This comment was posted to reddit on Jan 28, 2015 at 10:03 pm and was deleted within 14 minutes.

If a you stack a bunch of spheres, they don't take the entire volume. Think of all the air in a gumball machine. According to Wikipedia[1] depending on the model, somewhere between 25 and 48% of the larger sphere would be empty space. For randomly pouring them in, its most likely to be around 38% empty. Ignoring packing fraction, V = 1,000,000v And 4/3 pi R3= 1e6 * 4/3 pi r3 So R= (1e6)1/3 * r = 100 r Taking into account packing fraction, to fit 1 million spheres in a sphere, V = 1,000,000/(1-.38)

v Which means R3=1.61e6r3 And R=117 r So there would be 117 marbles across the diameter of the larger sphere if you put 1 million marbles in it. The diamter of the sun is actually 109 times bigger than the earth (1,391,684 km vs 12,742 km). We can figure out how many earths actually fit in the sun too. V * .62 = X * v X = R3 /r3 *.62 = 806,603 earths inside the sun Ignoring packing fraction its around 1.3 million.

This is true.

If a you stack a bunch of spheres, they don't take the entire volume. Think of all the air in a gumball machine. According to Wikipedia[1] depending on the model, somewhere between 25 and 48% of the larger sphere would be empty space. For randomly pouring them in, its most likely to be around 38% empty.
Ignoring packing fraction, V = 1,000,000v
And 4/3 pi R3= 1e6 * 4/3 pi r3
So R= (1e6)1/3 * r = 100 r
Taking into account packing fraction, to fit 1 million spheres in a sphere, V = 1,000,000/(1-.38)*v
Which means R3=1.61e6*r3
And R=117 r
So there would be 117 marbles across the diameter of the larger sphere if you put 1 million marbles in it. The diamter of the sun is actually 109 times bigger than the earth (1,391,684 km vs 12,742 km).
We can figure out how many earths actually fit in the sun too.
V * .62 = X * v
X = R3 /r3 *.62 = 806,603 earths inside the sun
Ignoring packing fraction its around 1.3 million.