The #Eclipse #Conspiracy
The Eclipse Conspiracy
by Alberto Vecchiato
August 21, 2017, will be remembered for a long time by astronomers, both professional and amateur, because of its exceptional solar eclipse. However, it isn't for its duration. With a Gamma value (https://en.wikipedia.org/wiki/Gamma_(eclipse)) of 0.4367 and a Magnitude (https://en.wikipedia.org/wiki/Magnitude_of_eclipse) of 1.0306, the longest duration of the totality was 2m40s (https://en.wikipedia.org/wiki/Solar_eclipse_of_August_21,_2017) while our celestial friends can showcase up to more than 7 minutes of totality in the most favorable conditions. Rather, it is because, with a path of totality starting in the north Pacific and ending in the Atlantic Ocean, it crossed the entire (contiguous) United States from Oregon to South Carolina. The most recent comparable event dates back to almost a century ago, on June 8, 1918!
News about this event started months in advance, and thanks to its particular conditions, the knowledge leaped over the usual specialized media, aired by newscasts and announced in the newspapers.
It was in one of these that I ran across an interesting observation. An Italian online newspaper, the day of the eclipse, had a feature about the event, and a reader commented the fact that it started in Oregon, in the morning, to finish hours later in South Carolina, more or less with these words: "Hey man, the Sun rises in the east and sets in the west. The same is for the Moon. They want us to believe that the eclipse starts in the west and end in the east. Houston we've a problem!"
This remark, vaguely suggesting a conspiracy to revert the paths of the celestial bodies, or maybe that we were witnessing another example of the (in)famous ignorance of the "average journalist," stimulated me to try to answer this curiosity. The explanation could be summarized in just two words: "relative velocity," but stop here if you want to figure it out by yourself, or continue reading otherwise.
First things first. We can be safely reassured that the Sun and the Moon cross the sky from east to west, no doubt about this, but why? Basically, this is due to the spin of the Earth, that is the rotation of our planet around its axis, which we all know that turns around once per day. The Moon instead orbits around the Earth. So the Earth spins, but its center is fixed, right? No, obviously not. As we all learned in school, the Earth also orbits around the Sun. So it is the Sun that is fixed, right? Well, not really... The astronomers say that the Sun orbits around the center of the Milky Way, our galaxy, at the respectable speed of about 830,000 km/h, or 515,000 miles per hour. Oh my goodness, and what about the center of the Milky Way then? OK, before all this twirling drives us all crazy, let us understand one important thing. In all this chatting we have always talked about movement with respect to something else. The Moon moves with respect to the Earth, that moves with respect to the Sun, that moves with respect to the Galaxy and so on.
This is an example of an important concept in Physics, that of the reference system. There is no such thing as an absolute movement, you first have to choose an (arbitrary) reference system, then you can define any movement with respect to it. So, when we say that the Earth orbits around the Sun, we are implicitly saying that we are choosing the center of the Sun as the origin of our reference system, fixed by definition.
Rewind, and let's go back to the spin of the Earth. We can now face in more detail why the Sun rises in the east and sets in the west. Have you ever asked yourself in which direction our planet spins around? If you imagine to lift yourself up over the orbital plane of the solar system, on the northern side, the Earth would be seen to spin counterclockwise. In the reference system with the Sun at the origin, moreover, the Earth and the Moon would orbit in the same sense with respect to the Sun and the Earth respectively (Figure 1). So let's now figure out what an observer on the Earth surface, facing the north, actually sees. The Sun starts to be visible on his/her right side, that is in the east, and sets in the left side, or the west. You can get it better by looking at Figure 2, where it is also apparent the difference between the northern and the southern hemisphere. Indeed, the figure shows clearly that, generally, if you are in the northern hemisphere you have to look to the south to see our star in front of you, so from the Earth the Sun moves clockwise, with the east on the left and the west on the right, whereas the opposite happens in the southern.
"Great," you would say, "but how in the world does this have to do with the marching direction of the solar eclipses?" Just a few lines and we'll get there.
While in Figure 1 we have depicted the motions of the Sun, the Moon and the Earth in a reference system centered in the Sun, in imagining the same motion as seen from the ground we have changed the reference system, namely we put ourselves from a point of view where the Earth is fixed (in the sense that it has neither orbital nor spin motion) and the Moon and the Sun are moving, instead. So the question now is, how does the motion of these two bodies look like from our new reference system?
