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padparadscha who asked to pick my brains about a planet with an 80°+ axial tilt. On the other hand, it means I can write about something that came up at work recently, so I thought I'd combine things.
So, I recommend What if the Moon Didn't Exist: Voyages to Earths that Might Have Been (by Neil Comins), since one of the chapters features a variant-Earth with a tilt like Uranus. On the other hand, I just realized that chapter got one of the details wrong: the status of our moon.
Moons over Uranus (Yes, I am Mentally Five Years Old)
So, consider the big moons of our Solar System. Except Neptune's moons, because the original moons were mostly smashed all to Hell when Triton came in and Neptune grabbed it. So, that leaves Jupiter, Saturn, Uranus and Earth. All four of them formed moons from a disk. In the case of J, S and U, that was a remnant of their formation, much like how the planets formed from a disk that was part of the Sun's formation. In the case of Earth, the disk was probably because something about the size of Mars gave us a slow, glancing blow, just as we were finished forming, and knocked a lot of stuff off the planet.
Now, moons have many different kinds of orbits. Disks and rings around planets, however, circle the equator. There's a reason for this, actually. It has to do with the fact most planets aren't exact spheres. Among other things, the fact they are spinning squishes them a bit at the poles, like a giant ball of pizza dough twirling on someone's finger. This causes precession -- basically if an orbit is oval (elliptical) or tilted relative to the equator (inclined), the direction of the ovalness/tiltedness moves with time, which it wouldn't do if the planet was a perfect sphere. Moreover, it moves by different amounts depending on how far away this is from the planet. This means if you start two particles on parallel orbits, they won't stay parallel (and not hitting one another), unless they are orbiting in circles around the planet's equator. And if they hit one another, they tend to lose their oval or tilted orbits.
So, you get something like Saturn's rings, which are amazingly flat -- seriously, they are 300,000 km across from one end of the A ring to the other, and are maybe ten meters thick. (If they were the size of a sheet of printer paper, they'd be 10 nanometers (0.01 microns) thick -- paper is on the order of 100 microns thick for reference.)
As a result, the moons that form out of disks tend to start out on orbits that aren't tilted -- they orbit around the planet's equator. If they are tilted, it's usually because of other moons. All of Jupiter's big moons, all of Saturn's save one, and all of Uranus's are like this. (Yes, I am ignoring the captured asteroids and stuff that orbits in the other parts of near-Jovian and near-Saturnian space. Their motions are a bit more complex.)
But you noticed that I didn't mention our moon here. The Moon doesn't orbit the Earth's equator -- it actually orbits very nearly in the same plane as the Earth's orbit, which is tilted relative to the Earth's equator. The reason is this -- remember how I mentioned that the reason most moons orbit the equator of their primary is because their primaries aren't spherical? Turns out that effect becomes much less strong as you go away from the planet -- something like Saturn's rings feel it a lot (to the point where you have things like the Titan Ringlet, a oval ring that precesses so quickly that it always points at Titan (which orbits Saturn every three weeks)), but a moon like Iapetus (Saturn's outermost big satellite) doesn't feel it that much.
Moreover, there's another effect: the Sun. Yeah, the Sun's kind of a big deal, what with it being the biggest thing in the solar system. Granted, if a moon is still orbiting its primary, the Sun is not the biggest effect on its motion, but it can still push orbits around. One thing the Sun does is put something like a tide on moons -- just like tides on Earth are caused by the fact the surface of the Earth under the Moon feels slightly more gravity than the center of the Earth, causing the ocean to rise towards the Moon a bit (and the surface of the Earth opposite the moon feels less gravity than the center of the Earth, pushing the center towards the moon (or the ocean away from the Moon)), a moon moving in front of and behind its primary will feel different amounts of the solar gravity. Among other things, this slowly forces the moon down into the planet's orbital plane from its nice perch around the equator. It also means that things like eclipses are a lot more common.
