## Wednesday, June 21, 2017

### 2017 Eclipse Corner #3 Kepler's Law 1

Several civilizations of the past kept records to allow accurate understanding of the night time sky. Europe had to get out of the Dark Ages using mathematics to describe natural phenomena. After Copernicus placed the planets in order around the Sun, science found both the Sun and the Moon vary in their distances from the Earth during different positions in their orbits. Based on Kepler’s First Law of Planetary Motion, the orbit of each planet around the Sun is the shape of an ellipse. An ellipse is an oval shaped conic section from which geometric exact calculations can be made of the objects position (where the sum of the distances from the two foci to every point on the loop is constant). The elliptical orbit of the Earth around the Sun has a minimal distance or closest point called perihelion and a maximum distance or farthest point called aphelion*. Perihelion was reached on January 4 this year and the aphelion will be reached in 2017 on July 3.
*Information from Comins, Discovering the Essential Universe

The distance of difference between the aphelion and perihelion is more than three million miles. That seems like a lot of miles until one understands that the average distance to the Sun is 93 million miles and the difference is only 3%. Living in the northern hemisphere means we are closer to the Sun in winter and farther away in the summer. Of course the tilt of the earth causes the seasons, and we are tilted away in winter and towards the Sun in the summer. Although there are a variety of factors that affect the earth’s temperature, the aphelion and perihelion may give us cooler summers and warmer winters?

The mathematics of an ellipse shows the distance Focus 1 to the planet + Focus 2 to the planet = the same sum at any planet position on the elliptical orbit. Please notice aphelion is farther than perihelion.

The revolution of the Moon also follows Kepler’s First Law being an ellipse. Because the Moon is closer to the Earth, the distances of the close and farther parameters are more noticeable. The orbit of the Moon occurs once a month so the closest point or perigee and farthest point or apogee occurs once a month. News media have recently used a new term “Supermoon” when the Full Moon Phase is at the perigee or closest point to the Earth and the Moon appeared much larger.
Sometimes during a Solar Eclipse, the Moon can be close to apogee, the Moon’s farthest point from the Earth, where it could be small enough to fit inside the Sun or produce what is called an Annular Eclipse. According to moonsighting.com, our 2017 Solar Eclipse, August 21, the Moon is only 3 days from perigee, its closest point. From www.eclipse2017.org, mid-Missouri will have a Total Solar Eclipse and we will get over 2 minutes and 30 seconds of totality at the center line.                –Dan Slais

Full moons at apogee(left) and perigee(right) in 2011.

Earthsky.corg/astronom-essentials Composite image by EarthSky community member C.B. Devgun in India