by Chris Peterson » Sat Dec 25, 2021 2:09 pm
David G wrote: ↑Sat Dec 25, 2021 7:08 am
An ellipse has two focal points. Many comets' orbits are elliptical. For those comets in our solar system, the sun is one focal point ... but where's the other? For those comets outside our solar system, has anyone been able to establish the two foci?
This comet is in the process of being perturbed from an elliptical orbit to a hyperbolic one. While both ellipses and hyperbolas have two foci, only one of them is physically meaningful. If you know the orbital parameters, you can trivially identify the location of the empty focus, but it has no physical significance, so nobody bothers. All that is important is the focus that lies at the Sun.
Keplerian orbits are fundamentally the product of two-body interactions- which don't physically exist anywhere in the Universe except as approximations. As this comet gets farther and farther from the Sun, it will be increasingly perturbed into a complex path that the word "orbit" only marginally describes (of course, the comet might still be reasonably seen as in a near Keplerian elliptical orbit around the center of the galaxy).
[quote="David G" post_id=319266 time=1640416087]
An ellipse has two focal points. Many comets' orbits are elliptical. For those comets in our solar system, the sun is one focal point ... but where's the other? For those comets outside our solar system, has anyone been able to establish the two foci?
[/quote]
This comet is in the process of being perturbed from an elliptical orbit to a hyperbolic one. While both ellipses and hyperbolas have two foci, only one of them is physically meaningful. If you know the orbital parameters, you can trivially identify the location of the empty focus, but it has no physical significance, so nobody bothers. All that is important is the focus that lies at the Sun.
Keplerian orbits are fundamentally the product of two-body interactions- which don't physically exist anywhere in the Universe except as approximations. As this comet gets farther and farther from the Sun, it will be increasingly perturbed into a complex path that the word "orbit" only marginally describes (of course, the comet might still be reasonably seen as in a near Keplerian elliptical orbit around the center of the galaxy).