(I mention that one of Saturn's moons doesn't orbit its equator -- Iapetus is sort of an intermediate case. Neither the forces from Saturn's non-sphericalness nor the solar tides really win out, so it orbits somewhere in the middle. This does give it a rather nice view of the rings, though. Technically our Moon's orbit also is slightly tilted with respect to the Earth's orbit, thanks to the fact at one point it was interacting with something.)
Anyway, back to my original point. If the Earth was tilted like Uranus, we don't need to assume that the Moon would orbit like Uranus's moons do -- around the equator. It might orbit near the Earth's orbit plane.
So what would the moon look like?
I'm going to take a page from Comins's book and call a Earth-with-Uranus's tilt Urania. Just because I like having a name for it. I'll also be talking a bit about the Sun and seasons, because knowing what the Sun is doing helps me visualize what the Moon is doing. (Or maybe I should call it Rhea or something, since she was one of the children of Gaea (Earth) and Uranus. So was Saturn/Cronos, but he has a planet already -- my second-favorite planet.)
Well, first off, you'd still get the normal phases in a 29.5 day cycle and its orbit with respect to the stars every 27.3 days. Basically the 27.3 day period is what controls the Moon's motion in the sky (outside of the rise and set which is dictated in part by Earth's spin). Earth's Moon has some variation in its height and rise/set position due to Earth's tilted axis (and a bit due to the fact our Moon isn't quite in our orbit plane -- why we only get an eclipse once or twice a year instead of every month), but on Urania, this is going to be noticeable to anyone who pays attention to the moon at all.
We'd also still get eclipses every so often. This is different from Urania's moon in Comins's book, which mostly has gibbous and crescent phases and eclipses are vanishingly rare.
One thing that might be interesting is that there'd be times of the month when there is no moonrise and times when there is a constantly-up moon -- just like the effect of the 'midnight sun'/endless night on Urania would occur at most latitudes. I'm going to step through this. I do about the same thing when talking about the Sun's motions when teaching Astro 101 -- talk about the extreme cases at the poles and equator, then go through the case in the mid-latitudes where my students live. I'm also going to keep general, and refer to winter and summer, rather than name months. (This makes it true for both hemispheres, but at six months' difference.)
Sun and Moon at the Poles of Urania
Let's start at the spring equinox. Like spring at the pole of Earth, this is the first time the Sun shows its face above the horizon. Here, the Full Moon will show up on the horizon. The gibbous moon will spiral higher and higher as it wheels around the pole, never setting, but slowly increasing in phase as the days pass -- it also will hang with the poles pointing parallel to the horizon. At third quarter, the Moon will be at the zenith, and will spin around there, then, as it goes towards new, it will descend, spiraling, towards the horizon, horns pointed away from the Sun (towards the zenith). At new moon, the Moon will set for two weeks. (Well, 27.3/2 days, which is a bit under two weeks.)
As spring progresses, the Sun will spiral higher in the sky and it will get warm. I hope you brought a boat, since the poles of Urania get quite toasty in the summer -- the summer pole is one of the warmest spots on the planet. The Moon's up time will also shift from Full-to-New during the equinox to Last-to-First-Quarter, which it reaches at the summer solstice. Here the Moon will rise in last quarter, curved limb facing the Sun, spiral up to the Sun (shining at zenith) for a week, decreasing in phase til New, then spiraling back down and increasing in phase. Then it's down for two weeks.
Fall is the reverse of spring. The Sun is in sunset, with the New Moon rising, the crescent spiraling up the heavens, the first-quarter hovering at zenith, the gibbous spiraling down, and the Full Moon at the horizon.
During the six-month-night, the moon will continue its habit of being up for two weeks. It will rise as a crescent, past through half-moon, gibbous and full, and set as a gibbous moon, until the winter solstice, where it will rise as a half-moon, pass as full overhead, and set as the other-half. For the rest of the winter, the phase at moonrise will continue to increase and the phase at moonset will continue to decrease until spring comes.
