# Speed of Point on Expanding Sphere

• B
In summary: If you take a ball and throw it in a certain way, it will follow a certain parabolic path. If you then take that same ball and throw it in a different way, it will follow a different parabolic path. This is not physics or mathematics, but merely your decision to throw it in a different way.So the question is not answerable as it stands.Summary: The tangential velocity of an object moving across the expanding surface of an expanding sphere is dependent on the initial conditions of the object's motion and cannot be determined by physics or mathematics alone. Clarification of the setup is needed to answer the question.

TL;DR Summary
Suppose we have an expanding sphere. That means that the surface ##4 \Pi r^{2}## is getting bigger and bigger. For example, suppose the area expansion rate is ##b r##. Does this limit the speed at which a point can move on the surface?

Suppose we have an expanding sphere. That means that the surface ##4 \pi r^{2}## is getting bigger and bigger. For example, suppose the area expansion rate is ##b \, r##. Does this limit the speed at which a point can move on the surface?

Limit in what way? In SR the speed of a particle as measured in an IRF is limited by ##c##. Having an expanding physical object, if that is what you mean, doesn't change that.

PeroK said:
I do not know how to re-edt the summary.

PeroK said:
Limit in what way? In SR the speed of a particle as measured in an IRF is limited by ##c##. Having an expanding physical object, if that is what you mean, doesn't change that.
I mean it purely mathematically.

I mean it purely mathematically.
I mean ##r(t) \, = \, b \, t## where ##t## represents time and ##0 \, < \, b##..

I mean ##r(t) \, = \, b \, t## where ##t## represents time and ##0 \, < \, b##..
And ##r## is the distance from the center of the sphere to a particle on the surface of the sphere (using an inertial frame in which the center of the sphere is at rest)?

Then ##\frac{dr}{dt}=b## is the speed of that particle using that frame. It will of course be less than ##c##.

I do not know how to re-edt the summary.
Report your post, include the correct link in your report, and one of us mentors can fix it for you.

I mean it purely mathematically.
There's no purely mathematical limit on the speed of a particle. But, if you apply the theory of SR, then there is a limit.