January 10. 360,048.
Step-by-step explanation:
The Earth and the Moon are two space bodies that have each other as the closest to one another. Both of them have their own gravitational pull, with the one of the Earth being much greater, while the one of the Moon being weaker than it is expected for a body of its size. Nevertheless they influence each other with the gravitational pull, which is most noticeable on Earth.
The gravitational pull between these two space bodies is the greatest when they are the closest to each other, while it is the smallest when they are the furthest from each other. On January 10 the distance between Earth and the Moon is the smallest and it is 360,048 km, so the gravitational pull is the greatest on this date. On December 19 the distance between Earth and the Moon is the greatest and it is 406,276 km, so the gravitational pull is the smallest.