If we compare this to the size of 1 AU, given to us as 149,598,000 km, we can see that the ratio is 0.000085; that is, the North Pole is only 0.0085% closer to the Sun than the South Pole. Do you think the difference in distance accounts for the varying temperatures between summer and winter on Earth? Why or why not?

It looks as though you are asking if the differing distances of the North and South Poles from the Sun, caused by the geometry of the tilt of the Earth on its axis, is a likely explanation for the different temperatures in summer and winter. Your figures of 149,598,000 kilometers and .000058 (for the fraction of the distance that the North Pole is nearer to the Sun than the South Pole during the northern hemisphere summer) suggest that the difference in distance is 8700 kilometers.
The very small fractional difference in distance makes us question whether it alone is responsible for the substantial difference in summer and winter temperatures. If we calculate the ratio of intensities of electromagnetic radiation (such as solar radiation) at those distances, using the known inverse square dependence of intensity on distance, we get
I/I_o = ((1-.000058)/1)^2
=0.99988
This does not seem to be much of a decrease in intensity. Even when acknowledging that the exact relationship between intensity of incident light and temperature is complex and unknown, we may want to look elsewhere.
The orbit of the Earth is not an exact circle; it is an ellipse with a certain amount of eccentricity. This means that the Earth is closer to the Sun in some parts of its orbit than in others. At the point of closest approach, the perihelion, Earth is only about 147,000,000 kilometers from the Sun. At its farthest point, the aphelion, Earth is 152,000,000 kilometers away! The difference is 5,000,000 kilometers—much, much greater than the 8700 kilometer difference caused by the Earth’s tilt.
We are not finished. We need to know when the perihelion and aphelion occur. It turns out that the Earth is closest to the Sun in January and farthest away in July! Clearly, if the Earth is 5 million kilometers further away from the Sun during the northern hemisphere's summer when compared to winter, something other than distance must explain the changing temperatures.
The key lies in the angle at which sunlight strikes the Earth. You can see the effect of angle by using a flashlight beam. If the beam strikes a surface perpendicularly, it makes a relatively small circle. The intensity of the light is concentrated in a small area. If you then shine the light at an angle to the surface, the spot made by the flashlight will be elongated. It is spread out over a greater area. The same total intensity of light spread over a greater area means less intensity per unit area. Less intensity means less energy input per square meter and less warming by the sun.
It is the same when sunlight strikes the Earth. During the northern hemisphere's summer, the northern hemisphere tilts toward the sun, and the sunlight strikes it more directly. At the same time, it strikes the southern hemisphere at a greater angle. Thus, equal amounts of light fall in a smaller area in the north while being spread out over a greater area in the south. When the light is more spread out, there is less intensity, that is, less energy per second per square meter. This is a large effect—much greater than the effect of small changes in distance from the Sun—and serves as the explanation for the seasonal temperature variation we observe.
The more angled light in the southern hemisphere also must travel farther through the atmosphere. This causes greater attenuation, but this is not as important as the simple spreading out of the incident intensity over a greater area.