Can one million Earths fit inside the sun? Yes & no!
By MUNGAI KIHANYA
The Sunday Nation
Nairobi,
19 February 2023
A reader asked me to confirm whether a post he saw on Twitter claiming
that 1.3 million Earths can fit inside the sun was correct. Well, it is
(somewhat) true; I wrote about it in October 2012.
At 1.5 million kilometres, the diameter of the sun is about 109 times
that of Earth (12,800km). Since the volume of a sphere is proportional
to the cube of its diameter, it turns out that the volume of the sun is
109 x 109 x 109 = 1,295,029 (about 1.3 million) times that of Earth.
However, this calculation assumes that the 1.3 million Earths are melted
and poured into the sun. Earth is spherical and when spheres are packed
in a closed place, they leave a lot of empty space. The volume of that
unoccupied regions depends the arrangement of the spheres.
Suppose that 1cm radius (2cm diameter) spheres are arranged in a cubic
pattern; that is, with their centres are at each of the 8 corners of a
cube. In that arrangement, the cube will have sides measuring 2cm each
and only an eighth (NB: not a quarter) of each sphere will be inside the
cube.
The volume of the cube will be 2 x 2 x 2 = 8 cubic cm (8cc). The volume
of each sphere is “fourthirdspircubed” which comes to about 4.19cc.
Now each sphere contributes an eighth inside the cube so eight eighths
make a whole. Thus, out of the 8cc volume of the cube, only 4.19cc is
occupied by the spheres. This comes to about 52 per cent. The rest (48
per cent) is empty space!
When this cubic arrangement is repeated over a wide space, the
fillfactor of 52 per cent is maintained throughout since every cube is
identical to all others. Obviously, this is not a very efficient way to
arrange spheres. If the Earths are arranged this way inside the sun,
only 678,000 would fit.
The most efficient arrangement would start with three spheres arranged
in a triangle and then a fourth one on top and the at the centre to form
a triangular pyramid. This is also known as a tetrahedron, or a tetra
pack. The calculation of the fillfactor is more involved than that of a
cubic pattern, but it turns that to be about 74 per cent. Thus, the
largest number of Earths that can fit inside the sun is about
958,000…perhaps we call that one million.
