Understanding Spherical Coordinates

[Miike012]

questioning what ρ does. What is the difference between the two equations?

Let k be the angle from the positive z-axis and w be the angle from the pos x-axis

parametric equation of a sphere with radius a
paramet eq. 1:
x = asin(k)cos(w)
y = asin(k)sin(w)
z= acos(k)

0≤w≤2pi
0≤k≤pi
a is constant

paramet equ 2:
x = ρsin(k)cos(w)
y = ρsin(k)sin(w)
z= ρcos(k)
0≤w≤2pi
0≤k≤pi
0≤ρ≤a

Is the first equation the surface of the sphere and the second would be the equation of a solid sphere?

second question: Look in paint document:
I originally thought that ρ = constant (which is the distance from the origin to the point) was the entire line segment from the origin to the point. But if my understanding is correct the coordinate ρ actually represents some point ρ units aways from the origin. Is this correct?

 

[pasmith]

questioning what ρ does. What is the difference between the two equations?

Let k be the angle from the positive z-axis and w be the angle from the pos x-axis

parametric equation of a sphere with radius a
paramet eq. 1:
x = asin(k)cos(w)
y = asin(k)sin(w)
z= acos(k)

0≤w≤2pi
0≤k≤pi
a is constant

paramet equ 2:
x = ρsin(k)cos(w)
y = ρsin(k)sin(w)
z= ρcos(k)
0≤w≤2pi
0≤k≤pi
0≤ρ≤a

Is the first equation the surface of the sphere and the second would be the equation of a solid sphere?

Yes.

second question: Look in paint document:
I originally thought that ρ = constant (which is the distance from the origin to the point) was the entire line segment from the origin to the point. But if my understanding is correct the coordinate ρ actually represents some point ρ units aways from the origin. Is this correct?

Yes.