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    Posted By: Andrew PalfreymanI sent them a comment. I asked if they were insane, except I used other words.

    They've updated the caption. Now it makes more sense.

    This artist's concept is of a Jupiter-mass planet orbiting the nearby star Epsilon Eridani. Located 10.5 light-years away, it was the closest known exoplanet to our solar system when it was discovered in 2007. The planet is in an elliptical orbit that carries it as close to the star as Earth is from the Sun, and as far from the star as Jupiter is from the Sun.
    People Power!
    I think a Jovian planet in a highly elliptical orbit is probably not very good for the rest of the planets trying to orbit in the near thereabouts.
    • CommentTimeApr 13th 2021 edited
    Starlink might not be a completely tragic disaster after all. Under certain assumptions. For some of the telescopes. Maybe.
    • CommentAuthorAsterix
    • CommentTimeApr 22nd 2021
    Two Black Holes

    (CGI simulation, NASA Goddard)
    • CommentAuthorkorkskrew
    • CommentTimeApr 23rd 2021
    Posted By: Andrew PalfreymanThe Unicorn
    Wow! 8.85km Swartzchild radius! Crazy tiny.
    • CommentTimeApr 25th 2021
    Our Moon looks beautiful tonight.
    Why Keyholes Make It So Difficult To Predict Asteroid Impacts

    I was vaguely musing about the problem of taking 2D telescope observations and turning them into viable 3D trajectory forecasts. One cannot simply apply the law of conservation of energy (in each dimension separately ofc) by regarding only the kinetic energy, but this works fine if the (variable) gravitational potential energy is also considered. The question that has me stumped, however, is how the law of conservation of momentum works in this environment of variable gravitational potential.

    Anyone got an equation for that?
    • CommentTimeMay 24th 2021
    That always bothered me. I think the answer is that when doing the potential energy calculation you assume that the sun is stationary, but of course in the momentum calculation you have to include its contribution to the momentum.
    It's weird that this is the first time that the question has occurred to me.

    Assume that the potential is known everywhere/everywhen.
    The easier case, energy conservation, cannot be split into 3 orthogonal dimensions, because the potential energy is a directionless scalar. So we can only talk about the total kinetic energy using the resultant velocity.


    Then, for the momentum case, we are dealing with vectors, so each dimension independently must obey whatever-it-is.
    • CommentTimeMay 25th 2021
    • CommentTimeMay 25th 2021
    It all comes out fairly clearly from the Lagrangian, I think.
    But that makes no reference to momentum - only energy.

    My question concerns the modification of the principle of conservation of momentum in a potential field.
    • CommentTimeMay 25th 2021
    But as I said, you apparently assume the potential field is rigidly fixed on the sun and relate the motion to the sun in the KE calculation, whereas to conserve momentum you have to include momentum of the sun as well as whatever is in its potential field. I assume this because you seem to be measuring motion relative to the earth and subtracting earth's orbital motion around the sun.

    Or maybe I'm just an old fart.
    Well I certainly am.

    I'm not thinking about Earths or suns or any particular astronomical arrangement. I just assume 2 massy bodies and a known potential field U(x,t). Maybe in a box. We can keep x a scalar for simplicity (1D). Then we know that sum(T + U) = constant for all x,t, where the sum is over (say) 2 bodies. I think that's enough to solve for anything at a later time, and that includes the momenta. All classically, ofc.

    So we don't need momentum conservation here?
    • CommentTimeMay 25th 2021 edited
    If there is no force between the two bodies you might as well have only one. The field U can apply any force anywhere to that one so its momentum is not conserved.

    If the two bodies exert force on each other then the momentum measured around their centre of mass is constant.