Solving a Term about gravitation to r

[wiegetz]

Homework Statement

I want to know how this equation is getting solved to r. I know the result, but I want to know how :)

Homework Equations

γ*m*M_e/r = 4Π²*m*r/T^2Solution does need to be: r = ^3√γM_eT^2/4Π^2 (^3√ should mean the 3rd root/radical)

The Attempt at a Solution

I am so far:
γ*m*M_e/r^2 = 4Π²*m*r/T^2 ( shortening the terms now)
γ*M_e/r = 4Π²/T^2
γ*M_e*/T^2/r*Π² = 0

Now I do not know how to continue, I am 99% sure that I have done something wrong.
Greetings from Germany! :)

Here is a picture about the term: http://[url=http://postimg.org/image/war0n6zxf/][ATTACH=full]200042[/ATTACH] [ATTACH=full]200043[/ATTACH]

 

[SteamKing]

Homework Statement

I want to know how this equation is getting solved to r. I know the result, but I want to know how :)

Homework Equations

γ*m*M_e/r = 4Π²*m*r/T^2Solution does need to be: r = ^3√γM_eT^2/4Π^2 (^3√ should mean the 3rd root/radical)

The Attempt at a Solution

I am so far:
γ * m * M_e / r² = 4π² * m * r / T² ( shortening the terms now)

The equation above seems to be the one taken from your text.

γ*M_e/r = 4Π²/T^2
γ*M_e*/T^2/r*Π² = 0

You canceled the variable r incorrectly. You should have multiplied both sides of the original equation by r².

After that, leave r³ one one side of the equation and move everything else to the other side. Solve for r.

This is just simple algebraic manipulation.

 

[wiegetz]

I understood it now. Thanks for the help!