by Galaxian » Sat Aug 17, 2013 2:28 pm
Spif wrote:Chris Peterson wrote:
Again, "vertical separation" is meaningless. Every body is orbiting on its own plane, with the Sun at the center, and crosses Earth's orbit perfectly in two spots.
Edit: that's still not quite clear, I think. Not every pair of inclined eccentric orbits have to intersect at two points (or any points). I'll try to think of a better way to visualize the geometry. In any case, all of these asteroids have orbital paths which intersect Earth's.
Another way to imaging two orbits not interesecting, EVER, is this... take two hula hoops. Squish one so it is eccentric. The circle lies flat (Earth orbit). The eccentric one then inclines (say 30 degrees for illustration). Insert the eccentric one into the circle (clinical geometry please, no jokes
![Wink :wink:](./images/smilies/icon_wink.gif)
) so that they share the same orbital focus. The eccentric orbit can share the same focus as the circular one without the two ever intersecting... This is true even if you drift the semimajor axis around over time. The two orbits never intersect simply because one is eccentric (skinny) and has an angle of inclination that ensures vertical separation out of the plane of the circularized orbit.
From the top down, they appear to be "intersecting" orbits. But when you take the 3rd dimension into account, it is clear that the two bodies do not threaten each other unless they are perturbed by a third body sometime in the future.
So if the asteroids in the 2D map are simply a random selection of orbits that "cross" Earth's orbit in a top-down view, odds are that only a fraction of those are an actual threat to the Earth because they happen to share an inclination that is very co-incident with Earth's orbit. The odds of such close coincidence seem fairly small to me.
-s
Rather like the orbits of the two planets Neptune and Pluto? Pluto[1] is usually way farther out from Sol than is Neptune but for a tiny fraction of its orbit, 20 years out of about 250, the order of distances is reversed. Pluto gets *closer* to Sol than Neptune would be. That last happened from 1979 to 1999and will next happen around 2227 to 2247 -ish. However, Pluto's orbit is *very* tipped relative to the other planets' and when it "crosses Neptune's orbit", when it is as close to Sol as Neptune gets, it is a long way "below" Neptune (or "above"?), many millions of miles away.
PHA's and Earth often have somewhat the same relationship, only the angles and distances are smaller. Still, as should be obvious from the fact that they are still around and aren't crashing into us, when a PHA "crosses Earth's orbit" it's often many millions of miles away.
Of course, as we famously found out in 2013, twice, that is not always true.
Sometimes they do come close. Sometimes they come so close it counts as an intersection.
Still, it only ever seems to happen in Russia so the rest of us can feel safe and happy.
http://asterisk.apod.com/posting.php?mo ... 9&p=205223#
[1] Pluto was a planet when I was younger, so, to me, it always will be a planet no matter what the IAU says. Technically, using the "cleared its orbit" rule, none of Earth, Luna, Neptune or Jupiter would be IAU planets. Earth certainly hasn't cleared its orbit of that rather large lump, Luna, Luna hasn't cleared her orbit of Earth [which may be a good thing] and both Neptune and Jupiter have Trojans. "Planet" is a sentimental term, not a scientific one and I'm rather sentimental about poor wee Pluto. [2]
[2] Tongue firmly in cheek.
http://asterisk.apod.com/posting.php?mo ... 9&p=205223#
[quote="Spif"][quote="Chris Peterson"]
Again, "vertical separation" is meaningless. Every body is orbiting on its own plane, with the Sun at the center, and crosses Earth's orbit [i]perfectly [/i]in two spots.
Edit: that's still not quite clear, I think. Not every pair of inclined eccentric orbits have to intersect at two points (or any points). I'll try to think of a better way to visualize the geometry. In any case, all of these asteroids have orbital paths which intersect Earth's.[/quote]
Another way to imaging two orbits not interesecting, EVER, is this... take two hula hoops. Squish one so it is eccentric. The circle lies flat (Earth orbit). The eccentric one then inclines (say 30 degrees for illustration). Insert the eccentric one into the circle (clinical geometry please, no jokes :wink: ) so that they share the same orbital focus. The eccentric orbit can share the same focus as the circular one without the two ever intersecting... This is true even if you drift the semimajor axis around over time. The two orbits never intersect simply because one is eccentric (skinny) and has an angle of inclination that ensures vertical separation out of the plane of the circularized orbit.
From the top down, they appear to be "intersecting" orbits. But when you take the 3rd dimension into account, it is clear that the two bodies do not threaten each other unless they are perturbed by a third body sometime in the future.
So if the asteroids in the 2D map are simply a random selection of orbits that "cross" Earth's orbit in a top-down view, odds are that only a fraction of those are an actual threat to the Earth because they happen to share an inclination that is very co-incident with Earth's orbit. The odds of such close coincidence seem fairly small to me.
-s[/quote]
Rather like the orbits of the two planets Neptune and Pluto? Pluto[1] is usually way farther out from Sol than is Neptune but for a tiny fraction of its orbit, 20 years out of about 250, the order of distances is reversed. Pluto gets *closer* to Sol than Neptune would be. That last happened from 1979 to 1999and will next happen around 2227 to 2247 -ish. However, Pluto's orbit is *very* tipped relative to the other planets' and when it "crosses Neptune's orbit", when it is as close to Sol as Neptune gets, it is a long way "below" Neptune (or "above"?), many millions of miles away.
PHA's and Earth often have somewhat the same relationship, only the angles and distances are smaller. Still, as should be obvious from the fact that they are still around and aren't crashing into us, when a PHA "crosses Earth's orbit" it's often many millions of miles away.
Of course, as we famously found out in 2013, twice, that is not always true.
Sometimes they do come close. Sometimes they come so close it counts as an intersection.
Still, it only ever seems to happen in Russia so the rest of us can feel safe and happy. http://asterisk.apod.com/posting.php?mode=quote&f=9&p=205223#
[1] Pluto was a planet when I was younger, so, to me, it always will be a planet no matter what the IAU says. Technically, using the "cleared its orbit" rule, none of Earth, Luna, Neptune or Jupiter would be IAU planets. Earth certainly hasn't cleared its orbit of that rather large lump, Luna, Luna hasn't cleared her orbit of Earth [which may be a good thing] and both Neptune and Jupiter have Trojans. "Planet" is a sentimental term, not a scientific one and I'm rather sentimental about poor wee Pluto. [2]
[2] Tongue firmly in cheek. http://asterisk.apod.com/posting.php?mode=quote&f=9&p=205223#