The Sun sits at one of those foci, labelled F1 in the diagram — Page 377, Lesson 335

Let’s start with the big picture, because this whole chapter is about time — and time, for a navigator, is really about the Earth’s motion. Before we can talk about hours and minutes, we have to understand how the Earth moves around the Sun. That motion is governed by Kepler’s laws of planetary motion, and I want to walk you through the first two of those laws right now. Kepler’s First Law says that a planet travels around the Sun in an elliptical orbit. An ellipse is an oval shape, and it has two special points inside it called foci — the plural of focus. The Sun sits at one of those foci, labelled F1 in the diagram. There’s a second focal point, F2, shown as well, but you can ignore it; it’s not physically occupied by anything. What matters is that because the orbit is an ellipse and the Sun is off-centre at F1, the planet’s distance from the Sun changes as it goes around. That changing distance gives us two key positions. The closest point to the Sun is labelled P, and it’s called perihelion. The name comes from Greek: peri means near, and helios means sun. So perihelion literally means “near sun.” The furthest point from the Sun is labelled A, and it’s called aphelion — apo meaning away from, so “away from sun.” Now, here’s the practical timing you need to remember: perihelion occurs in early January, around the 4th, and aphelion occurs in early July, around the 4th. So in the northern winter, the Earth is actually closest to the Sun, and in the northern summer, it’s furthest away. That’s a fact that surprises a lot of people, but it’s true. Now let’s move to Kepler’s Second Law, which is about speed. Look at position B on the orbit, where the planet is approaching aphelion. The line from the Sun to the planet is called the radius vector — it’s just the line connecting the Sun to the planet. As the planet moves from B to A, that radius vector SB sweeps out an area, and that area is labelled SBA. Now consider a corresponding situation at position Q, where the planet is approaching perihelion. The radius vector there is SQ, and it’s shorter than SB — because the planet is closer to the Sun near perihelion. For the area swept out between Q and P, labelled SQP, to be exactly the same area as SBA, the shorter radius vector SQ has to move faster than SB. Think of it this way: if you sweep a shorter line, you have to swing it through a bigger angle to cover the same area. So the planet must move faster near perihelion and slower near aphelion. That gives us the summary statement, and I want you to hold onto it: in an elliptical planetary orbit, the orbital speed is fastest at perihelion and slowest at aphelion. So the Earth speeds up in early January and slows down in early July. Now, let’s orient ourselves in space. 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 — imagine standing at the North Pole and looking straight up; that point in the sky is the NCP. When we view the Earth from that vantage point, we see two rotations, and both are anticlockwise. 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 come back to that later in the chapter. Second, the Earth orbits the Sun in an anticlockwise direction when viewed from the NCP. So both the spin and the orbit go the same way when seen from above the North Pole. Let me show you the geometry of this orbit so you can see the ellipse, the Sun at F1, and the perihelion and aphelion positions clearly. So to tie it all together: the Earth’s orbit is an ellipse with the Sun off-centre at one focus. That makes the Earth’s distance from the Sun vary, giving us perihelion in early January and aphelion in early July. And because of Kepler’s Second Law, the Earth moves fastest at perihelion and slowest at aphelion. Both the Earth’s spin and its orbit are anticlockwise when viewed from the North Celestial Pole. That’s the foundation we need before we can talk about how we actually measure time.