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Will the Earth be colder in a billion years?
Answer 1:

Great question! Models for the earth’s heat flux (basically a measure of how fast the earth is losing heat) definitely predict that it will be colder in a billion years, just as it is colder today than it was a billion years ago. This is because the earth is losing heat faster than it gains it from sources such as the sun’s radiation. Geophysical studies show that the mean heat flux of the earth is about 87 milliwatts per square meter– that’s 44 trillion Watts of heat flow for the whole earth (Francis & Oppenheimer, 2004, and references therein). Even though we are losing heat on the long-term, our atmosphere is definitely heating up on the short term

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There are two major sources of the earth’s heat– accretionary energy and radioactive decay. The earth formed about 4.6 billions years ago by the gravitational attraction of smaller bodies (planetesimals). As this material in our solar nebula came together, the gravitational potential energy was converted to heat energy. More heat was liberated when the earth’s core and mantle formed, or differentiated. This accretionary energy has slowly been lost through convection and conduction from the core and the mantle through the crust, and eventually radiation out into space.

The most important source of heat in the earth’s crust is the decay of radioactive isotopes, primarily 40K (potassium), 238Uranium, 235Uranium, and 232Thorium. These isotopes (especially 40K) are abundant in the crust, and they release a lot of heat as they decay to their stable daughter isotopes. They were formed in stars and supernovae long before the earth was formed. Their budget in the earth is limited, and they decay exponentially, so there is less and less heat producing isotopes in the crust over time.

Eventually the earth will be so cold that plate tectonics will not be able to operate. This will have serious consequences for the atmosphere and water on the surface of the earth, and therefore life. DON’T WORRY! The earth is cooling at a rate of only ~100 C per billion years (Francis & Oppenheimer, 2004), so it won’t be noticeably colder for quite some time.

References
Francis, P. & Oppenheimer, C. (2004). Volcanoes. Oxford: Oxford University Press.


Answer 2:

There are many factors that influence the Earth's temperature, and a lot can happen in a billion years. Many astronomers believe the Earth will become too hot to sustain life in ~0.5 billion years, as the sun will change and get too hot for our liking. That said, here are a couple things to consider.

If we took a simple model where we looked only at the Earth, it is likely that the world will be colder in a billion years. One of the largest sources of heat for the planet is the radioactive decay of Uranium, Thorium, and Potassium. The Earth loses a lot of heat (energy) to the void of space, in a similar way that you lose heat to the air if the air is cold and you're warm. (It's not quite the same, but the idea is similar, in that if something is hot and it's surrounded by something cold, the hot object will lose heat through one of several possible ways.) If it wasn't for the radioactive decay of these elements, the Earth would have already cooled down after less than 100 million years. (The earth is 4.5 billion years old). At the same time, the Earth is slowly moving away from the sun, which will cause a slight cooling.

However, over the course of 0.5-1 billion years, it's expected that the sun will run out of hydrogen and will become a red dwarf (i.e. it will become larger and hotter), causing the temperature of the Earth to increase and the oceans to evaporate. Things don't look good for us long-term.


Answer 3:

The Earth will almost certainly be a great deal hotter in a billion years, because the sun will be quite a bit brighter in a billion years. Exactly how hot the Earth will be by then I don't think we know at this time (e.g. will life on Earth still exist a billion years from now?), but it will be hotter than it is now.



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