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I have read that the estimated age of our Milky Way galaxy is 13.61 billion years which is by using our current size and status of our galaxy about 59.17 Galactic years which each galactic year representing the time taken our sun to make a full rotation around the current galactic center (i.e. 230 million years).

However, since our galaxy has started with a much smaller size and evolved and also known that the age of the Earth is 4.543 billion years, I am asking if there is way to estimate how many full rotations around the galactic center Earth has done so far since its creation?

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There is no guarantee or likelihood that the Sun was in its present orbit in the past. In fact it is more likely that it has migrated to its present position ($r \simeq 8$ kpc) from a smaller galactocentric radius ($4<r<7$ kpc). This is inferred from the fact that the Sun has a larger metallicity than most of the stars in its current neighbourhood together with the fact that there is a negative metallicity gradient with galactocentric radius (e.g. Minchev et al. 2013; although others disagree - see Martinez-Barbosa et al. 2015).

That being so (and it is by no means certain), and with the Galactic rotation curve being approximately flat, this means that the orbital velocity at smaller galactocentric radius was the same, so the orbital period would have been shorter.

In other words, it is likely that the Sun has executed more circuits of the Galaxy than 4.57 billion/230 million $\simeq 20$ and perhaps as many as $\simeq 30$.

You are right that the Milky Way has evolved over time, but I think its gravitational potential has probably been reasonably settled for the last 5 billion years.

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  • $\begingroup$ It is intriguing to learn that our sun has turned around the galaxy about just 30 times since the creation of planet Earth! Reminds me of clockwork, another 30 minutes and then...BOOM!!?... :) or more precisely it will condense to a white dwarf after the explosion. $\endgroup$
    – Markoul11
    Commented Feb 1, 2022 at 14:37

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