# Revolving around a sphere helically?

• ManDay

#### ManDay

Dumb question maybe, since I'm not a mathematician, but is there something like a specific kind of space in which an entity given a certain initial velocity parallel to the surface of a sphere and constrained to equal distance to the surface of it will revolve arround the square helically (not equatorially), without being exerted any force other than the one running perpendicular to the surface?

Dumb question maybe, since I'm not a mathematician, but is there something like a specific kind of space in which an entity given a certain initial velocity parallel to the surface of a sphere and constrained to equal distance to the surface of it will revolve arround the square helically (not equatorially), without being exerted any force other than the one running perpendicular to the surface?

Hi ManDay!

(btw, "helically" means like a spring … did you mean like a sort-of sine function?)

If the only force is radial, then good ol' Newton's second law means that the particle will have no reason to turn, and so will move along a great circle ("an equator").

The radial force may change the speed along that great circle, but can't make it deviate from the great circle.

Like a spring, yes.

Since this is the physics-forum I assume you can assume that everyone can presume at least a basic knowledge. Know about that "Newton-stuff" :D I'm concerning the mathematical aspects since this is the maths-subsection. I was asking for a sort of special topology or reference-space in this would be possible.

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Like a spring, yes.

Mathematically, you can't have a spring on the surface of a sphere, or "constrained to equal distance to the surface".
I was asking for a sort of special topology or reference-space in this would be possible.

Changing the coordinates won't alter this basic reality.

If you hand an infinitely-long cylinder of matter as the source of the force, then there would be helical orbits around it.

Consequently, for a finite cylinder, if it is sufficiently long and dense, and you stay near the center (away from the endpoints), then there are orbits which locally look like helices. But since the cylinder is finite, these orbits will distort as they get closer to the endpoints.