How Big Are You In The Grand Scheme of Things?

One of the joys of being a window cleaner is that you get plenty of time to let your mind wander whilst you work. This is where my mind wandered the other day:

The Universe is pretty big, in fact I would go further and say it's ridiculously enormous. Browsing around the internet it does appear that there is no absolute agreement on just how ridiculously enormous it is, but there seems to be some consensus that the furthest objects we have thus been able to observe are somewhere in the vicinity of 13.8 billion light years away. So I am going to take that as my universe radius figure. "Hold your horses", I hear you cry, "you're assuming that we are the centre of the Universe!" Yes, yes I am, it just makes things easier, as will become clear shortly.

Assuming that light travels 9.46 billion kilometres a year, that gives us a universe radius of 130,548,000,000,000,000,000 kilometres. Wait, there's more.

The Earth has a mean radius of 6,371 kilometres, which means that the universe is 20,490,974,729,241,900 times bigger than our little planet.

Here's where I hope my calculations hold up because I want to try and work out how big the Earth would be if the Universe was reduced to its (the Earth's) size. Don't ask me why, I told you, my mind wanders when I am at work.

I have divided the Earth's radius (6371 km) by 20,490,974,729,241,900 to get a distance in kilometres of 3.11x10^-13 (I hope my notation format is correct, or at least acceptable. Please let me know if not...) That means the Earth's diameter is 6.22x10^-13 kilometres.

Now if assuming that any of the forgoing is right, how big am I in this tiny universe? Well, I'm about .00183 kilometres tall, so applying the same factor of tinyfication (2x10^16) I am about 8.93x10^-23 metres tall. Which I think is about the size of an electron, or something.

Now, I am not a physicist or a mathmatician (I did get grades C and B respectively at O level, but that was twenty six years ago) so I am not holding out a lot of hope that these figure are accurate or that I have used the correct notation system for my numbers, or that I haven't mixed my units to end up with a nonsensical conclusion, however I did come across this thread whilst browsing for some information which makes me think I'm not a million miles away from a ballpark figure of some sort.

I'll leave that with you...