Imagine, for a moment, that you are an intrepid space explorer, jaunting through the solar system for adventure and, if there’s time, scientific exploration. After launching from Earth in your rocket ship, you eventually find yourself on the surface of formerly-known-as-a-planet Pluto, gazing upward at the stars. Earth now lies six billion kilometers sunward, faded to invisibility by the distance, and you struggle in vain to even identify the sun. It’s lost—one star among countless thousands, or so an old sci-fi trope would have you believe.
I’ve heard versions of this vignette many times, but there’s one small problem with it: it’s wrong.
The sun is indeed a star not so very different from many billions of others in the Milky Way. To us humans, though, what matters most is its proximity. Earth resides in a fairly circular orbit around the sun at a distance of 150 million kilometers (give or take a few million at perihelion and aphelion)—so close on an astronomical scale that the sun is by far the brightest object in the sky. Even a furtive glance at its radiance makes your eyes water and can damage your retinas.
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But what about the view from Pluto? That icy world is much farther out, so the sun should appear dimmer. But how dim is “dim”? We can figure that out!
Like all stars, the sun emits light in every direction. Anyone at the same distance from the sun will therefore see it shining with exactly the same brightness. That fixed distance defines the surface of a sphere—for example, one with a radius equal to that of Earth’s orbit.
Now imagine someone who is twice as far from the sun. Our star’s emitted light now encompasses a much larger spherical surface and has been…
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