# What is Spherical: Definition and 1000 Discussions

A sphere (from Greek σφαῖρα—sphaira, "globe, ball") is a geometrical object in three-dimensional space that is the surface of a ball (viz., analogous to the circular objects in two dimensions, where a "circle" circumscribes its "disk").
Like a circle in a two-dimensional space, a sphere is defined mathematically as the set of points that are all at the same distance r from a given point in a three-dimensional space. This distance r is the radius of the ball, which is made up from all points with a distance less than (or, for a closed ball, less than or equal to) r from the given point, which is the center of the mathematical ball. These are also referred to as the radius and center of the sphere, respectively. The longest straight line segment through the ball, connecting two points of the sphere, passes through the center and its length is thus twice the radius; it is a diameter of both the sphere and its ball.
While outside mathematics the terms "sphere" and "ball" are sometimes used interchangeably, in mathematics the above distinction is made between a sphere, which is a two-dimensional closed surface embedded in a three-dimensional Euclidean space, and a ball, which is a three-dimensional shape that includes the sphere and everything inside the sphere (a closed ball), or, more often, just the points inside, but not on the sphere (an open ball). The distinction between ball and sphere has not always been maintained and especially older mathematical references talk about a sphere as a solid. This is analogous to the situation in the plane, where the terms "circle" and "disk" can also be confounded.

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2. ### I Range of projectile launched from a non-rotating spherical planet

I figured this would be a problem in some classical mechanics book but so far I can't find an answer anywhere. Assume there is no drag or lift, and since the planet is not rotating we don't have to worry about Coriolis effects. I'm working on a solution but I want to see if my work is correct...
3. ### Spherical pendulum confusion [Issue resolved]

For this problem, I am confused my what they mean by ##\phi##. I have looked at the figure, but it is confusing. Makes it look like the x-axis and y-axis are not perpendicular, even thought I'm assuming they are since this is a right handed coordinate system. Does someone please know what...
4. ### Why Is Deriving the Motion Formula for Hoops More Complex?

I've worked out how to derive the formulas for a solid cylinder and a solid sphere rolling down a hill. E.g., for a cylinder: Emech = KE + PE mgh = 1/2 mv^2 + 1/2 Iw^2 gh = 1/2 v^2 + 1/2 (1/2r^2) v^2/r^2 gh = 3/4 v^2 v^2 = 4/3 gh I then performed a derivative with respect to time and found a...
5. ### B Can Earth or any spherical object in space act as a particle collider?

This is most probably a dumb idea as I'm far from deep physics knowledge but I was thinking. What if Earth is hot inside not because of the pressure and the radioactivity but because it's mass attracts particles (similarly to gravitational lensing) and they collide right in the Earth's center?
6. ### I The electron is not point-like?

Let me start with my understanding of a photon. A source emits a single photon, which can be described as an excitation of the EM field. This excitation radiates outward, producing isochrons which in pure vacuum would be spherical. Then at some point the photon is absorbed by some atom. By...
7. ### Height of a stable droplet on a perfectly wetting surface

I would assume that the droplet on the ceiling is spherical, since it is the shape that minimizes the surface energy for a given volume. The droplet is held by the surface tension force, which acts along the contact line between the droplet and the ceiling and is balanced by the weight of the...
8. ### Gradient and Divergence in spherical coordinates

Vectorfield for the divergence

40. ### A Crank-Nicholson method for spherical diffusion

The code I have for solving the diffusion equation on the spherical domain. The solution seems to differ drastically depending on the refinement of the mesh which obviously shouldn't be the case. I have checked and double checked my derivation and code and I can't seem to find an error. One...
41. ### Point charge in cavity of a spherical neutral conductor

For (a) this problem, the only thing I can see changing is the distribution of the negative charge on the inner wall of the cavity. When the point charge is in the center of the cavity, you could say the induced charged is spread symmetrically on the inner cavity wall in order to oppose the...
42. ### A Spherical aberration in Biconvex lens

I was recently looking for proven relations between focal length, radius of curvature, refractive index etc of a convex lens as I was working on an experiment, I did Find a relation, between Height from principal axis and focal length, and it was a huge relation!I did the experiment to verify...
43. ### A reflective spherical balloon

From ray tracing I would say that the image is upright. Using the equation ##\frac{1}{p}+\frac{1}{q}=\frac{1}{f}## with ##f=-\frac{R}{2}=-2## and ##M=-\frac{q}{p}=\frac{3}{4}## I get ##p=\frac{2}{3}cm\simeq 0.67 cm##. Is this correct? Thanks
44. ### I Calculating an increasing angle in Spherical Coordinates for a curve

I'm making a program that generates lines in 3D space. One feature that I need is to have an incrementally increasing angle on a line (a bending line / curve). The problem is simple if the line exists in the xy-plane, then it would be a case of stepping say 1m, increase the azimuthal angle φ...
45. ### Maximum charge on a spherical capacitor

The electric field is the one generated by the charge ##+Q## on the inner sphere of the capacitor, which generates a radial electric field ##\vec{E}=\frac{1}{4\pi\varepsilon_0}\frac{Q}{r^2}\hat{r}## which, due to the presence of the dielectric, become...
46. ### I Spherical aberration in Biconvex and Plano Convex lenses

I wanted to know about spherical aberration in a biconvex and plano convex lens as I was planning an experiment with them. I was reading about them and came upon the following passage. I don't know whether the given equation is an empirical one or a derived equation. Can anyone help me if you...
47. ### When to use the Jacobian in spherical coordinates?

Greetings! here is the solution which I undertand very well: my question is: if we go the spherical coordinates shouldn't we use the jacobian r^2*sinv? thank you!
48. ### Potential on each of these concentric spherical shells

Each spherical shell will contribute to potential on the surface of inner shell and the same will apply to outer shell. Due to inner shell ##V_1 = \frac {kQ} {{r_1}}## and due to outer shell ##V_1 = \frac {-kQ} {r_1}##. Therefore potential on inner surface is zero. But the answers are ##V_1...