Find the Jacobians ∂ x , y / ∂ u , v of the given transformations from variables x , y to variables u , v Compute the gravitational attraction on a unit mass at the origin due to the mass (of constant density) occupying the volume inside the sphere r = 2 a and above the plane z = a . Hint: The magnitude of the gravitational force on the unit mass due to the element of mass r , θ , ϕ is G / r 2 d M . You want the z component of this since the other components of the total force are zero by symmetry. Use spherical coordinates.
Find the Jacobians ∂ x , y / ∂ u , v of the given transformations from variables x , y to variables u , v Compute the gravitational attraction on a unit mass at the origin due to the mass (of constant density) occupying the volume inside the sphere r = 2 a and above the plane z = a . Hint: The magnitude of the gravitational force on the unit mass due to the element of mass r , θ , ϕ is G / r 2 d M . You want the z component of this since the other components of the total force are zero by symmetry. Use spherical coordinates.
Find the Jacobians
∂
x
,
y
/
∂
u
,
v
of the given transformations from variables
x
,
y
to variables
u
,
v
Compute the gravitational attraction on a unit mass at the origin due to the mass (of constant density) occupying the volume inside the sphere
r
=
2
a
and above the plane
z
=
a
.
Hint: The magnitude of the gravitational force on the unit mass due to the element of mass
r
,
θ
,
ϕ
is
G
/
r
2
d
M
.
You want the z component of this since the other components of the total force are zero by symmetry. Use spherical coordinates.
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