g-field on ellipsoid

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Posted by dennis on September 06, 2002 at 11:40:51:

I'm trying to determine where the gravitational field of a uniformly dense, regular ellipsoid is strongest - at the 'sharp' end or the 'rounded' end?? I can't think of any definite reasoning off the top of my head why it should be stronger at the rounded end or vice versa, so I tried to use calculus:

field strength, g = GM/r^2

I considered the case of a laminar ellipse. To compare g at the 2 locations I came up with the following function:

g = 2pG Int [y/x^2] dx

wnere p is the mass per unit area and G is the gravitational constant. g would be the field strength at the origin. y is the equation of the *positive* half of an ellipse with vertex at the origin.

For y, I intended to test 2 cases:

1) An ellipse with major axis lying on the x-axis and left vertex on the origin.

2) An ellipse with minor axis lying on the x-axis and left covertex on the origin.

(Both ellipses being of the same area.)

I haven't tried to work out the problem yet because I'm not sure if my expression for g is right. I considered vertical strips of thickness dx, length 2y and centre of mass (x,0). If someone could tell me if this is correct or give me an entirely different (and simpler) approach I'd be grateful. Thanks.

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