I love astronomy stuff, not an expert at all, but have always been so fascinated by it. I am totally baffled by how we seem to claim that we can approximate how long the sun has been around. Like the margin of error for a number like that is crazy…. totally incomprehensible to me. Say that we are 25% off, that means we are over 1 billion years off. So, how do people confidently claim that the sun is 4.6 billion years, rather than 3 billion or 10 billion?
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Our Sun and all of the objects in its solar system were formed at roughly the same time in astronomical terms (a few hundred thousand to a few millions of years). So all of the matter is about the same age.
Moreover, the matter clumps differently at different distances from the Sun’s gravitational center. Objects closest to the Sun (such Mercury, Venus, and Earth) are quite dense, while the objects farther out are much less dense (such as Jupiter, Saturn, Neptune, and Uranus). Even though these objects have different amounts of elements (with the heaviest elements being found in greater proportion closer to the sun), all of those elements are about the same age.
So what is their age? In the case of elements that have a radioactive half-life, we can calculate how much decay has taken place. Isotopes of these elements have different rates of decay. For instance, carbon-14 decays quite rapidly (thousands of years) so it doesn’t surprise that most of this has all decayed. Carbon-12, in constrast, is stable and it doesn’t surprise us that it’s all still here. How much of each isotope is left can be used to calculate how long it’s been here.
One important element to look at is lead (Pb). Lead is formed when uranium decays, so the ratio of Pb-207 to Pb-206 changes because U-235 decays to Pb-207 and U-238 decays to Pb-206. By comparing these, we can figure out how they have been hanging around, and the number comes to about 4.54 billion years.
We can check our math by comparing really old stuff like meteorites. We know how old they are by how much of each kind of lead isotope they have. The oldest ones seem to be about 4.568 billion years old if we do that. So this might be the higher possible age of the solar system and the Sun.
We can also check our math with rocks from the Moon, which hasn’t had the same biological and geological action as rocks on Earth. If we calculate based on those rocks, we get an age 4.51 billion years, which is probably the lower possible age of the solar system.
That’s really a pretty tight range on astronomical scales, so we can be quite confident the actual age is within that narrow range. However, we can do even better than that.
Remember we compared the proportion of isotopes U-238 to U-235 and assumed that this proportion was about the same through the solar system. However, in places where curium (which has a very short half-life) we find a little more U-235 than we expected. That’s because curium also decays to U-235. This helps us be even more confident of our estimation of the age of the Sun. We sometimes want to account for the Sun being formed slightly earlier than the planets, so we add a little extra and use a age of 4.6 billion years.
Oversimplified TL;DR: We can calculate how old the Sun is quite precisely by looking at how old the different rocks are.
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