Where Are the Sun’s First Photons Today?

The Sun has been shining for about 4.603 billion years. At first glance, the answer seems simple: the very first photons emitted by the Sun should now be 4.5 billion light-years away, since light travels one light-year every year.

But the universe does not sit still.

Space itself is expanding, which means distances in our universe do not act as they would in a static cosmos. This is why the observable universe is not merely 13.8 billion light-years across, even though the universe is about 13.8 billion years old. Its observable radius is actually around 46.5 billion light-years, roughly 3.37 times larger than a naive “age times speed of light” estimate would suggest.

The same idea applies to the earliest photons emitted by the Sun. As those photons travel away from us, the space between them and the Sun continues to stretch. The farther they get, the more space there is in between, the more expansion contributes to their distance.

Astronomers estimate the expansion rate of the universe using measurements such as the average stellar luminosity of giant elliptical galaxies. One value obtained in this way is about 73.3 kilometers per second per megaparsec. In other words, for every megaparsec—about 3.3 million light-years—space expands by 73.3 kilometers per second.

Expressed differently, this corresponds to an expansion rate of approximately 2.35 × 10⁻¹⁸ per second, or about 0.074 per billion years.

So, to estimate where the Sun’s first photons are today, we can model their motion with the following differential equation: v(t) = x′(t) = c + rx(t), with the initial condition x(0) = 0.

Here, t is time, x(t) is the photon’s distance from the Sun, x′(t) is its recession speed, c is the speed of light, and r is the expansion rate of space.

The solution is x(t) = c/r · (eʳᵗ − 1).

Now we insert the values: c = 1, meaning one light-year per year; r = 0.074 × 10⁻⁹ per year; and t = 4.603 × 10⁹ years.

This gives rt ≈ 0.34, and therefore x = (1.40 − 1) / (0.074 × 10⁻⁹), which gives approximately 5.5 × 10⁹ light-years.

So the first photons ever emitted by the Sun are not merely 4.6 billion light-years away. Because the universe has expanded while they were traveling, they are now roughly 5.5 billion light-years from the Sun.

A tiny beam of ancient sunlight has been crossing the cosmos for the entire lifetime of our star—and space itself has been quietly stretching beneath it the whole time.