If the earth was reduced to the size of an atom how big would the galaxy be?

Question

Josiah Adams · Accepted Answer

#x=((1xx10^(-10))(1xx10^21))/12742000=(1xx10^11)/12742000~=7848m~~8km#

We have a ratio question - given the size of the Earth and reducing it to the size of an atom, how big will the galaxy be? That looks like:

#"Earth"/"atom"="galaxy"/x#

So first off we can solve for x:

#x=("atom"xx"galaxy")/"Earth"#

And now we need to make a decision - the size of an atom depends on which atom we're talking about. They typically run between #0.1 to 0.5# nanometres. I'm going to assume we're using a smaller atom (it'll make the math easier).

And now let's get some numbers:

#"Earth"=12,742 km=12,742,000 m#

https://tutor.hix.ai

#"Atom"= 1 xx 10^-10 m#

https://tutor.hix.ai

#"Galaxy" = 1,000,000,000,000,000,000,000=1xx10^21m#

https://tutor.hix.ai

And now the math:

#x=((1xx10^(-10))(1xx10^21))/12742000=(1xx10^11)/12742000~=7848m~~8km#

Josiah Adams · Answer

undefined The Milky Way galaxy would remain roughly the same size if Earth were shrunk to the size of an atom because an atom is incredibly small in comparison to a galaxy's enormous scale.