Is this orbit possible?

[PlonioFludrasco]

It can also be a parabolic orbit seen from an angle, assuming one between the upper or the lower point (depends if you are seeing the orbit from above or from below) is the limit of position(t) when t goes to + or - infinite (is the same), and also at infinite distance.

Sorry, too much projective geometry today...

[Rakaydos]

Hmm... Eliptical orbit shown in a double-period rotating frame of reference.

That is, imagine a satelite over the equator that orbits once every 12 hours... as seen from a point above the north pole that rotates with the planet.

The satelite reaches Apoapse over point A at time 0. 6 hours later, it has reached periapse 180 degrees away... but the planet has rotated 90 degrees under it, effectively putting the satelite in point c.

6 hours later, the satelite is back at apoapse, but the planet is 180 degrees out of alignment. This means from the PLANET's view, the satelite is at Point B. it'll take another orbit for the planet to rotate back under it to put Apoapse at Point A.

...it is true, from a certian point of view.

[PB666]

No, it should also be restricted to the focus. The same goes for hyperbolas.

But truly parabolic orbits (e=1) should, like circles (e=0), not exist.

A circular orbit could exist in deep intergalactic space for a small object orbiting close to a very massive but energetically inactive object. What is your level of precision, the higher the level of precision, the less likely it is to exist.

A truely parabolic cannot exist on a galactic scale, there are simply too many massive perturbations.

- - - Updated - - -

Hmm... Eliptical orbit shown in a double-period rotating frame of reference.

That is, imagine a satelite over the equator that orbits once every 12 hours... as seen from a point above the north pole that rotates with the planet.

The satelite reaches Apoapse over point A at time 0. 6 hours later, it has reached periapse 180 degrees away... but the planet has rotated 90 degrees under it, effectively putting the satelite in point c.

6 hours later, the satelite is back at apoapse, but the planet is 180 degrees out of alignment. This means from the PLANET's view, the satelite is at Point B. it'll take another orbit for the planet to rotate back under it to put Apoapse at Point A.

...it is true, from a certian point of view.

Shhhhhhh, KSK will go all ragey on you.

[GigaG]

You are mistaken. The gravity must scale as r instead of 1/r² to produce an ellipse centered at the body. 1/r produces completely different orbits, most of which are not closed.

Is there any sort of program online that can simulate "changing the laws of physics", like changing gravity's scaling?

[GoSlash27]

I'm going to go out on a limb and assume that the OP meant "gravity".

Yes, you are correct. It's not possible.

Best,

-Slashy

[YNM]

No, it should also be restricted to the focus. The same goes for hyperbolas.

But truly parabolic orbits (e=1) should, like circles (e=0), not exist.

Hmm... I thought it was tried on some simulation, dunno using what (matlab ?). The point was if you keep the magnitude the same (at escape speed) but the direction different, some directions would result in such orbit. Could've been just some paralaxes due to viewing through...

[ZetaX]

Hmm... I thought it was tried on some simulation, dunno using what (matlab ?). The point was if you keep the magnitude the same (at escape speed) but the direction different, some directions would result in such orbit. Could've been just some paralaxes due to viewing through...

Must have been the latter then. The focal property follows purely formally/mathematically form Newton's laws. Or another reason: consider parabolas as degenerated ellipses (or hyperbolas); if there would be a parabola without the focal property, then (by some continuity argument) there must be an example with ellipses; but that contradict's Kepler.

[K^2]

Doh. So this sort of ellipse should show up if one abused a hooke's law problem enough?

Or even just a pendulum with small oscillations. But yeah, it's 2D harmonic oscillator. It's separable in (x,y) coordinates and periods match on both axes.

Is there any sort of program online that can simulate "changing the laws of physics", like changing gravity's scaling?

Any generic enough PDE solver should be able to. Just enter equations of motion for the differential equations to be solved.

[YNM]

Must have been the latter then. The focal property follows purely formally/mathematically form Newton's laws. Or another reason: consider parabolas as degenerated ellipses (or hyperbolas); if there would be a parabola without the focal property, then (by some continuity argument) there must be an example with ellipses; but that contradict Kepler's.

Hmm... Yeah, semi-major axis and eccentricity are the result (or results in ?) of angular momentum and energy of orbit. I don't know through, should ask again (or try to simulate that myself)...

Aren't degenerate ellipse real ? I mean, consider going in a shaft though the centre of the Earth from pole to pole, wouldn't the falling object (at one pole) stops at the other pole, not at the center of the Earth ?

[ZetaX]

Hmm... Yeah, semi-major axis and eccentricity are the result (or results in ?) of angular momentum and energy of orbit. I don't know through, should ask again (or try to simulate that myself)...

Aren't degenerate ellipse real ? I mean, consider going in a shaft though the centre of the Earth from pole to pole, wouldn't the falling object (at one pole) stops at the other pole, not at the center of the Earth ?

Falling through earth is a different setting (more akin to pendulums) where the orbit from the starting post is possible (assuming you clear the path). For the usual gravitational orbits (with the parent body at a focus) one needs to consider point masses or spheres (as long as one stays outside of them)

[K^2]

Hmm... Yeah, semi-major axis and eccentricity are the result (or results in ?) of angular momentum and energy of orbit.

Neither causes the other. As constants of motion, they are alternative representations of the same quantities. But energy and angular momentum are conserved quantities in a more general scope. So they are certainly related, and the later pair is more fundamental, but it's still not a cause and effect situation.

Aren't degenerate ellipse real ? I mean, consider going in a shaft though the centre of the Earth from pole to pole, wouldn't the falling object (at one pole) stops at the other pole, not at the center of the Earth ?

Because gravity inside Earth starts to drop a few km in and goes to zero at the gravitational center of the Earth. The gravitational force bellow surface is roughly linear on the large scale, so if you were to dig out a tunnel, the falling mass would, indeed, follow an ellipse with center at the center of the Earth. But that's because we aren't talking about object orbiting a point mass anymore.

[YNM]

Hmm... I forgot how gravitational force increase with r for things inside Earth. Which fits for the given case, no ?

[K^2]

Not quite. Earth's density isn't uniform. If it was, then yeah, it'd be exactly like r. In reality, it's quite different until you hit the core, and even then it's not quite linear because of differences in densities of inner core and outer core. Blue line is the estimate for actual gravity.

[PB666]

Not quite. Earth's density isn't uniform. If it was, then yeah, it'd be exactly like r. In reality, it's quite different until you hit the core, and even then it's not quite linear because of differences in densities of inner core and outer core. Blue line is the estimate for actual gravity.

http://upload.wikimedia.org/wikipedia/commons/thumb/5/50/EarthGravityPREM.svg/750px-EarthGravityPREM.svg.png

Thank you, I was looking for that graphic.