Sun and Moon at the Equator of Urania
The equator of Urania is probably the only part of the system where there's something resembling a normal day-night cycle for most of the year -- it will always be twelve hours from sunup to sundown. As long as you have a good northern and southern horizon, that is. Unlike Earth, the equator of Urania probably has seasons -- the solstices will be colder and the equinoxes warmer, so on a six-month cycle (not a twelve-month).
At (spring) equinox, the Sun rises due east and sets due west, and the Moon follows the same path as is familiar. New and full moon will follow a similar path as the Sun. However, the crescent Moon will rise and set to the north, until first quarter barely peaks above the north horizon, lit face tracking the Sun. The gibbous moon will slowly return to the rise-due-east-set-due-west at Full. Then the cycle will repeat itself in the south for the next two weeks.
As spring moves into northern-summer, the Sun rises and sets farther to the north. The Moon will continue its monthly journey from north point to south point and back, but the phase it reaches will be different. At summer solstice, where the Sun is at the north horizon all day (making it rather cold), the full moon would sit at the southern horizon, the gibbous rising and setting in the southern sky, the half-moon rising and setting due east and west, the crescent in the northern sky, and a new moon due north.
You can pretty much reverse the directions to everything to describe fall and northern-winter. The equator really runs more on a solstice-equinox cycle rather than spring-summer-fall-winter, on Earth or on Urania.
Sun and Moon at the Mid-Latitudes of Urania
Here's where it gets fun. Let's say we're at 45° latitude. First day of spring actually looks rather like what it does on Earth -- the Sun rises due east, sets due west, and passes about halfway between horizon and zenith at midday. The new and full moon will follow the same kind of path. The crescent moon will rise and set poleward until about 3 or 4 days in, one notices it's merely skimming the north (or south) horizon and not setting. For the next week around first-quarter, the moon will be up day and night, circling around the pole star, about the same way the moon would spiral around the zenith at the pole. About halfway between first-quarter and full, the Moon will set again, its rise and set moving anti-poleward. Full Moon will track the Sun, but as the moon wanes, it will continue to move anti-poleward. Halfway between Full Moon and Third Quarter, it will barely peak above the anti-pole horizon, then it will set for a week (27.3/4 days). The crescent moon will then return, and edge back towards rising and setting due east/west at New.
As spring progresses, the phases in this motion will shift. The Sun will also be shifting north. About halfway between equinox and summer solstice, the Sun will stop setting. It will also pass overhead at noon -- and if you thought summers were hot on Earth, Urania's have 3 months of constant sun. The Moon will be still visible during the day when it isn't close to the Sun in the sky.
At summer solstice, the Sun will be hanging in the sky as a giant pole star. New Moon would hang here, and the crescent will be circumpolar, never setting for a week around new moon. The weeks around first and last quarter will have a moon that rises and sets, while the week around Full Moon, the moon will never rise.
Six weeks later, the Sun will finally set for the first time in three months, and six weeks after that is the fall equinox, which is pretty much like that of spring. The Sun's path will continue to move anti-poleward in the sky, until six weeks into fall it will barely rise. Then we get three months of night.
At midwinter, assuming the skies are clear, the week around New Moon will have a moon that never rises above the horizon. The week around First Quarter will have a Moon facing anti-poleward rising and setting much like it does on Earth. For the week around Full Moon, the Moon will be constantly up in the poleward-sky, wheeling around as a gibbous moon. Then for the last week around Third Quarter, the moon will go back to rising and setting.
Summary
Pretty much the Moon follows the same path as the Sun, except over 27.3 days instead of 365.25 days. You can also predict the behavior of the Full Moon as what the Sun did six months ago, the New Moon as what the Sun is doing now, and the Quarter Moon as what the Sun did three months ago (or is going to do three moons hence). The phases also make a 29.5 day cycle.
