How Do Gravitational Forces Vary with Distance on a Neutron Star?

ps2983
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I am terrible at finding ratios, so I was wodering if someone can help me with this problem.

Consider two point masses, each having mass m, that are separated vertically by a distance of 1cm just above the surface of a neutron star of radius R and mass M. Using Newton's law of gravity, find an expression for the ratio of the gravitational force on the lower mass to that on the upper mass.

Any help will be greatly appriciated.
 
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Well, clearly the first thing you ought to do is right down an expression for the force on each particle, right?
 
To solve this, I first used the units to work out that a= m* a/m, i.e. t=z/λ. This would allow you to determine the time duration within an interval section by section and then add this to the previous ones to obtain the age of the respective layer. However, this would require a constant thickness per year for each interval. However, since this is most likely not the case, my next consideration was that the age must be the integral of a 1/λ(z) function, which I cannot model.
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