How many times round the world is a light year?

This question was inspired by a student in one of my lessons on Standard Form*. He asked "how far around the world would I have to go before I travelled a light year?"

To make this simple, and because we're only looking for a ball-park figure, I'm going to use heavily rounded numbers in this post!

What is a light year?
See this post for a slightly more in-depth look at what a light year is, but a light year is a unit of distance that equates to about  9.5 x 1015 metres.

That's a '95' with fourteen zeroes after it: 9,500,000,000,000,000 metres, or nine-and-a-half quadrillion metres.

I've tried to give that number some context or clarity by stating it in different ways, but in reality it probably doesn't mean much to you: it sure as hell doesn't to me. It's just too big. In the post linked to at the beginning of this section I offered some further examples, but they all use other units that are far too big to comprehend. So lets try bringing it down to size a bit: if we look at it in kilometres, it's only a paltry 9,500,000,000,000 (nine-and-a-half trillion) of those. The image above (Credit: NASA/CXC/SAO) is of Proxima Centauri, the closest star (other than the Sun) to Earth, which is about four light years away.

How far is it around the world?
Earth's radius (the distance from its centre to the crust) is, on average, a bit less than 6,500 km. If we assume that the Earth is a perfect sphere we can use that trusty formula from GCSE maths, C = 2 x π x r to find the distance around its equator, where r = radius of the Earth: 2 x π x 6,500 = 40,000 km (ish).

So how many times would we have to travel around the world before we could say we'd travelled a light year?
  • A light year measures around 9,500,000,000,000 km.
  • One trip around the world is about 41,000 km

Divide one by t'other and we'll find out how many times a trip around the world would fit into a light year:

9,500,000,000,000 / 41,000 = 2.31707 x 108

That's about 200,000,000 (two hundred million). So we'd have to book two hundred million round-the-world trips to be able to say that we'd travelled a light year.

I wonder how much that'd cost...

* 'Standard Form' is a way of writing numbers that takes up less space (most of the time). For example, the number 5,000,000,000,000,000,000,000,000 can be written 5 x 1024, which takes up much less space on twitter. If you'd like a better post on Standard Form, you'd be better off asking for one over at MathsQS.


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