Wednesday, January 4, 2012

Perihelion

Tonight, January 4 at 8:00 pm EST (0100 UTC July 5), the Earth will be at perihelion. The word is derived from the Greek words for "near" (peri) and "Sun" (helios). It's the closest we'll be to the Sun all year.  As I write this, however, at 9:00 am, my outdoor thermometer says it's currently 12° F outside.  If we're so close to the Sun, why is it so damn cold outside?

Well, first of all, it's only cold for us here in the Northern Hemisphere.  It's early summer down in the Southern Hemisphere and quite warm.  That's because the real reason the Earth has seasons is its 23.5° axial tilt.  Right now, two weeks after the winter solstice, those of us in the Northern Hemisphere are tilted about as far away from the Sun as we can be.  Those in the Southern Hemisphere are tilted toward the Sun.  We get less hours of daylight, the Sun is lower in the sky all day, and the sunlight is spread out over a larger area - ergo, it's colder.

In the early 1600s, German mathematician/astronomer Johannes Kepler developed his Three Laws of Planetary Motion.  He showed that as planets orbit the Sun, they actually move in ellipses, not perfect circles as was previously thought from the times of the ancient Greeks.  This means that planets are sometimes closer to the Sun (perihelion as mentioned above) and sometimes further from the Sun (called aphelion).  Therefore, when we talk about the distance of a planet from the Sun, we have to specify the average distance.

According to Wikipedia, the average distance from the Earth to the Sun, also known as an astronomical unit (1 A.U.) is 149,597,870.7 km (92,955,807.3 mi).  We can also look up the values for perihelion and aphelion as 147,098,290 km (91,402,640 mi) and 152,098,232 km (94,509,460 mi) respectively.

In astronomy, the shape of an elliptical orbit is given by its eccentricity (e) which can be defined as:

e= [(aphelion - perihelion) / (aphelion + perihelion)]
e = [(152,098,232 km - 147,098,290 km) / (152,098,232 km + 147,098,290 km)]
e = 0.01671123

An eccentricity of 0.0 would be a perfect circle.  An eccentricity of 0.0167, like the Earth has, is pretty darn close to circular.  Looking at the numerical difference between aphelion and perihelion, and comparing that to the average distance from the Sun gives us:

(152,098,232 km - 147,098,290 km) / (149,597,870.7 km) * 100% = 3.34% difference

It's really not that much of a difference.

How much does this change in distance affect the amount of incoming solar radiation (insolation) from the Sun?  Imagine the Sun radiating energy outward in all directions.  As you move away from the Sun, the energy is distributed over larger and larger spherical areas as seen at left.  Since the surface area of a sphere is 4πr2, the total insolation decreases by the inverse square of the distance (r) (this is called the inverse square law).

Let's look at the difference between aphelion and perihelion distances.

Aphelion Insolation = [(149,597,870.7 km) / (152,098,232 km)]2 = 0.9674
Perihelion Insolation = [(149,597,870.7 km) / (147,098,290 km)]2 = 1.0343

That's about a 6.5% difference in insolation.  Not really noticeable in our surface temperatures, but it is a difference you can see if you observe the Sun through an appropriately filtered telescope (here's where every blogger writes "Don't stare at the Sun with your naked eye!"  Not me.  If you're stupid enough to go outside and stare slack-jawed at the Sun, go right ahead.  Hurts, don't it?).

So, yes we're closest to the Sun for the year today.  And we still have two months of bitterly cold weather to live through here in the Hudson Valley.  The Hudson Valley Geologist is not a fan of winter - the snow covers up all the beautiful rocks!