Register to reply

Circle Expansion on Expanding Sphere

by Kryptonite-19
Tags: circle, expanding, expansion, sphere
Share this thread:
Kryptonite-19
#1
Nov22-13, 07:05 PM
P: 5
1. The problem statement, all variables and given/known data

How would a circle on a sphere expand as a function of the sphere's radius as the sphere expands?

2. Relevant equations
none were provided

3. The attempt at a solution

[tex]\S=4\,\pi \,{R}^{2}[/tex]
[tex]A=\pi \,{r}^{2}[/tex]

[tex]{\it dA}=2\,\pi \,r{\it dr}[/tex]
[tex]{\it dS}=8\,\pi \,R{\it dR}[/tex]

[tex]{\frac {{\it dA}}{{\it dR}}}=2\,{\frac {\pi \,r{\it dr}}{{\it dR}}}[/tex]

[tex]{\frac {{\it dA}}{{\it dS}}}{\frac {{\it dS}}{{\it dR}}}={\frac {{\it dA}}{{\it dR}}}[/tex]

[tex]{\frac {{\it dr}}{{\it dR}}}=1/2\,{\frac {{\it dA}}{{\it dR}\,\pi \,r}}[/tex]


Stuck at this point.
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution
Phys.Org News Partner Science news on Phys.org
Scientists discover RNA modifications in some unexpected places
Scientists discover tropical tree microbiome in Panama
'Squid skin' metamaterials project yields vivid color display

Register to reply

Related Discussions
Universe Expansion: is it really expanding? Cosmology 10
Why is the Hubble sphere expanding? Cosmology 16
DA/dt of expanding circle Calculus & Beyond Homework 7
Expanding Sphere in Vacuum Classical Physics 1
Expanding surface of sphere Calculus & Beyond Homework 3