If I am in a car moving at 100 km/h to the north with respect to the ground, surpassing a bicycle having a speed of 10 km/h, then in my personal reference system (the one attached to my car) the car would be still, while the bike would be moving with a speed of 90 km/h with respect to me in the opposite direction, that is to the south. In other words, the car and the bicycle have a relative speed of 90 km/h, and the direction depends on the reference system. From the point of view of the car, the direction is south, from that of the bike it is the car that is moving at 90 km/h to the north.
The movements of the Sun, the Moon, and the Earth are expressed in angles per unit time, instead of lengths per unit time, but the concept is the same. With respect to a reference system centered in the Sun and with axes fixed with respect to the stars, the Earth completes an orbit in 1 year, which means that it has an angular velocity of about 1 degree per day (one orbit per year is equivalent to, say, 360/365 deg/day) counterclockwise. But with respect to a reference system centered in the Earth, and with axes "attached" to our planet, the total relative angular velocity of the Sun is the sum of two velocities: that of the spin of the planet and that of the orbital motion. The former counts as a velocity of 360 deg/day, the latter is 360/365 deg/day, both clockwise because, as we have seen in Figure 1, the spin and the orbital motion have the same direction. As in the case of the car and the bicycle, then, the relative angular velocity of the Sun with respect to the ground is (approximately) 359 deg/day clockwise, if we keep our point of view from the northern side of the orbital paths, or from east to west if we put ourselves on the ground (Figure 3).
If you got safely to this point, the rest is a piece of cake. The same reasoning, in fact, can be done for the Moon, which however orbits around the Earth in about 30 days counterclockwise, in the reference system centered on the Sun, which means in about 30 days clockwise from that of the "fixed Earth ground" (DISCLAIMER: to be more precise, it would be something more than 27 days, but we don't want to mess up with more complicated numbers here). Then you can easily understand that, exactly as it was for the Sun, the total relative angular velocity of the Moon with respect to the ground is about 360-360/30 deg/day=348 deg/day. In other words, from our point of view, the Moon is slower than the Sun.
So what happens during an eclipse? To have a solar eclipse the Moon must be seen between us and the Sun. Looking at Figure 4 we can understand that the eclipse happens in the region of the Earth where the Sun projects the shadow of our satellite. But if we pay attention at how this evolves in time, since the Moon is slower than the Sun, it must be that the former is already high in the sky when the latter rises. Our star slowly "chases" our satellite until, at a certain point, the shadow of the Moon falls on the surface of the Earth... starting from a western point and going to the east exactly because the Sun surpasses the Moon coming from the east and going to the west!
And that's all folks. No conspiracy out there, just a typical physics' recipe, with a pinch of kinematics on a basis of geometry.
by Alberto Vecchiato
August 21, 2017, will be remembered for a long time by astronomers, both professional and amateur, because of its exceptional solar eclipse. However, it isn't for its duration. With a Gamma value (https://en.wikipedia.org/wiki/Gamma_(eclipse)) of 0.4367 and a Magnitude (https://en.wikipedia.org/wiki/Magnitude_of_eclipse) of 1.0306, the longest duration of the totality was 2m40s (https://en.wikipedia.org/wiki/Solar_eclipse_of_August_21,_2017) while our celestial friends can showcase up to more than 7 minutes of totality in the most favorable conditions. Rather, it is because, with a path of totality starting in the north Pacific and ending in the Atlantic Ocean, it crossed the entire (contiguous) United States from Oregon to South Carolina. The most recent comparable event dates back to almost a century ago, on June 8, 1918!
News about this event started months in advance, and thanks to its particular conditions, the knowledge leaped over the usual specialized media, aired by newscasts and announced in the newspapers.
It was in one of these that I ran across an interesting observation. An Italian online newspaper, the day of the eclipse, had a feature about the event, and a reader commented the fact that it started in Oregon, in the morning, to finish hours later in South Carolina, more or less with these words: "Hey man, the Sun rises in the east and sets in the west. The same is for the Moon. They want us to believe that the eclipse starts in the west and end in the east. Houston we've a problem!"
This remark, vaguely suggesting a conspiracy to revert the paths of the celestial bodies, or maybe that we were witnessing another example of the (in)famous ignorance of the "average journalist," stimulated me to try to answer this curiosity. The explanation could be summarized in just two words: "relative velocity," but stop here if you want to figure it out by yourself, or continue reading otherwise.
