What steps do I take to get (G M_p M_*)/((r_p)^2) = (M_p (V_p)^2)/(r_p) to r_p = ...?

[InfamousTurtle]

\(\displaystyle \dfrac{G\, M_p\, M_*}{r_p^2}\, =\, \dfrac{M_p\, V_p^2}{r_p}\)

\(\displaystyle r_p\, =\, \dfrac{G\, M_*}{V_p^2}\)

https://gyazo.com/71986e9acd88bd3899ea4d14b938886a

I was watching a video and I wondered what steps he took to get it like that.

 

[tvanhooz]

You cross multiply...or, in essence, multiply the left side by the right side's denominator (r_p)and vice versa...multiply right side by (r_p²).

Your result is then:

r_p²m_pv_p²= Sm_pm_tr_pNow, divide each side by r_p and m_p...



Then you arrive at his result

 

[Harry_the_cat]

https://gyazo.com/71986e9acd88bd3899ea4d14b938886a
I was watching a video and I wondered what steps he took to get it like that.

Multiply both sides by r^2 then divide both sides by mv^2