We begin with Kepler’s First Law — Page 377, Lesson 335

Let’s start with a clean slate on time and the Earth’s motion, because this is the foundation for everything else in navigation. I’m going to walk you through Kepler’s laws first, because they explain why the Earth moves the way it does around the Sun, and that motion is what we use to define time itself. We begin with Kepler’s First Law. A planet travels around the Sun in an elliptical orbit — that’s an oval, not a perfect circle. The Sun sits at one of the two foci of that ellipse, labelled F1 in the figure. The second focal point is shown as F2, but you can ignore it; it’s just there for the geometry. Because the orbit is elliptical, the planet’s distance from the Sun changes as it goes around. The closest point to the Sun is labelled P, and it’s called perihelion — from the Greek peri, meaning near, and helios, meaning sun. The furthest point is labelled A, called aphelion. Now, here’s the key calendar fact: perihelion occurs in early January, around the 4th, and aphelion occurs in early July, also around the 4th. So when it’s winter in the northern hemisphere, the Earth is actually closest to the Sun. Now Kepler’s Second Law, which is about speed. Imagine the planet at position B, approaching aphelion at A. The line from the Sun to the planet — that’s the radius vector, here called SB — sweeps out an area, SBA, over the time it takes to go from B to A. Now look at the corresponding situation at Q, as the planet approaches perihelion at P. The radius vector SQ is shorter than SB, because the planet is closer to the Sun. For the area SQP to equal the area SBA in the same time, the shorter radius vector SQ must move faster than SB. In plain terms: the planet travels faster near perihelion and slower near aphelion. So the summary is this — in an elliptical planetary orbit, orbital speed is fastest at perihelion and slowest at aphelion. Now let’s bring this down to Earth, literally. The Earth’s orbital situation is viewed from the North Celestial Pole, or NCP — that’s the point in the sky directly above the geographic North Pole. Two things to note here. First, the Earth rotates about its geographic north/south axis in an anticlockwise direction when viewed from the NCP. That rotation is what determines our measurement of a day — we’ll get into that later. Second, the Earth orbits the Sun in an anticlockwise direction when viewed from the NCP as well. So both the spin and the orbit go the same way when you look down from above the North Pole. That’s the setup. We have the elliptical orbit, the speed variation from Kepler’s second law, and the direction of both rotation and revolution. That’s what we build time on.