How Big Is A Light Year?

Question

Some say it is 100 million marathons! Others say it is 100 billion marathons across!

Answer 1

A light-year is the distance traversed by light in a year.

Since you are looking only for an order-of-magnitude approximation,

I will use approximate numbers.

Let

v ≈ 3×10⁵ km/s be the speed of light

t ≈ 10⁷π s be the length of a year in seconds

h ≈ 42 km be the length of a marathon.

So the number of marathons in a light year is

vt/h = 3×10⁵×10⁷π / 42 ≈ 2×10¹¹

So the estimate of 100 billion marathons is closer to reality.