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TIL about Kirkwood gaps. I knew about Jupiter leading to Hilda and Trojan groupings, but my understanding of the main belt was more in line with a representati

by slg 2y ago

TIL about Kirkwood gaps. I knew about Jupiter leading to Hilda and Trojan groupings, but my understanding of the main belt was more in line with a representation like this one from Wikipedia[1]. However, this imaging shows a clear gap and a quick search led me to learn about Kirkwood gaps. Is there a specific reason why the gap is more evident in this imaging rather than the above one from Wikipedia? [1] - https://en.wikipedia.org/wiki/File:InnerSolarSystem-en.png https://en.wikipedia.org/wiki/File:InnerSolarSystem-en.png [2] - https://en.wikipedia.org/wiki/Kirkwood_gap https://en.wikipedia.org/wiki/Kirkwood_gap

o11c 2y ago
You should not be able to see the Kirkwood gaps if the simulation is accurate; the Wikipedia image is more realistic. The "gap" only applies to the semi-major axis (which is proportional to the 3/2th power of the period); since most asteroids are somewhat eccentric (and since semi-major axis is relative to the center but orbits are based on a focus, which "moves" rapidly as the circle deforms) there are always asteroids crossing the "gap" between perihelion (far short of the semi-minor axis, even) and aphelion (far beyond the semi-major axis). I'm too lazy to do the math, but based on planets with similar eccentricity, most asteroids are between 10% and 25% farther at aphelion than at perihelion (or, often between 0.25AU and 0.75AU farther), which easily crosses any single gap, and almost always multiple gaps. See the images at https://en.wikipedia.org/wiki/Orbital_eccentricity https://en.wikipedia.org/wiki/Orbital_eccentricity for informative images of ellipses.
- d_silin 2y ago
  I suspect the gap is at least 50% rendering artifact, but all 1.4M asteroids are plotted as (small) fraction of its orbital ellipse, so the density distribution is reflective of the real data (more specifically, orbit types)
  - slg 2y ago
    If I understand both the code and o11c's comment correctly, it sounds like the difference is less rendering artifact rather than what is being rendered. This code is rendering the asteroids based off their semi-major axis, but Wikipedia appears to be rendering their actual positions at a specific moment in time with the asteroids all at various points in their eccentric orbit.
    - d_silin 2y ago
      I am pretty sure it is the opposite :)
      - slg 2y ago
        Care to expand on that? Wikipedia image has the Greeks ahead of Jupiter and the Trojans behind Jupiter. Doesn't that clearly show it is an image of a moment in time? And the only attributes of an asteroid this code[1] seems to use are the eccentricity, semi-major axis, and perihelion. Although I'm no expert in either Python or astrophysics so I may be missing something. [1] - https://github.com/DarkStar1982/Orbidium/blob/536afc2e12e9a25ce3288c882bcaca83ef8af15c/pages/static/canvas.js#L54 https://github.com/DarkStar1982/Orbidium/blob/536afc2e12e9a2...
        d_silin 2y ago
        The code draws full orbit ellipse if selected to do so, but the original picture was rendered using a different mode, where just a small slice of the orbit arc is rendered, pretty much showing an instantaneous position of asteroid. Now, I am pretty sure actual positions are not correct relative to each other (it is the same position on ellipse arc, should be actual position of the asteroid) but MPC file doesn't provide this information - you need ephemeris from here: https://www.minorplanetcenter.net/iau/MPEph/MPEph.html https://www.minorplanetcenter.net/iau/MPEph/MPEph.html After all, it is mostly a data visualization demo (although I tried to be precise with scale too)
        slg 2y ago
        >Now, I am pretty sure actual positions are not correct relative to each other (it is the same position on ellipse arc That sounds to me just like a rephrasing of what I originally said. The locations in the Wikipedia image are correct relative to each other (because it is representing a moment in time) while the locations from the code are not correct relative to each other and are instead "the same position on ellipse arc" (although maybe I was wrong with my assumption that the "same position" was at the semi-major axis).
westurner 2y ago
TIL about Kirkwood gaps too: https://en.wikipedia.org/wiki/Kirkwood_gap https://en.wikipedia.org/wiki/Kirkwood_gap : > A Kirkwood gap is a gap or dip in the distribution of the semi-major axes (or equivalently of the orbital periods) of the orbits of main-belt asteroids. They correspond to the locations of orbital resonances with Jupiter. (Similarly, shouldn't it be possible to infer photon phase without causing wave state collapse?) /? Jupiter’s effect on Earth’s climate https://www.google.com/search?q=Jupiter%E2%80%99s+effect+on+Earth%E2%80%99s+climate https://www.google.com/search?q=Jupiter%E2%80%99s+effect+on+...

