they have done for billions of years. With no other gravitational bodies to consider, that shared center of mass will continue to move in a straight line at whatever the initial velocity was. But, since there are no other bodies to compare against, we may as well say that the center of mass is the center of the universe, and is stationary (yay, back to a roughly geocentric universe!)

The Earth's rotation will continue as it had before essentially unchanged, completing one full rotation once every 24 hours or so, but since there is no sun, there will be no daylight.

Now for a start on the harder part (presumably others will take it further than I can):

Surface temperatures will fall very quickly. Think about how quickly it gets cold going from day to night now. Say it's 5 °C when the sun sets, and falls to –8 °C by the time the sun should rise again. But the sun doesn't come. So the temperature just keeps falling. It won't be a linear decline--the surface will radiate less and less energy as it gets colder, and there will be a few plateaus as various phase changes occur--as the oceans freeze, as the mantle and core solidify, as the atmosphere condenses etc.

Depending on how much math you know, or want to learn, and how much effort you want to put in, you could model the Earth as a blackbody, and calculate some projected temperature curves based on the initial surface temp, surface area and heat capacity, and the equations shown here: https://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law

Good luck!

[Colin2B]

I assume it would just continue in its current orbital trajectory until it reaches its next apsis when I think it would go off in a straight line.

Hi Luke
Without the sun to keep it in circular orbit the earth/moon system would go off in straight line immediatly.
Without the sun, the orbit of the earth and moon around a common centre of mass should change to a simpler rotation. Without the sun the tides would also change with no spring or neap tides, less variation.
I'm sure there are others who will add a lot more detail + the cooling, which I think will be very rapid.

EDIT: Whoops Chiral, looks as though our answers collided

[alancalverd]

Hot deserts like the Sahara can freeze overnight in the absence of clouds. Once you remove the external heat source (the sun) there's no mechanism to make clouds or move air masses around, so my guess is the land surface would freeze in a week or so. The specific heat capacity of water is 5 - 10 times greater than that of rock and its emissivity about one fifth, so it might be a year or two before the oceans freeze over, but that would happen very quickly once it began because the anomalous convection of water below 4 deg C would bring cold water to the surface.

Deep down, however, the earth is heated by radioactive decay and is at a very high temperature - molten iron - so we would be talking about billions of years for any noticeable cooling below about 100 meters depth.

If the sun were to disappear instead of just stop shining, the planet would move off at a tangent to its present orbital position until it collided with something else or got sucked into another solar system.