BAFact math: How bright is the Sun from Pluto?

# BAFact math: How bright is the Sun from Pluto?

The entire universe in blog form
March 15 2012 11:07 AM

# BAFact math: How bright is the Sun from Pluto?

[On January 4, 2012, I started a new features: BAFacts, where I write an astronomy/space fact that is short enough to be tweeted. A lot of them reference older posts, but some of the facts need a little mathematical explanation. When that happens I'll write a post like this one that does the math so you can see the numbers for yourself. Why? Because MATH!]

Phil Plait

Phil Plait writes Slate’s Bad Astronomy blog and is an astronomer, public speaker, science evangelizer, and author of Death From the Skies!

Today's BAFact:

From Pluto, the Sun is fainter than it is from Earth, but still can be 450x brighter than the full Moon.

I remember reading a science fiction story many years ago which took place on Pluto. The author described the Sun as being so faint that it looked like just another bright star (too bad I don't remember the name of the story anymore). I was thinking about that again recently, and wondered just how bright the Sun does look from Pluto. This turns out to be pretty easy to calculate!

First, you need to understand how an object like the Sun -- really, any source of light -- dims with distance. The Sun emits light in all directions, so as you get farther away from the Sun, that light gets spread out. Imagine a sphere perfectly encasing the Sun right at its surface. Each square centimeter has a certain amount of light passing through it. If I double the size of the sphere, there's a lot more surface area to that sphere, but the total amount of light passing through it hasn't changed. Therefore the amount of light passing through each square centimeter has dropped. Since I doubled the sphere's diameter, I can figure out how much its dropped, too!

The formula for the surface area of a sphere is

Surface area = 4 × π × radius 2

If I double the size of the sphere, everything on the right side of the equation stays the same except for the radius, which is now twice as big. Therefore the area increases by 22 = 4. So the light passing through each square centimeter of the bigger sphere drops by a factor of four. Someone standing on that sphere would see the Sun being 1/4 as bright as if they were on the surface.

If I make the sphere ten times bigger, the area goes up by 10 × 10 = 100 times, and the brightness drops by 100. You get the picture.

So now we're ready to figure out how bright the Sun is from Pluto!