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I have read that the lifetime of stars is much less than the period of rotation for a spiral galaxy. For example https://www.coursera.org/learn/evolvinguniverse/lecture/wlYhz/the-origin-of-spiral-arms the professor uses the existence of young blue stars whose creation is triggered by a persistent density wave to claim that the stars lifetime is less than the rotation period. I am not satisfied with this. Given the enormous timescale, how do we know this?

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We know how long stars take to orbit in a spiral galaxy, because we know how big galaxies are (we can measure the size by knowing the distance using various methods such as Cepheid variables, and type Ia supernovae) and we know how fast the stars are moving. (We can measure the velocity of stars using the doppler method)

We know how long stars last for because we have a good model of how stars work. We can use this model to predict that large, hot stars will burn themselves out in a short time. We can verify this model by looking at the numbers of blue stars, red supergiants and supernovae.

From the first part we know that stars take about 250 million years to complete an orbit of the Milky way (which is typical for similar sized galaxies) From the second part, we know that giant blue stars live for only tens of million years, and so could not complete a full orbit of the milky way.

On the other hand, smaller stars like the sun live for billions of years and so make multiple orbits.

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