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How Does the Photon Density From a Star Change With Distance?

-- David | November 19, 2021

Question:

I have a question about the dispersal of light from a star: How can we possibly see the light from sources over a billion light years away?

Our own star puts out 1 e+45 photons a second. As those photons travel out into space they expand and separate. Some rough calculations on my part indicate that somewhere around 941,000 light years the photon density would have decreased to 1 photon per square meter, on average. I know our star is not the largest or most energetic, but the thought of being able to see photons from billions of light years away seems like it would be impossible. I know a galaxy would have more stars, but those individual star’s photons do not add to the energy of the other stars.

-- David

Answer:

I believe that your question has been answered on the Physics Stack Exchange. For a star of radius R at distance L the solid angle that the photons from the star will cover will scale as (R/L)^2, which is also the percentage of the retina in your eye that will receive photons. Since the number of photons from the star that are received by your eye also scales as (R/L)^2, the ratio of these two expressions, which gives you the number of photons per unit area, is independent of the distance L.

-- Jeff Mangum

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