I’ll give it a shot, but I think it will make more sense for me to make the conversion from meters to years without using light years. I’m a chemist, not a physicist and don’t want to look up the conversions I don’t remember.

The sun travels ~940,000,000 km/human year…

= 940,000,000 km/yr × 1000 m/km = 940,000,000,000 m/yr

= 940,000,000,000 m/yr × 1 year/365.256 days

= 2573537464.1 m/day × 1 day/24 hr × 1 hr/60 min × 1 min/60 s

= 29786.3132423 m/s

16 m × 1 s/29786.3132423 m = 0.000537 s (human)

The dog is about half a millisecond old (in human years).

I found some human-to-dog years calculator online that cites a scientific paper. The formula it uses is:

Human years = 16 × ln(Dog years) + 31

Therefore… Dog years = e^(((Human Years-31)^)/16)

To use the dog calculator, it’s easier to start back at m/yr.

16 m × 1 year/940,000,000,000 m = 1.70212765E−11 human years

Human to dog years = e^{(((1.70212765E−11)}-31)/16)

= 0.14406 dog years x 365.524 dog days / 1 dog year

= 52.6 dog days.

The human to dog year equation isn’t meant for times less than 0.001 human year, so take the dog days number with a grain of salt.

Hopefully I didn’t mess anything up along the way, I did this all on the phone and it’s harder to double-check than on paper!