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There are a few theories as to the causes of glaciation.
There's the Milankovitch Theory, which says that there are cyclical changes in Earth's orbit and in the tilt of Earth's axis that occur over thousands of years and cause climate changes.
Some scientists believe that the solar energy made by the sun is not constant and that may be why it gets so cold that glaciers form sometimes.
Others say that when volcanic dust blocks the sun's rays, making it harder for solar radiation to reach Earth's surface.

While the first one can't exactly be proven, it can't be disproven either, and is the theory most go with. So why or why don't the second and third theories work/what makes them less popular?

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Your question is framed as if any model of glaciation were only allowed to consider one of those influences. I think practically any palaeoclimatologist would accept that astronomical forcing, solar output, and volcanic eruptions all have effects on glaciation. It's true, however, that on long timescales (tens of kiloyears and up), Milankovitch forcing generally gets more attention than the other two you mention. There are further important drivers of glaciation which you don't mention. Perhaps the most obvious is greenhouse gas concentration: if atmospheric levels of CO2, methane, and other greenhouse gases drop, the Earth cools and glaciation becomes more likely (see e.g. DeConto and Pollard, 2003). Another influence is tectonics and geography, the best-known example perhaps being the theory that Antarctic glaciation was caused by the break-up of Gondwana, which left Antarctica thermally isolated (Kennett, 1977).

To return to your main question, there's a good reason to consider Milankovitch forcing as a (or the) dominant driver of glaciation on longer timescales: it's simply that glaciation (as deduced from δ18O records) varies in time with the astronomical cycles. Hays et al. (1976) is one of the classic papers on this, and they sum the situation up neatly:

Over the frequency range 10−4 to 10−5 cycle per year, climatic variance of these records is concentrated in three discrete spectral peaks at periods of 23,000, 42,000, and approximately 100,000 years. These peaks correspond to the dominant periods of the earth's solar orbit, and contain respectively about 10, 25, and 50 percent of the climatic variance.

To put it another way: if you want to discount astronomical forcing and attribute those variations to (say) volcanic aerosols, you need to explain why you have volcanoes going off at precise 42,000-year intervals. This isn't to say that we fully understand how these drivers interact with the climate system yet (the 100,000-year problem is perhaps the best-known "wrinkle" in the theory), but the fact remains that if your glaciations are dancing to 23, 42, and 100-kiloyear beats, and your solar system happens to be providing beats at precisely those frequencies, there's probably a pretty strong connection there.

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