The View from Down Under
I was in touch with Phil Plait, aka The Bad Astronomer, about my photos of the Venus-Moon-Jupiter conjunction. His sky in California has been clouded over but he did say that there were some other nice photos of the conjunction at a blog in Australia called Two Cents, by Beche-La-Mer. Her photos include one bright body that did not appear in mine (the star Spica), and they show the Moon almost touching Venus: Australia turned toward the conjunction half a day after New York was facing it, so Beche saw a Moon that had had about 12 to 14 extra hours to move across the sky. Beche left a comment on my first post and noted how interesting it was to see the perspective from the other side of the planet. I agree, it's actually quite engrossing when you think about it.
Beche's photos have Venus, Jupiter and the Moon in a nearly vertical line while my photos have them close to horizontal. I've been using the sky charts provided by SkyView Cafe and AstroViewer to learn a little more. In Australia (a country I have never visited), the planets and moons of our solar system are rising at a slant in the morning, and setting almost in a vertical line, while in New York the situation is reversed. Consequently Beche was able to catch these bodies while they were still very high in the sky, with Jupiter, for instance, about twice as high at sunset than was the case in New York. (Here, Jupiter was 16 degrees above the horizon at sunset). You can see an astronomical object more clearly the higher it lies above the horizon, not just because the object is far from the city lights typically on the horizon, but because you're looking through less air, clouds, smog, etc. If you saw something directly overhead, you'd be looking essentially through the depth of the earth's atmosphere -- about 100 miles, no more. The light from an overhead object cuts through the air as efficiently as possible before it gets to our eyes. The light from an object sitting just above our horizon has to cut diagonally through our atmosphere before it gets to our eyes. The Moon that I saw the night of the conjunction was clear and white at first but grew more turbulent and yellow as it approached the horizon, which can be seen in the photos I published.
Now the reason that New York and Australia should see objects setting at different angles, or at any angle, is a complex little problem that has taken up more pages in my personal astronomy journals than any other "problem" or subject. More than once I've tried to work out in my head, or with a globe, the best way to think about it or to describe it. What follows is a new description. Comments are welcome.
Imagine you're on the sun and watching the earth spin, with a dark line running along the equator. And where is that line exactly? Well the sun's view of it changes. At the summer solstice in late June, the northern hemisphere was turned directly toward the sun, so from the sun you would have imagined the equator's line to look like a smile; at the December solstice, with the southern hemisphere turned to the sun, you'd see a frown. At most other times you would see something like a sideways smile or frown, one in which only the left or the right corner of the mouth was curling much. I say "most other times" because there are two brief exceptions. At the September and March equinoxes, you'd imagine a straight line representing the equator, running diagonally across the face of the earth. If you think of the round face of the earth as a clock, you would draw your imaginary line from about 8:13 to 2:13 in September, and from about 9:47 to 3:47 in March. The basis for these reference points is simple: the clock represents 360 degrees, with each hour representing 30 degrees, and 47 minutes representing 23.5 degrees, which is only 1/20 of a degree more than the actual tilt of the earth's axis.
On the dates of the equinoxes, the equator runs in a straight line from the sun's perspective. So if you're on the sun on September 22 of this year, and you're watching the earth spinning from left to right, watch for the city of Quito, Ecuador (a country I have visited, since my parents are from there). Quito is almost directly on the equator. You'd watch the city emerge into view at 8:13 on the clock, and it would appear to be making its way directly towards you. You'd watch it move across the earth's face until it arrived at 2:13 and disappeared from view, in a seemingly direct line away from you. Now, from Quito's point of view you'd see the sun and all the planets rise in a vertical line from a point lying exactly East, travel directly overhead, and sink back into the horizon in a vertical line at a point exactly West.
