Multiply by 60 to get light seconds per scale inch.
Multiply by C (speed of light) to get answer in whatever unit of measure you use for C. I use 186000 miles per second. Multiply by the paper line width. That's the width of the line, to scale.
Cook math. Order of magnitude. Close enough. I don't launch Mars orbiters, and if I did, I'd keep the units the same, even if we were using furlongs per fortnight.
You're scaling the line up to "actual size", with units unspecified, which begs the question. That question is namely, what is the ratio of the major and minor axes of earth's orbit? and how does it compare with the ratio of an 0.5 mm pencil line to an 8" diameter drawn circle?