The analemma plays into the sunrise and sunset times. On the solstice, the sun is slightly west of where it would be if the Earth’s orbit were circular, so it sets a little earlier. A few weeks after the solstice, the sun has come around to the other side of the analemma’s figure-eight, and it sets a little later than it would if the Earth’s orbit were a circle. And that means that on the solstice, both sunset and sunrise are a few minutes earlier than they would be if we had a circular orbit, and in early January a few minutes later than they would be. When you mix the two effects together—the solstice and the analemma—sunset times are earliest a few weeks before the solstice, and sunrise times are latest a few weeks after.