Can you show the formula(s) you use? The Shell theorem can be derived from vector calculus (for a uniform density sphere) and already takes all the vectors into account. How can your calculation differ if they're doing the same thing?
I do not disagree with Shell theorem proving A spherically symmetric body affects external objects gravitationally as though all of its mass were concentrated at a point at its center at various distances in space.
I am saying you can not tie those various points in space from the centre of a mass to inverse square law because
Newton did not allow for the variation in the amount of cancellation due to the vector nature of gravitational attraction when at different distances in space from a mass.
I don't understand what you mean by "partial cancellation". I presume by "vector nature" you mean that the force is the summation of many forces that are not coincident, but maybe I'm not getting that right either.
Yes that's what i mean,and on the partial cancellation in the example i gave earlier in the 3-4-5 triangle.
If you had a standard 1 kg mass on a frictionless surface and applied a force of 3 newtons in one direction and also applied a force of 4 newtons at 90 degrees to the other force on the body you would have a resulting acceleration of 5 m/s squared just like a 3-4-5 triangle.
The total force that is applied to the 1 kg mass is however 7 newtons so a partial cancellation of 2 newtons
and if that force was applied at a angle of anything less than 90 degrees the amount of acceleration of the mass would be greater as the amount of partial cancellation of the vector sum would be less.
And you will note the further you travel from the mass the more acute gets the angle of interaction.
Can you show the formula(s) you use?
I am only using simple vector analysis and basic geometry and as stated earlier i only differ in the need to factor in the value of the variation of the partial cancellation due to the vector nature of the force, meaning you need to know what the gross value of the attraction is.
And also another aspect of this is as the distance between the mass of the two bodies changes only the particles that are in a direct line with the centre to centre actually travel the distance prescribed by inverse square law relative to each other.
see the diagram i posted on this post on the same subject with a less controversial heading