45° is a nice latitude since it breaks up the sidereal month (27.3 days) into eight even periods, much like how you can break the year up into the solstices and equinoxes and cross-quarters. You could also use that to keep track of time of year when the Sun is constantly up/down (if you could see the Moon) -- the moon phase will tell you where the Sun is and when it will come back.
padparadscha who asked to pick my brains about a planet with an 80°+ axial tilt. On the other hand, it means I can write about something that came up at work recently, so I thought I'd combine things.So, I recommend What if the Moon Didn't Exist: Voyages to Earths that Might Have Been (by Neil Comins), since one of the chapters features a variant-Earth with a tilt like Uranus. On the other hand, I just realized that chapter got one of the details wrong: the status of our moon.
Moons over Uranus (Yes, I am Mentally Five Years Old)
So, consider the big moons of our Solar System. Except Neptune's moons, because the original moons were mostly smashed all to Hell when Triton came in and Neptune grabbed it. So, that leaves Jupiter, Saturn, Uranus and Earth. All four of them formed moons from a disk. In the case of J, S and U, that was a remnant of their formation, much like how the planets formed from a disk that was part of the Sun's formation. In the case of Earth, the disk was probably because something about the size of Mars gave us a slow, glancing blow, just as we were finished forming, and knocked a lot of stuff off the planet.
Now, moons have many different kinds of orbits. Disks and rings around planets, however, circle the equator. There's a reason for this, actually. It has to do with the fact most planets aren't exact spheres. Among other things, the fact they are spinning squishes them a bit at the poles, like a giant ball of pizza dough twirling on someone's finger. This causes precession -- basically if an orbit is oval (elliptical) or tilted relative to the equator (inclined), the direction of the ovalness/tiltedness moves with time, which it wouldn't do if the planet was a perfect sphere. Moreover, it moves by different amounts depending on how far away this is from the planet. This means if you start two particles on parallel orbits, they won't stay parallel (and not hitting one another), unless they are orbiting in circles around the planet's equator. And if they hit one another, they tend to lose their oval or tilted orbits.
So, you get something like Saturn's rings, which are amazingly flat -- seriously, they are 300,000 km across from one end of the A ring to the other, and are maybe ten meters thick. (If they were the size of a sheet of printer paper, they'd be 10 nanometers (0.01 microns) thick -- paper is on the order of 100 microns thick for reference.)
As a result, the moons that form out of disks tend to start out on orbits that aren't tilted -- they orbit around the planet's equator. If they are tilted, it's usually because of other moons. All of Jupiter's big moons, all of Saturn's save one, and all of Uranus's are like this. (Yes, I am ignoring the captured asteroids and stuff that orbits in the other parts of near-Jovian and near-Saturnian space. Their motions are a bit more complex.)
But you noticed that I didn't mention our moon here. The Moon doesn't orbit the Earth's equator -- it actually orbits very nearly in the same plane as the Earth's orbit, which is tilted relative to the Earth's equator. The reason is this -- remember how I mentioned that the reason most moons orbit the equator of their primary is because their primaries aren't spherical? Turns out that effect becomes much less strong as you go away from the planet -- something like Saturn's rings feel it a lot (to the point where you have things like the Titan Ringlet, a oval ring that precesses so quickly that it always points at Titan (which orbits Saturn every three weeks)), but a moon like Iapetus (Saturn's outermost big satellite) doesn't feel it that much.
Moreover, there's another effect: the Sun. Yeah, the Sun's kind of a big deal, what with it being the biggest thing in the solar system. Granted, if a moon is still orbiting its primary, the Sun is not the biggest effect on its motion, but it can still push orbits around. One thing the Sun does is put something like a tide on moons -- just like tides on Earth are caused by the fact the surface of the Earth under the Moon feels slightly more gravity than the center of the Earth, causing the ocean to rise towards the Moon a bit (and the surface of the Earth opposite the moon feels less gravity than the center of the Earth, pushing the center towards the moon (or the ocean away from the Moon)), a moon moving in front of and behind its primary will feel different amounts of the solar gravity. Among other things, this slowly forces the moon down into the planet's orbital plane from its nice perch around the equator. It also means that things like eclipses are a lot more common.
