[math-fun] Mercury's locked rotation & orbit
When I was in high school, I was taught that Mercury's orbit and rotation were locked 1:1. I recently discovered (to my chagrin) that NASA's knowledge had improved, but mine had not; Mercury actually rotates 1.5x faster that it's orbital period -- i.e., two full elliptical orbits = 3 full rotations. Here's a link to a .gif animation of Mercury's rotation & orbit. https://commons.wikimedia.org/wiki/File:Orbital_resonance_of_Mercury.gif *I'm not 100% convinced that this particular gif animation is correct w.r.t. timing; it doesn't seem to follow Kepler's Second (Equal Area) Law, whereby equal areas are swept out in equal times, and thus Mercury should actually be moving faster when closer to the Sun.* https://en.wikipedia.org/wiki/Mercury_%28planet%29 Astronomers call Mercury's orbit/rotation a "resonance", but I don't understand why. The whole point of a 1:1 orbit/rotation locking is to eliminate the tidal effects on the planet, but any other ratio still produces tides. I'm not sure what effect is causing a "lock" to the 3:2 ratio; perhaps it is related to the excessive eccentricity of Mercury's orbit? In any case, when I was in high school, we talked about the "dark side of Mercury", still thinking that it had a 1:1 ratio -- like that of the Earth's Moon. In such a case, the "dark side" should be quite cold -- particularly since Mercury has essentially no atmosphere to transfer energy from the "bright side" to the "dark side". I would imagine that the temperature of the "dark side" in such a case would be determined by an equilibrium between the temperature of deep space and the *mean* temperature of Mercury (averaged over the entire body), because in that case, Mercury would be *conducting* heat from the bright side to the dark side solely by conducting the heat through the interior of the planet's body. However, there is actually no "dark side" of Mercury, which is a pity, because it might be an interesting place for various scientific measurements. I do hope that no science fiction stories were harmed in the making of the discovery that Mercury was not in 1:1 resonance!
I guess the full answer is here: http://www.nature.com/nature/journal/v429/n6994/abs/nature02609.html à+ É. Catapulté de mon aPhone Le 3 janv. 2017 à 05:25, Henry Baker <hbaker1@pipeline.com<mailto:hbaker1@pipeline.com>> a écrit : When I was in high school, I was taught that Mercury's orbit and rotation were locked 1:1. I recently discovered (to my chagrin) that NASA's knowledge had improved, but mine had not; Mercury actually rotates 1.5x faster that it's orbital period -- i.e., two full elliptical orbits = 3 full rotations. Here's a link to a .gif animation of Mercury's rotation & orbit. https://commons.wikimedia.org/wiki/File:Orbital_resonance_of_Mercury.gif *I'm not 100% convinced that this particular gif animation is correct w.r.t. timing; it doesn't seem to follow Kepler's Second (Equal Area) Law, whereby equal areas are swept out in equal times, and thus Mercury should actually be moving faster when closer to the Sun.* https://en.wikipedia.org/wiki/Mercury_%28planet%29 Astronomers call Mercury's orbit/rotation a "resonance", but I don't understand why. The whole point of a 1:1 orbit/rotation locking is to eliminate the tidal effects on the planet, but any other ratio still produces tides. I'm not sure what effect is causing a "lock" to the 3:2 ratio; perhaps it is related to the excessive eccentricity of Mercury's orbit? In any case, when I was in high school, we talked about the "dark side of Mercury", still thinking that it had a 1:1 ratio -- like that of the Earth's Moon. In such a case, the "dark side" should be quite cold -- particularly since Mercury has essentially no atmosphere to transfer energy from the "bright side" to the "dark side". I would imagine that the temperature of the "dark side" in such a case would be determined by an equilibrium between the temperature of deep space and the *mean* temperature of Mercury (averaged over the entire body), because in that case, Mercury would be *conducting* heat from the bright side to the dark side solely by conducting the heat through the interior of the planet's body. However, there is actually no "dark side" of Mercury, which is a pity, because it might be an interesting place for various scientific measurements. I do hope that no science fiction stories were harmed in the making of the discovery that Mercury was not in 1:1 resonance! _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com<mailto:math-fun@mailman.xmission.com> https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
The word "resonance" is used when periods are in in low integer ratios like 2:3. I have long heard that many of the planets' years are in low integer ratios, and that this is because this makes for a relative minimum of potential energy. —Dan Henry wrote: ----- I recently discovered (to my chagrin) that NASA's knowledge had improved, but mine had not; Mercury actually rotates 1.5x faster that it's orbital period -- i.e., two full elliptical orbits = 3 full rotations. ... Astronomers call Mercury's orbit/rotation a "resonance", but I don't understand why. The whole point of a 1:1 orbit/rotation locking is to eliminate the tidal effects on the planet, but any other ratio still produces tides. I'm not sure what effect is causing a "lock" to the 3:2 ratio; perhaps it is related to the excessive eccentricity of Mercury's orbit? ... -----
In case it isn't clear from Dan's explanation, the potential energy is locally minimized when Mercury's "gravitational axis" is pointing through the center of the Sun at perihelion. Other inner-system weirdness: at least when I was a young adult, it was believed that Venus was in a tidal lock with the Earth, rotating slowly in retrograde so that at each pass of the Earth, Venus would keep one side facing us as it went past. On Tue, Jan 3, 2017 at 12:17 AM, Dan Asimov <asimov@msri.org> wrote:
The word "resonance" is used when periods are in in low integer ratios like 2:3.
