gravitational field (1 Viewer)

k02033

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would you like to tell me how to calculate the gradient, divergence and curl of the gravitational field while you are at it please even though gravity is a

conservative field?
there is no such thing as a gradient for gravity
in fact there is no such thing as gradient for any general vector field
you can take the gradient of a muti variable SCALAR field ie input into the function is a vector, and its output is a scalar. And the gradient for that scalar field is defined

to be a vector field, with components that are partial derivatives of the scalar function.

ie if f(x,y,z) =xyz then gradient of f is < yz,xz,xy >

you know dot products and cross products yea?

well the divergence of a vector field is just a dot product between the del operator with the vector field. so the divergence of a vector field is actually a scalar field.



 

k02033

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oh i guess i should point out that these stuff falls under vector calculus.. and vectors are used EVERYWHERE once you get to uni. and the yr 12 syllabus makes no mention to vectors explicitly, which is sad
 

Uncle

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there is no such thing as a gradient for gravity
in fact there is no such thing as gradient for any general vector field
you can take the gradient of a muti variable SCALAR field ie input into the function is a vector, and its output is a scalar. And the gradient for that scalar field is defined

to be a vector field, with components that are partial derivatives of the scalar function.

ie if f(x,y,z) =xyz then gradient of f is < yz,xz,xy >

you know dot products and cross products yea?

well the divergence of a vector field is just a dot product between the del operator with the vector field. so the divergence of a vector field is actually a scalar field.

(Large pic omitted from quoting)
yeah my bad, i knew there were three operators in vector calculus i.e. grad, div and curl, but only div and curl are used for vector fields.

otherwise i can evaluate scalar products, vector products, grad, div and curl easily.
the only problem was wether the exponent for the radius of the universal gravitation formula should be a 3 or 2.
thanks for showing me.

and yea for those still doing the hsc, this is beyond what you learn.
this is 2nd year maths and physics.
 

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