But this would never happen for Australia or New York. Imagine for a moment that the earth's axis is not tilted: the equator appears from the sun to run from 9 o'clock to 3 o'clock. Objects on the equator rotate from 9 toward 3. Someone on the equator sees the sun passing directly over him, any day of the year. But imagine what someone at the north pole sees. The earth is a ball; someone at the top of the ball is almost on the other side of the ball; if he were very tall, lets say many miles tall, someone at the sun might see this person standing on top of the earth. This person is nearly in night-time. Bring this person back to normal size: he sees the sun peeking just over the horizon. As the earth turns him around, he sees the sun going around in a circle that hugs the horizon. It's an extremely narrow angle, in other words, compared to the 90-degree line that the sun forms with the horizon for an observer at the equator.
So it's the curve of the ball we live on that ensures angles for rising and setting objects. There is another way I think about it which is perhaps more direct and simple. At 9 o'clock you see the line of the equator coming to an intersection, an apparently 90-degree angle, with the edge of the clock. A line running parallel to the equator, either above or below, such as the line of latitude that New York sits on, meets the edge of the clock at something other than 90 degrees. A city at 45 degrees of latitude will meet the edge at an apparently 45-degree angle. (New York sits very close to that line). A line running left to right just below the north pole intersects the top edge of the clock at a very small angle; such a line is almost running parallel with the section of the clock's edge that it cuts off.
All this by itself would produce angles for rising and setting objects. But if we go back and imagine the earth with its actual 23-degree tilt, things become more complicated. Now the equator appears as a straight line from the sun's perspective only on the dates of the equinoxes; at all other times it appears to be either a smile or a frown, as either the northern or southern hemisphere tilts toward the sun. Now the line on which New York sits will meet the edge of the clock at an angle further removed from what we could expect if the earth had no tilt. Whatever the exact angle, however, we know that what happens with New York would be the opposite of what happens with Australia, since only the northern or the southern hemisphere can be turned toward the sun at any one time.
This past week the north was tilted toward the sun, as it always is between March 21 and September 21. Between September and March the south will be turned toward the sun. On December 21 the south will be turned to its maximum sunward direction, and the north pole will be pointed at a maximum 23 degrees away from the sun. At that time the equator will look from the sun's perspective like a deep and perfectly symmetrical "frown" in which both corners of the mouth look the same: the frown will meet the left side of the clock at the same angle that it intersects the right side. This will be true for all imaginary lines of latitude: their frowns will meet the sides of the clock at angles that are produced according to how close they are to the bottom edge of the clock, as noted, but they will all intersect the sides of the clock in symmetrical frowns. Objects rising in Australian skies will do so at exactly the same angle that they do when they set. Right now objects are setting close to vertically and rising close to horizontally, as we see in Beche's photos; starting on December 21 and going all the way till June 21, it will be more accurate to say that they're setting horizontally and rising vertically. The contrast between sunrise and sunset will be smallest when the two angles "switch" places on December 21, and it will be greatest on March 21, when the contrast will begin to reduce, on its way to finally reversing itself again on June 21.
Confused? Good. There are good and bad ways to explain these things in words, and I hope mine were not too bad, but in the end words are not going to get these things across. A globe is handier, as is personal experience watching the skies.
A final note: Beche's photos captured a descent of Venus, Jupiter and the Moon that was nearly vertical, but to the extent that there was a sideways descent of these bodies, she saw them moving from right to left. This sideways motion, as noted, would currently be more noticeable in Australian sunrises, but it's there at sunset: if you look at the Moon in Beche's photo, the illuminated part of it is the lower-left section, suggesting the presence of the sun off to the moon's left. By contrast, I saw a lunar crescent curved in reverse, on the lower right of the moon's face: I saw the three bodies and the sun descend from left to right. This can also be seen here at sunrise, though currently the sideways motion at dawn is less noticeable than the vertical.
These perceptions of sideways motion do not reverse themselves throughout the year, since this phenomenon has nothing to do with the changing direction of the earth's tilt. It comes about only because someone in Australia must look north to see solar system objects, while someone in New York must look south. To say it this way can be a bit confusing since we see sunrise in the east and sunset in the west, but I've imagined it sometimes by picturing a very large human figure on the ball of the earth. Someone in New York is looking more or less "down" at the equator when looking out at the solar system and everything in its plane (objects well above or below the solar system are a different story), while someone in Australia is looking more or less "up" at the equator. In short, they are facing each other, so each person's "left" and "right" is a matter of perspective. They would use these subjective terms, but they would still speak of the sun rising in the east and setting in the west.
