Moon – Bartosz Ciechanowski

In the vastness of empty space surrounding Earth, the Moon is our closest celestial neighbor. Its face, periodically filled with light and devoured by darkness, has an ever-changing, but dependable presence in our skies.In this article, we’ll learn about the Moon and its path around our planet, but to experience that journey first-hand, we have to enter the cosmos itself. Let’s take a look at the Moon as seen from space in all its sunlit glory. You can drag it around to change your point of view, and you can also use the slider to control the date and time: In this convenient view, we can freely pan the camera around to see the Moon and its marvelous craters and mountains from various angles. Unfortunately, we don’t have that freedom of motion in our daily experience – the Moon wanders on its own path across the daily and nightly skies. We can simulate these travels below, where you can see the current position of the Moon in the sky. You can drag that panorama around to adjust your viewing direction – this lets you see the breadth of the sky both above and below the horizon. By dragging the sliders you can witness how the position of the Moon changes in the sky across days and hours of your local time. As the Moon’s placement in the sky shifts, the little arrow will guide you to its position. You can also drag the little figurine on the globe in the bottom-right corner to see how the sky looks at that location on Earth. If your browser allows it, clickingtapping the button will automatically put the figurine at your current location. This may all feel quite overwhelming at the moment, but we’ll eventually see how all these pieces fit together: Over the course of one day, the Moon travels on an arc in the sky almost completing a loop around the Earth. As the days pass, the Moon’s illumination also visibly changes. You’ll probably admit that it’s a little hard to focus on the tiny Moon as it shifts its position in the sky. To make things easier to see, I’ll zoom in the camera and lock its position on the Moon: Notice that across a single day the Moon seems to rotate, and over many days it quite visibly wobbles. These wobbly variations let us occasionally see some hidden parts on the “edges” of the Moon, but our neighbor ultimately shows us only one of its sides. In our space-floating demo we could easily see the Moon from all sides, but on Earth we can never see most of the far side of the Moon. Over the course of days, the lighting on the Moon also changes dramatically. The line between the lit and unlit parts of the Moon, known as the terminator, sweeps across the Moon, revealing the details of its surface. Although the Moon has a spherical shape, the fully lit Moon looks more like a flat disk. In this article I’ll explain all the effects we’ve just seen, and we’ll also learn about gravity, ocean tides, and eclipses. Let’s begin by exploring how celestial bodies move through space and how their mere presence influences the motion of their neighbors. Motion in Space Let me introduce a little cosmic playground in which we’ll do our experiments. Inside it, I put a little planet that floats freely in space. You can drag the planet around to change its position. The arrow symbolizes the initial velocity of this body – you can tweak this velocity by dragging the dashed outline at the end of the arrow. To get things going, you can press the button in the bottom-left corner: Notice that I’m drawing a ghost trail behind the moving planet, making it easier to track its motion. As you can see, once you let the planet go, it travels through space in a straight line, only to eventually get out of visible bounds. Let’s complicate things a little by adding another body to this sandbox. You can tweak the positions and velocities of both bodies to see how their mutual presence impacts one another. I’m also marking the thin lines of trajectories that the bodies will take even before you let things go, making it easier to plan their motion: The motion we see now isn’t as straightforward as before. In some scenarios, the two bodies travel past each other after tweaking their initial trajectories. In other configurations, both objects roam through space together, permanently locked in a swinging dance. You may have also managed to make the two bodies run into each other. We’ll eventually see a more realistic visualization of that scenario, but in this simplified simulation when two objects collide, they just stick together and continue their coupled journey. What’s responsible for all these effects is the force of gravity acting on the objects. Let’s explore that interaction up close. As before, you can drag the two bodies around, and you can also change their masses using the sliders below: The arrows represent the force of gravity acting on the two bodies – the longer the arrow, the larger the force. For completeness, I’m displaying the values and units of masses and distances, but the numbers aren’t particularly important here. What matters is that when we increase either the mass of the first body m1 or the mass of the second body m2, the force of gravity grows too. Moreover, the magnitude of gravity also depends on the distance r between the objects. As bodies move farther apart, the gravity weakens. Notice how the forces acting on each body have the same magnitude, but they point towards the other body, which indicates an attractive force. If you paid close attention to the lengths of the arrows, you might have noticed that the force decreases quite rapidly with distance. We can visualize this with a plot, in which the white line shows the magnitude of gravity as a function of distance. More precisely, it shows that gravity is inversely proportional to the square of that distance: Let’s take a very brief mathematical interlude to describe what we’ve seen in more detail. All these dependencies are captured in the following equation for the force of gravity F, between two objects with masses m1 and m2 separated by distance r: F = G × m1 × m2 / r2 The gravitational constant G seen in front of the right-hand side of the equation is incredibly small, making gravity a very weak force. We have no issues lifting everyday objects despite the might of the mass of the entire Earth pulling them down. While the strength of gravity between any two bodies is equal, the resulting change in motion is not. You may recall from elementary physics classes that force F is equal to mass m times acceleration a. We can encapsulate this idea in a pair of simple formulas that tie these values for the first and second body: F = m1 × a1 F = m2 × a2 By plugging in the equation for the force of gravity F and reducing the masses, we end up with a set of two equations for accelerations of the bodies: a1 = G × m2 / r2 a2 = G × m1 / r2 Notice that the acceleration of the first body a1 depends on the mass of the second body m2. Similarly, the acceleration of the second body a2 depends on the mass of the first body m1. Let’s see this in practice in the demonstration below, where I’m temporarily making the big body twenty times more massive than the small body: Notice that the body with smaller mass drastically changes its course, while the motion of the larger body is only marginally affected. This tracks with our day-to-day experience, where every item left hanging in the air very visibly accelerates towards the staggeringly massive Earth, but our planet doesn’t jump out of its way to meet the falling object. Now that we understand that it’s the force of gravity that makes the bodies move towards each other, let’s do a better job of tracking the motions of these objects over time. Right now our camera is fixed in space, so the two bodies often fly out of visible bounds. Thankfully, we can easily fix this by moving the camera with the bodies. In the demonstration below, I’m presenting the same scenario from two different vantage points. On the left, I’m showing the scene from the familiar point of view that’s fixed in space – you can plan the trajectories of the two bodies on that side. On the right, you can see this simulation from the point of view of the camera that’s tied to the motion of the these objects. I’m marking the position of that camera with a white dot on the thin line joining the bodies. By dragging the slider you can move the camera between them: With the camera following the bodies we can now track their motion forever. More importantly, we can also see the relative motion of the two objects. When you make the bodies move together, you can witness how from the perspective of the teal body, it’s the yellow body that orbits around the teal body, but from the perspective of the yellow body, it’s the other way around. Better yet, if we position the camera halfway, or even anywhere else between the two bodies, both objects seem to orbit the camera. The perception of relative motion depends on the point of view, but there is one point that’s particularly useful for observation. In this next demonstration, I’ve added a little white trail to the camera itself. Watch how the path of the camera in space changes as you reposition it with the slider: In general, the camera traverses some squiggly path in space. However, there is one special position between the two bodies for which the camera travels in a perfectly straight line. This point is known as the barycenter, and it’s located at the center of mass of these objects. Let’s explore the concept of the barycenter a little closer. In the demonstration below, you can once again drag the bodies around to change the distance between them, and you can also use the sliders to tweak their masses. The center of mass of these two bodies is marked with a black and white symbol: The equation in the bottom part explains the placement of the center of mass of these two objects – it is located at a point where its distance from the first body r1 multiplied by that body’s mass m1, equals that point’s distance