Hello, I'm trying to code the equation shown below and get a curve or possible solution as shown below as well (not all of them). This is my attempt but not sure if it is correct and how to obtain a similar plot?. Are the units right? Any help will be appreciated. Thanks
ClearAll["Global`*"];
T = Quantity[1.2 * 10^6, "Kelvins"];
kb = Quantity[1, "BoltzmannConstant"];
Ms = Quantity[1.99 *10^30, "Kilograms"];
G = Quantity[6.67 *10^-11, "Meters^2*Newton/Kilograms^2"];
mH = Quantity[1.99 * 10^30, "Kilograms"];
r = Quantity[1*10^9, "Meters"]
u = Quantity[17, "Meters"/"Second"]
uc = Sqrt[2*kb*T/mH]
rc = G*Ms*mH/4*kb*T
eq = (u/uc)^2 - 2 * Log[u/uc] == 4 *Log[r/rc] + 4 *(rc/r) - 3