(I mention that one of Saturn's moons doesn't orbit its equator -- Iapetus is sort of an intermediate case. Neither the forces from Saturn's non-sphericalness nor the solar tides really win out, so it orbits somewhere in the middle. This does give it a rather nice view of the rings, though. Technically our Moon's orbit also is slightly tilted with respect to the Earth's orbit, thanks to the fact at one point it was interacting with something.)
Anyway, back to my original point. If the Earth was tilted like Uranus, we don't need to assume that the Moon would orbit like Uranus's moons do -- around the equator. It might orbit near the Earth's orbit plane.
So what would the moon look like?
I'm going to take a page from Comins's book and call a Earth-with-Uranus's tilt Urania. Just because I like having a name for it. I'll also be talking a bit about the Sun and seasons, because knowing what the Sun is doing helps me visualize what the Moon is doing. (Or maybe I should call it Rhea or something, since she was one of the children of Gaea (Earth) and Uranus. So was Saturn/Cronos, but he has a planet already -- my second-favorite planet.)
Well, first off, you'd still get the normal phases in a 29.5 day cycle and its orbit with respect to the stars every 27.3 days. Basically the 27.3 day period is what controls the Moon's motion in the sky (outside of the rise and set which is dictated in part by Earth's spin). Earth's Moon has some variation in its height and rise/set position due to Earth's tilted axis (and a bit due to the fact our Moon isn't quite in our orbit plane -- why we only get an eclipse once or twice a year instead of every month), but on Urania, this is going to be noticeable to anyone who pays attention to the moon at all.
We'd also still get eclipses every so often. This is different from Urania's moon in Comins's book, which mostly has gibbous and crescent phases and eclipses are vanishingly rare.
One thing that might be interesting is that there'd be times of the month when there is no moonrise and times when there is a constantly-up moon -- just like the effect of the 'midnight sun'/endless night on Urania would occur at most latitudes. I'm going to step through this. I do about the same thing when talking about the Sun's motions when teaching Astro 101 -- talk about the extreme cases at the poles and equator, then go through the case in the mid-latitudes where my students live. I'm also going to keep general, and refer to winter and summer, rather than name months. (This makes it true for both hemispheres, but at six months' difference.)
Sun and Moon at the Poles of Urania
Let's start at the spring equinox. Like spring at the pole of Earth, this is the first time the Sun shows its face above the horizon. Here, the Full Moon will show up on the horizon. The gibbous moon will spiral higher and higher as it wheels around the pole, never setting, but slowly increasing in phase as the days pass -- it also will hang with the poles pointing parallel to the horizon. At third quarter, the Moon will be at the zenith, and will spin around there, then, as it goes towards new, it will descend, spiraling, towards the horizon, horns pointed away from the Sun (towards the zenith). At new moon, the Moon will set for two weeks. (Well, 27.3/2 days, which is a bit under two weeks.)
As spring progresses, the Sun will spiral higher in the sky and it will get warm. I hope you brought a boat, since the poles of Urania get quite toasty in the summer -- the summer pole is one of the warmest spots on the planet. The Moon's up time will also shift from Full-to-New during the equinox to Last-to-First-Quarter, which it reaches at the summer solstice. Here the Moon will rise in last quarter, curved limb facing the Sun, spiral up to the Sun (shining at zenith) for a week, decreasing in phase til New, then spiraling back down and increasing in phase. Then it's down for two weeks.
Fall is the reverse of spring. The Sun is in sunset, with the New Moon rising, the crescent spiraling up the heavens, the first-quarter hovering at zenith, the gibbous spiraling down, and the Full Moon at the horizon.
During the six-month-night, the moon will continue its habit of being up for two weeks. It will rise as a crescent, past through half-moon, gibbous and full, and set as a gibbous moon, until the winter solstice, where it will rise as a half-moon, pass as full overhead, and set as the other-half. For the rest of the winter, the phase at moonrise will continue to increase and the phase at moonset will continue to decrease until spring comes.
