Force between a unform sphere and a particle* outside of the sphere

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Q. a particle of mass m is located outside a uniform sphere of mass M at a distance R from its centre find:-

a) potential energy of gravitational interaction of the particle and the sphere

b)the gravitional force which sphere exerts on the particle



using G=-г m/r^3 R and ф=-г m/r this is unsolveable


it would be kind enough of anybody who can help
 

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collinsmark
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Q. a particle of mass m is located outside a uniform sphere of mass M at a distance R from its centre find:-

a) potential energy of gravitational interaction of the particle and the sphere

b)the gravitional force which sphere exerts on the particle



using G=-г m/r^3 R and ф=-г m/r this is unsolveable
Could you define your variables? The representations you are using are a little different from the way I'm familiar with. To me, the best I can tell from your equations,
  • G: The gravitational vector field. (Force per unit mass, at a particular location R.)
  • г: Newton's gravitational constant.
  • m: mass of the object* creating the gravitational field. (*either a point particle or spherically symmetrical object.)
  • r: The magnitude of the distance between the mass creating the field and the test mass.
  • R: The vector displacement between the mass creating the field and the test mass. The direction is from the mass creating the field to the test mass.
  • ф: [strike]Negative[/strike] gravitational potential. (i.e. [strike]the negative of the[/strike] potential energy per unit mass, relative to r = ∞)
However, I'm not sure that's exactly what you mean. (I typically use different variables to represent some of those things. But we can use your notation if you'd like.)

If my above assumptions are corect, why do you think the problem is unsolvable? (It seems perfectly solvable to me in terms of masses 'm', 'M', distances 'r', 'R', and constant 'г'.)

[Edit: Nevermind what I originally wrote about the "negative of" gravitational potential energy. The value of ф is naturally a negative number with respect to ∞, as your equation shows. I've corrected my mistaken phrasing.]
 
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