Beche's photos have Venus, Jupiter and the Moon in a nearly vertical line while my photos have them close to horizontal. I've been using the sky charts provided by SkyView Cafe and AstroViewer to learn a little more. In Australia (a country I have never visited), the planets and moons of our solar system are rising at a slant in the morning, and setting almost in a vertical line, while in New York the situation is reversed. Consequently Beche was able to catch these bodies while they were still very high in the sky, with Jupiter, for instance, about twice as high at sunset than was the case in New York. (Here, Jupiter was 16 degrees above the horizon at sunset). You can see an astronomical object more clearly the higher it lies above the horizon, not just because the object is far from the city lights typically on the horizon, but because you're looking through less air, clouds, smog, etc. If you saw something directly overhead, you'd be looking essentially through the depth of the earth's atmosphere -- about 100 miles, no more. The light from an overhead object cuts through the air as efficiently as possible before it gets to our eyes. The light from an object sitting just above our horizon has to cut diagonally through our atmosphere before it gets to our eyes. The Moon that I saw the night of the conjunction was clear and white at first but grew more turbulent and yellow as it approached the horizon, which can be seen in the photos I published.
Now the reason that New York and Australia should see objects setting at different angles, or at any angle, is a complex little problem that has taken up more pages in my personal astronomy journals than any other "problem" or subject. More than once I've tried to work out in my head, or with a globe, the best way to think about it or to describe it. What follows is a new description. Comments are welcome.
Imagine you're on the sun and watching the earth spin, with a dark line running along the equator. And where is that line exactly? Well the sun's view of it changes. At the summer solstice in late June, the northern hemisphere was turned directly toward the sun, so from the sun you would have imagined the equator's line to look like a smile; at the December solstice, with the southern hemisphere turned to the sun, you'd see a frown. At most other times you would see something like a sideways smile or frown, one in which only the left or the right corner of the mouth was curling much. I say "most other times" because there are two brief exceptions. At the September and March equinoxes, you'd imagine a straight line representing the equator, running diagonally across the face of the earth. If you think of the round face of the earth as a clock, you would draw your imaginary line from about 8:13 to 2:13 in September, and from about 9:47 to 3:47 in March. The basis for these reference points is simple: the clock represents 360 degrees, with each hour representing 30 degrees, and 47 minutes representing 23.5 degrees, which is only 1/20 of a degree more than the actual tilt of the earth's axis.
On the dates of the equinoxes, the equator runs in a straight line from the sun's perspective. So if you're on the sun on September 22 of this year, and you're watching the earth spinning from left to right, watch for the city of Quito, Ecuador (a country I have visited, since my parents are from there). Quito is almost directly on the equator. You'd watch the city emerge into view at 8:13 on the clock, and it would appear to be making its way directly towards you. You'd watch it move across the earth's face until it arrived at 2:13 and disappeared from view, in a seemingly direct line away from you. Now, from Quito's point of view you'd see the sun and all the planets rise in a vertical line from a point lying exactly East, travel directly overhead, and sink back into the horizon in a vertical line at a point exactly West.
But this would never happen for Australia or New York. Imagine for a moment that the earth's axis is not tilted: the equator appears from the sun to run from 9 o'clock to 3 o'clock. Objects on the equator rotate from 9 toward 3. Someone on the equator sees the sun passing directly over him, any day of the year. But imagine what someone at the north pole sees. The earth is a ball; someone at the top of the ball is almost on the other side of the ball; if he were very tall, lets say many miles tall, someone at the sun might see this person standing on top of the earth. This person is nearly in night-time. Bring this person back to normal size: he sees the sun peeking just over the horizon. As the earth turns him around, he sees the sun going around in a circle that hugs the horizon. It's an extremely narrow angle, in other words, compared to the 90-degree line that the sun forms with the horizon for an observer at the equator.
