When is Earth closest to the Sun?
Well, you say, perihelion of course. But perihelion is when the Earth-Moon barycentre is closest to the Sun. Not Earth itself.
The barycentre is on average 4,671 km from the Earth, which should mean that even if the orbit of the Earth-Moon barycentre around the Sun were perfectly circular, the Earth-Moon orbit around the barycentre would cause an oscillation in the Earth-Sun distance by twice that amount on a monthly basis. That should be enough to move Earth's closest approach to the Sun away from perihelion.
Considering this, how many days from perihelion may Earth's closest approach to the Sun be?
Question inspired by: What place on Earth is closest to the Sun?