First things first. We can be safely reassured that the Sun and the Moon cross the sky from east to west, no doubt about this, but why? Basically, this is due to the spin of the Earth, that is the rotation of our planet around its axis, which we all know that turns around once per day. The Moon instead orbits around the Earth. So the Earth spins, but its center is fixed, right? No, obviously not. As we all learned in school, the Earth also orbits around the Sun. So it is the Sun that is fixed, right? Well, not really... The astronomers say that the Sun orbits around the center of the Milky Way, our galaxy, at the respectable speed of about 830,000 km/h, or 515,000 miles per hour. Oh my goodness, and what about the center of the Milky Way then? OK, before all this twirling drives us all crazy, let us understand one important thing. In all this chatting we have always talked about movement with respect to something else. The Moon moves with respect to the Earth, that moves with respect to the Sun, that moves with respect to the Galaxy and so on.
This is an example of an important concept in Physics, that of the reference system. There is no such thing as an absolute movement, you first have to choose an (arbitrary) reference system, then you can define any movement with respect to it. So, when we say that the Earth orbits around the Sun, we are implicitly saying that we are choosing the center of the Sun as the origin of our reference system, fixed by definition.
 |
| Figure 1: schematic and not-in-scale representation of the orbit of the Earth around the Sun (blue circle), of that of the Moon around the Earth (yellow circle) and of the spin of the Earth (red circle) as seen from over the north pole. Credits: Slyavula Education, Flickr (CC-BY), and NASA/JPL/ASF. |
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| Figure 2 |
"Great," you would say, "but how in the world does this have to do with the marching direction of the solar eclipses?" Just a few lines and we'll get there.
While in Figure 1 we have depicted the motions of the Sun, the Moon and the Earth in a reference system centered in the Sun, in imagining the same motion as seen from the ground we have changed the reference system, namely we put ourselves from a point of view where the Earth is fixed (in the sense that it has neither orbital nor spin motion) and the Moon and the Sun are moving, instead. So the question now is, how does the motion of these two bodies look like from our new reference system?
If I am in a car moving at 100 km/h to the north with respect to the ground, surpassing a bicycle having a speed of 10 km/h, then in my personal reference system (the one attached to my car) the car would be still, while the bike would be moving with a speed of 90 km/h with respect to me in the opposite direction, that is to the south. In other words, the car and the bicycle have a relative speed of 90 km/h, and the direction depends on the reference system. From the point of view of the car, the direction is south, from that of the bike it is the car that is moving at 90 km/h to the north.
The movements of the Sun, the Moon, and the Earth are expressed in angles per unit time, instead of lengths per unit time, but the concept is the same. With respect to a reference system centered in the Sun and with axes fixed with respect to the stars, the Earth completes an orbit in 1 year, which means that it has an angular velocity of about 1 degree per day (one orbit per year is equivalent to, say, 360/365 deg/day) counterclockwise. But with respect to a reference system centered in the Earth, and with axes "attached" to our planet, the total relative angular velocity of the Sun is the sum of two velocities: that of the spin of the planet and that of the orbital motion. The former counts as a velocity of 360 deg/day, the latter is 360/365 deg/day, both clockwise because, as we have seen in Figure 1, the spin and the orbital motion have the same direction. As in the case of the car and the bicycle, then, the relative angular velocity of the Sun with respect to the ground is (approximately) 359 deg/day clockwise, if we keep our point of view from the northern side of the orbital paths, or from east to west if we put ourselves on the ground (Figure 3).
 |
| Figure 3: the motions of the Earth and of the Sun as they appear from three reference systems. |
If you got safely to this point, the rest is a piece of cake. The same reasoning, in fact, can be done for the Moon, which however orbits around the Earth in about 30 days counterclockwise, in the reference system centered on the Sun, which means in about 30 days clockwise from that of the "fixed Earth ground" (DISCLAIMER: to be more precise, it would be something more than 27 days, but we don't want to mess up with more complicated numbers here). Then you can easily understand that, exactly as it was for the Sun, the total relative angular velocity of the Moon with respect to the ground is about 360-360/30 deg/day=348 deg/day. In other words, from our point of view, the Moon is slower than the Sun.
 |
| Figure 4 |
So what happens during an eclipse? To have a solar eclipse the Moon must be seen between us and the Sun. Looking at Figure 4 we can understand that the eclipse happens in the region of the Earth where the Sun projects the shadow of our satellite. But if we pay attention at how this evolves in time, since the Moon is slower than the Sun, it must be that the former is already high in the sky when the latter rises. Our star slowly "chases" our satellite until, at a certain point, the shadow of the Moon falls on the surface of the Earth... starting from a western point and going to the east exactly because the Sun surpasses the Moon coming from the east and going to the west!
And that's all folks. No conspiracy out there, just a typical physics' recipe, with a pinch of kinematics on a basis of geometry.
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