Sun and Moon at the Equator of Urania
The equator of Urania is probably the only part of the system where there's something resembling a normal day-night cycle for most of the year -- it will always be twelve hours from sunup to sundown. As long as you have a good northern and southern horizon, that is. Unlike Earth, the equator of Urania probably has seasons -- the solstices will be colder and the equinoxes warmer, so on a six-month cycle (not a twelve-month).
At (spring) equinox, the Sun rises due east and sets due west, and the Moon follows the same path as is familiar. New and full moon will follow a similar path as the Sun. However, the crescent Moon will rise and set to the north, until first quarter barely peaks above the north horizon, lit face tracking the Sun. The gibbous moon will slowly return to the rise-due-east-set-due-west at Full. Then the cycle will repeat itself in the south for the next two weeks.
As spring moves into northern-summer, the Sun rises and sets farther to the north. The Moon will continue its monthly journey from north point to south point and back, but the phase it reaches will be different. At summer solstice, where the Sun is at the north horizon all day (making it rather cold), the full moon would sit at the southern horizon, the gibbous rising and setting in the southern sky, the half-moon rising and setting due east and west, the crescent in the northern sky, and a new moon due north.
You can pretty much reverse the directions to everything to describe fall and northern-winter. The equator really runs more on a solstice-equinox cycle rather than spring-summer-fall-winter, on Earth or on Urania.
Sun and Moon at the Mid-Latitudes of Urania
Here's where it gets fun. Let's say we're at 45° latitude. First day of spring actually looks rather like what it does on Earth -- the Sun rises due east, sets due west, and passes about halfway between horizon and zenith at midday. The new and full moon will follow the same kind of path. The crescent moon will rise and set poleward until about 3 or 4 days in, one notices it's merely skimming the north (or south) horizon and not setting. For the next week around first-quarter, the moon will be up day and night, circling around the pole star, about the same way the moon would spiral around the zenith at the pole. About halfway between first-quarter and full, the Moon will set again, its rise and set moving anti-poleward. Full Moon will track the Sun, but as the moon wanes, it will continue to move anti-poleward. Halfway between Full Moon and Third Quarter, it will barely peak above the anti-pole horizon, then it will set for a week (27.3/4 days). The crescent moon will then return, and edge back towards rising and setting due east/west at New.
As spring progresses, the phases in this motion will shift. The Sun will also be shifting north. About halfway between equinox and summer solstice, the Sun will stop setting. It will also pass overhead at noon -- and if you thought summers were hot on Earth, Urania's have 3 months of constant sun. The Moon will be still visible during the day when it isn't close to the Sun in the sky.
At summer solstice, the Sun will be hanging in the sky as a giant pole star. New Moon would hang here, and the crescent will be circumpolar, never setting for a week around new moon. The weeks around first and last quarter will have a moon that rises and sets, while the week around Full Moon, the moon will never rise.
Six weeks later, the Sun will finally set for the first time in three months, and six weeks after that is the fall equinox, which is pretty much like that of spring. The Sun's path will continue to move anti-poleward in the sky, until six weeks into fall it will barely rise. Then we get three months of night.
At midwinter, assuming the skies are clear, the week around New Moon will have a moon that never rises above the horizon. The week around First Quarter will have a Moon facing anti-poleward rising and setting much like it does on Earth. For the week around Full Moon, the Moon will be constantly up in the poleward-sky, wheeling around as a gibbous moon. Then for the last week around Third Quarter, the moon will go back to rising and setting.
Summary
Pretty much the Moon follows the same path as the Sun, except over 27.3 days instead of 365.25 days. You can also predict the behavior of the Full Moon as what the Sun did six months ago, the New Moon as what the Sun is doing now, and the Quarter Moon as what the Sun did three months ago (or is going to do three moons hence). The phases also make a 29.5 day cycle.
45° is a nice latitude since it breaks up the sidereal month (27.3 days) into eight even periods, much like how you can break the year up into the solstices and equinoxes and cross-quarters. You could also use that to keep track of time of year when the Sun is constantly up/down (if you could see the Moon) -- the moon phase will tell you where the Sun is and when it will come back.
