The fraction of the circle that the Earth moves in that time is (1hour/1year). Massage the fraction to get the same units on top and bottom. At that point, it's just a ratio, with no units.
There are 2•π radians in a full circle, so the angle is that same fraction of 2π .
Angular displacement is measured counterclockwise anyway, so you don't have to worry about signs.
The only actual work I see here is converting 1hr to a fraction of 365da.
I'm typing on my phone right now. I'll go a little farther when I get back to my PC, if you need it.
Notice that with 365 days in a year, that means very close to 1° per day. I think it's something like 57.3 degrees in 1 radian, so the result would be something like (1/57.3) = 0.017 radian per day. Now I'll be interested to see if it's anything like this cocktail-napkin estimate, when I get back to my computer.
