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Orbit of almost 1 eccentricity

  1. Mar 23, 2006 #1
    You make a 100 m diameter tunnel that goes from the north pole to the south one.
    You put into orbit a tennisball by dropping it in the tunnel from the north hemisphere
    Supposing it makes an ellipse 99 m the minor axe and the earth radius the bigger axe wouldnt the ball get into an orbit of eccentricity almost one which focus would be the center of the earth
    Wouldnt this mean that a ball dropped from the north hemisphere would get such an orbit it would come out the northern hemisphere?
  2. jcsd
  3. Mar 23, 2006 #2


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    The ball would come out at both poles. You wouldn't get a standard eliptical orbit where the center of the main mass (in this case, The Earth) is located at one of the foci of the elipse, instead, it would be located at the center of the elipse. This is because, in this case, you cannot treat the entire Earth's mass as a point mass at its center.
  4. Mar 23, 2006 #3


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    More specifically, when the ball is a distance r from the center of the earth, you can treat the mass of that part of the Earth that is inside radius r as a point mass at the center, and ignore the rest of the Earth. (assuming spherical symmetry)

    Therefore, as the ball falls towards the center of the Earth, the "effective mass" of the Earth acting on it decreases.
  5. Mar 24, 2006 #4
    Imagine a body with the earths mass and 1 cm radius you drop a ball10kmfromthenorth zenith of the body and make it an ellipse with a minor axe of 1 m and a bigger axe of 10km,an ellipse with an eccentricity of almost one

    According to kepler the ball will orbit in an ellipse shape and the masive body will be at one of the focus of the ellipse

    This means the ball will drop almost straight 10 km from the zenith of the north of the body will rise 10 cm in the south zenith and will return to the north zenith 10 km up and so on

    My question is isnt gravity so odd it reverses the direction of the ball almost 180º when its a full speed? just like an ufo

    How do newtonian physics deal with this revers of sense at full speed?
  6. Mar 24, 2006 #5


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    Calculate the acceleration of the ball, produced by the gravitational force exerted on it by an earth-mass located at a distance of 1 m. That will give you a clue. :smile:
  7. Mar 24, 2006 #6


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    This does not model the situation you have set up. Note that as mentioned in previous posts that the mass effecting the falling object changes with the radius, and is exactly zero when the falling body passes the center of the earth. This would not be a Keplerian orbit which assumes a constant mass as the attracting body.
  8. Mar 24, 2006 #7
    My point is to understand orbits with an eccentricity close to one.

    Lets take two particles under a common gravity field and with an orbit of eccentricity 0.999periodic.

    If we consider one of the particles fixed, the fixed particle will be at the focus of an ellipse that will be almost a segment

    The orbiting particle will almost perfectly fall and rebound up(trully it will be an allipse of eccentricity almost one)

    my question is how is it possible the orbiting particle changes course almost 180º when its at a distance of 1 m of the other particle in the way down but changes almost 0º its course when its at a distance of the focus of 1.m in the way up(ellipses are symmetrical)?
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