How to normalize (dimensionless) the relativistic Binet's equation for mercury $$\frac{\delta^2 u}{\delta\theta^2}+u=\frac{\mu}{h^2}+3\mu u^2. $$ This is Binet's relativistic equation. I was trying to make perihelion precession path of mercury through python for doing this I need to make it dimensionless first and I am facing problem doing it so please help me. where $u = 1/r$ and $r$ is the radius and $\mu$ is reduced the mass of sun and mercury

Following the dimensionaly correct equation on wikipedia, you have $$\frac{d^2 u}{d\theta^2}+u=\frac{r_s c^2}{2h^2}+\frac{3r_s}2 u^2$$ with $$r_s=\frac{2G\mu}{c^2}$$ Now $u$ is inverse distance, so in order to make it dimensionless you need to multiply it with a constant with units of distance. The obvious choice would be $r_s$. Then for $x=ur_s$, you multiply the first equation with $r_s$ to get $$\frac{d^2 x}{d\theta^2}+x=\frac{r_s^2 c^2}{2h^2}+\frac 32 x^2$$ All terms are now dimensionless.