Today the Earth is at the point on its orbit at which it is at its closest to the Sun, i.e. at its perihelion. To be precise, this event takes place at 14.18 GMT today 4th January 2017; aphelion (the furthest distance from the Sun) is at 20.11 GMT on July 3rd 2017. You can find a list of times and dates of perihelion and aphelion for future years here.
It surprises me how many people think that the existence of the seasons has something to do with the variation of the Earth’s distance from the Sun as it moves in its orbit. The fact that perihelion occurs in the depth of winter should convince anyone living in the Northern hemisphere that this just can’t be the case, as should the fact that it’s summer in the Southern hemisphere while it is winter in the North.
The real reason for the existence of seasons is the tilt of the Earth’s axis of rotation, as explained in a nice little video here. I used to do a little demonstration with a torch (flashlight to American readers) to illustrate this when I taught first-year astrophysics. If you shine a torch horizontally at a piece of card it will illuminate a patch of the card. Keep the torch at the same distance but tilt the card and you will see the illuminated patch increase in size. The torch is radiating the same amount of energy but in the second case that energy is spread over a larger area than in the first. This means that the energy per unit area incident on the card is decreases when the card is tilted. It is that which is responsible for winter being colder than summer. In the summer the sun is higher in the sky (on average) than in winter. From this argument you can infer that the winter solstice (which passed on 21st December), not the perihelion, is the relevant astronomical indicator of winter.
That is not to say that the shape of the Earth’s orbit has no effect on temperatures. The eccentricity of the Earth’s orbit is e=0.017. Estimate the percentage difference in the flux of energy arriving at Earth from the Sun at the extremes of its orbit (i.e. at perihelion and aphelion).
I leave it as an exercise for the student that the fractional difference in distance between perihelion and aphelion in an elliptical orbit is 2e. The fractional change in flux received between the two extremes is thus 4e or about 6.8%, which is indeed a significant in the insolation at the Earth’s surface.
Assuming (for the sake of illustration only) that the Earth behaves like a black body then the incident flux would go as the fourth power of the temperature, which means that the temperature should change by about 1.7% between perihelion and aphelion. Taking the mean temperature to be about 300 K the difference should be around 5° C.
Ignoring any effects other than insolation this means that summer in the Southern hemisphere (when the Earth is at perihelion) should be significantly warmer than summer in the Northern hemisphere (when the Earth is at aphelion).
Things are not as simple as that, however, because the Earth’s surface possesses a significant North-South asymmetry: there is a much larger fraction of ocean in the Southern hemisphere, for example, which could be responsible for moderating. The climate is a non-linear system that involves circulating air and ocean currents that respond in complicated ways and on different timescales not just to insolation but to many other parameters, including atmospheric composition (especially water vapour).
The perihelion effect on summer temperatures can be readily verified by observations of Mars, which has no oceans and a much thinner, drier atmosphere, as well as a much more eccentric orbit (e=0.0934).
P.S. Of course, at perihelion the Earth is not only closest to the sun but also moving with its greatest orbit speed. That no doubt explains why January is often very windy…
P.P.S. That was a joke.