Light crosses the Milky Way's disc of stars from one edge to the other. How many years does that trip take?

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Answer

About 100,000 years

The Sun sits roughly 26,000 light-years from the galactic centre and needs about 230 million years to complete a single lap around it.

How to estimate it

Light covers one light-year per year, so the answer equals the disc's width in light-years. Take 100 billion stars, each claiming about 100 cubic light-years as near the Sun: 10 trillion cubic light-years. A disc 1,000 light-years thick then has an area of 10 billion square light-years, which means a diameter near 110,000 light-years. The accepted crossing time is about 100,000 years.

Source: NASA

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