I have long heard that many of the planets' years are in low integer ratios, and that this is because this makes for a relative minimum of potential energy.
—Dan
Henry wrote: ----- I recently discovered (to my chagrin) that NASA's knowledge had improved, but mine had not; Mercury actually rotates 1.5x faster that it's orbital period -- i.e., two full elliptical orbits = 3 full rotations.
...
Astronomers call Mercury's orbit/rotation a "resonance", but I don't understand why. The whole point of a 1:1 orbit/rotation locking is to eliminate the tidal effects on the planet, but any other ratio still produces tides. I'm not sure what effect is causing a "lock" to the 3:2 ratio; perhaps it is related to the excessive eccentricity of Mercury's orbit?
... ----- _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Kim Stanley Robinson has suggested building an equatorial train track around Mercury, and using heat expansion to put a city around it, so that it’s always at the terminator. There are also some nice 1:2:4 resonances among Jupiter’s moons, and a 2:3 resonance between Pluto and Neptune: https://en.wikipedia.org/wiki/Orbital_resonance - Cris
On Jan 2, 2017, at 10:07 PM, Eric Angelini <Eric.Angelini@kntv.be> wrote:
I guess the full answer is here:
http://www.nature.com/nature/journal/v429/n6994/abs/nature02609.html
à+ É. Catapulté de mon aPhone
Le 3 janv. 2017 à 05:25, Henry Baker <hbaker1@pipeline.com<mailto:hbaker1@pipeline.com>> a écrit :
When I was in high school, I was taught that Mercury's orbit and rotation were locked 1:1.
I recently discovered (to my chagrin) that NASA's knowledge had improved, but mine had not; Mercury actually rotates 1.5x faster that it's orbital period -- i.e., two full elliptical orbits = 3 full rotations.
Here's a link to a .gif animation of Mercury's rotation & orbit.
https://commons.wikimedia.org/wiki/File:Orbital_resonance_of_Mercury.gif
*I'm not 100% convinced that this particular gif animation is correct w.r.t. timing; it doesn't seem to follow Kepler's Second (Equal Area) Law, whereby equal areas are swept out in equal times, and thus Mercury should actually be moving faster when closer to the Sun.*
https://en.wikipedia.org/wiki/Mercury_%28planet%29
Astronomers call Mercury's orbit/rotation a "resonance", but I don't understand why. The whole point of a 1:1 orbit/rotation locking is to eliminate the tidal effects on the planet, but any other ratio still produces tides. I'm not sure what effect is causing a "lock" to the 3:2 ratio; perhaps it is related to the excessive eccentricity of Mercury's orbit?
In any case, when I was in high school, we talked about the "dark side of Mercury", still thinking that it had a 1:1 ratio -- like that of the Earth's Moon. In such a case, the "dark side" should be quite cold -- particularly since Mercury has essentially no atmosphere to transfer energy from the "bright side" to the "dark side". I would imagine that the temperature of the "dark side" in such a case would be determined by an equilibrium between the temperature of deep space and the *mean* temperature of Mercury (averaged over the entire body), because in that case, Mercury would be *conducting* heat from the bright side to the dark side solely by conducting the heat through the interior of the planet's body.
However, there is actually no "dark side" of Mercury, which is a pity, because it might be an interesting place for various scientific measurements.
I do hope that no science fiction stories were harmed in the making of the discovery that Mercury was not in 1:1 resonance!
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com<mailto:math-fun@mailman.xmission.com> https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (5)
-
Allan Wechsler -
Cris Moore -
Dan Asimov -
Eric Angelini -
Henry Baker