by slg 2y ago

o11c 2y ago

You should not be able to see the Kirkwood gaps if the simulation is accurate; the Wikipedia image is more realistic. The "gap" only applies to the semi-major axis (which is proportional to the 3/2th power of the period); since most asteroids are somewhat eccentric (and since semi-major axis is relative to the center but orbits are based on a focus, which "moves" rapidly as the circle deforms) there are always asteroids crossing the "gap" between perihelion (far short of the semi-minor axis, even) and aphelion (far beyond the semi-major axis). I'm too lazy to do the math, but based on planets with similar eccentricity, most asteroids are between 10% and 25% farther at aphelion than at perihelion (or, often between 0.25AU and 0.75AU farther), which easily crosses any single gap, and almost always multiple gaps. See the images at https://en.wikipedia.org/wiki/Orbital_eccentricity https://en.wikipedia.org/wiki/Orbital_eccentricity for informative images of ellipses.

d_silin 2y ago
I suspect the gap is at least 50% rendering artifact, but all 1.4M asteroids are plotted as (small) fraction of its orbital ellipse, so the density distribution is reflective of the real data (more specifically, orbit types)
- slg 2y ago
  If I understand both the code and o11c's comment correctly, it sounds like the difference is less rendering artifact rather than what is being rendered. This code is rendering the asteroids based off their semi-major axis, but Wikipedia appears to be rendering their actual positions at a specific moment in time with the asteroids all at various points in their eccentric orbit.
  - d_silin 2y ago
    I am pretty sure it is the opposite :)
    - slg 2y ago
      Care to expand on that? Wikipedia image has the Greeks ahead of Jupiter and the Trojans behind Jupiter. Doesn't that clearly show it is an image of a moment in time? And the only attributes of an asteroid this code[1] seems to use are the eccentricity, semi-major axis, and perihelion. Although I'm no expert in either Python or astrophysics so I may be missing something. [1] - https://github.com/DarkStar1982/Orbidium/blob/536afc2e12e9a25ce3288c882bcaca83ef8af15c/pages/static/canvas.js#L54 https://github.com/DarkStar1982/Orbidium/blob/536afc2e12e9a2...
      - d_silin 2y ago
        The code draws full orbit ellipse if selected to do so, but the original picture was rendered using a different mode, where just a small slice of the orbit arc is rendered, pretty much showing an instantaneous position of asteroid. Now, I am pretty sure actual positions are not correct relative to each other (it is the same position on ellipse arc, should be actual position of the asteroid) but MPC file doesn't provide this information - you need ephemeris from here: https://www.minorplanetcenter.net/iau/MPEph/MPEph.html https://www.minorplanetcenter.net/iau/MPEph/MPEph.html After all, it is mostly a data visualization demo (although I tried to be precise with scale too)
        slg 2y ago
        >Now, I am pretty sure actual positions are not correct relative to each other (it is the same position on ellipse arc That sounds to me just like a rephrasing of what I originally said. The locations in the Wikipedia image are correct relative to each other (because it is representing a moment in time) while the locations from the code are not correct relative to each other and are instead "the same position on ellipse arc" (although maybe I was wrong with my assumption that the "same position" was at the semi-major axis).

westurner 2y ago

TIL about Kirkwood gaps too: https://en.wikipedia.org/wiki/Kirkwood_gap https://en.wikipedia.org/wiki/Kirkwood_gap : > A Kirkwood gap is a gap or dip in the distribution of the semi-major axes (or equivalently of the orbital periods) of the orbits of main-belt asteroids. They correspond to the locations of orbital resonances with Jupiter. (Similarly, shouldn't it be possible to infer photon phase without causing wave state collapse?) /? Jupiter’s effect on Earth’s climate https://www.google.com/search?q=Jupiter%E2%80%99s+effect+on+Earth%E2%80%99s+climate https://www.google.com/search?q=Jupiter%E2%80%99s+effect+on+...