# How to write a normalized, dimensionless form of Binet's relativistic equation?

$$\frac{\delta^2 u}{\delta \theta^2} + u = \frac{\mu}{h^2} + 3 \mu u^2$$

This is Binet's relativistic equation. Here $$u = 1/r$$ where $$r$$ is the radial distance, and $$\mu$$ is the reduced mass of the Sun and Mercury.

I am trying to calculate the perihelion precession path of Mercury numerically in Python and for doing so I would like to use a dimensionless form of this expression.

• I've converted your screen shot to MathJax format. Can you add a link to the source for the expression in its current form or at least mention where the screen shot comes from? It will be helpful to readers (including me!) to better understand the math here. Thanks, and Welcome to Astronomy! – uhoh Jun 4 '19 at 23:42
• What's the problem with simply doing $u=av$ where $a$ is an arbitrary constant with units of length$^{-1}$ and $v$ is dimensionless ? – StephenG Jun 5 '19 at 3:36
• Shouldn't $\frac{\delta^2 u}{\delta^2 \theta^2}$ be written as $\frac{\mathrm{d}^2 u}{\mathrm{d}\theta^2}$ ? – PM 2Ring Jun 5 '19 at 4:15
• @PM2Ring I've transcribed the OP's equation from the original screen shot faithfully, and asked the OP to add a link to the source. Let's wait and see why it was written in that particular way. It could be something as simple as the typesetter didn't have a $\partial$ available so they substituted $\delta$, or it could be some other reason. – uhoh Jun 5 '19 at 14:42