So it's the curve of the ball we live on that ensures angles for rising and setting objects. There is another way I think about it which is perhaps more direct and simple. At 9 o'clock you see the line of the equator coming to an intersection, an apparently 90-degree angle, with the edge of the clock. A line running parallel to the equator, either above or below, such as the line of latitude that New York sits on, meets the edge of the clock at something other than 90 degrees. A city at 45 degrees of latitude will meet the edge at an apparently 45-degree angle. (New York sits very close to that line). A line running left to right just below the north pole intersects the top edge of the clock at a very small angle; such a line is almost running parallel with the section of the clock's edge that it cuts off.
All this by itself would produce angles for rising and setting objects. But if we go back and imagine the earth with its actual 23-degree tilt, things become more complicated. Now the equator appears as a straight line from the sun's perspective only on the dates of the equinoxes; at all other times it appears to be either a smile or a frown, as either the northern or southern hemisphere tilts toward the sun. Now the line on which New York sits will meet the edge of the clock at an angle further removed from what we could expect if the earth had no tilt. Whatever the exact angle, however, we know that what happens with New York would be the opposite of what happens with Australia, since only the northern or the southern hemisphere can be turned toward the sun at any one time.
This past week the north was tilted toward the sun, as it always is between March 21 and September 21. Between September and March the south will be turned toward the sun. On December 21 the south will be turned to its maximum sunward direction, and the north pole will be pointed at a maximum 23 degrees away from the sun. At that time the equator will look from the sun's perspective like a deep and perfectly symmetrical "frown" in which both corners of the mouth look the same: the frown will meet the left side of the clock at the same angle that it intersects the right side. This will be true for all imaginary lines of latitude: their frowns will meet the sides of the clock at angles that are produced according to how close they are to the bottom edge of the clock, as noted, but they will all intersect the sides of the clock in symmetrical frowns. Objects rising in Australian skies will do so at exactly the same angle that they do when they set. Right now objects are setting close to vertically and rising close to horizontally, as we see in Beche's photos; starting on December 21 and going all the way till June 21, it will be more accurate to say that they're setting horizontally and rising vertically. The contrast between sunrise and sunset will be smallest when the two angles "switch" places on December 21, and it will be greatest on March 21, when the contrast will begin to reduce, on its way to finally reversing itself again on June 21.
Confused? Good. There are good and bad ways to explain these things in words, and I hope mine were not too bad, but in the end words are not going to get these things across. A globe is handier, as is personal experience watching the skies.
A final note: Beche's photos captured a descent of Venus, Jupiter and the Moon that was nearly vertical, but to the extent that there was a sideways descent of these bodies, she saw them moving from right to left. This sideways motion, as noted, would currently be more noticeable in Australian sunrises, but it's there at sunset: if you look at the Moon in Beche's photo, the illuminated part of it is the lower-left section, suggesting the presence of the sun off to the moon's left. By contrast, I saw a lunar crescent curved in reverse, on the lower right of the moon's face: I saw the three bodies and the sun descend from left to right. This can also be seen here at sunrise, though currently the sideways motion at dawn is less noticeable than the vertical.
These perceptions of sideways motion do not reverse themselves throughout the year, since this phenomenon has nothing to do with the changing direction of the earth's tilt. It comes about only because someone in Australia must look north to see solar system objects, while someone in New York must look south. To say it this way can be a bit confusing since we see sunrise in the east and sunset in the west, but I've imagined it sometimes by picturing a very large human figure on the ball of the earth. Someone in New York is looking more or less "down" at the equator when looking out at the solar system and everything in its plane (objects well above or below the solar system are a different story), while someone in Australia is looking more or less "up" at the equator. In short, they are facing each other, so each person's "left" and "right" is a matter of perspective. They would use these subjective terms, but they would still speak of the sun rising in the east and setting in the west.
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