<p><span class="math-container">$$\frac{\delta^2 u}{\delta \theta^2} + u = \frac{\mu}{h^2} + 3 \mu u^2$$</span></p>

<p>This is <a href="https://en.wikipedia.org/wiki/Binet_equation" rel="nofollow noreferrer">Binet's relativistic equation</a>. Here <span class="math-container">$u = 1/r$</span> where <span class="math-container">$r$</span> is the radial distance, and <span class="math-container">$\mu$</span> is the reduced mass of the Sun and Mercury.</p>

<p>I am trying to calculate the perihelion precession path of Mercury <a href="https://astronomy.stackexchange.com/q/32067/7982">numerically in Python</a> and for doing so I would like to use a dimensionless form of this expression.</p>

CC BY-SA 4.0
2019-06-04T23:42:01.490Z
I've converted your [screen shot](https://i.sstatic.net/LRJaT.png) to [MathJax](https://math.meta.stackexchange.com/q/5020/284619) 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
CC BY-SA 4.0
2019-06-05T03:36:57.453Z
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 - Help Ukraine
CC BY-SA 4.0
2019-06-05T04:15:06.657Z
Shouldn't $\frac{\delta^2 u}{\delta^2 \theta^2}$ be written as $\frac{\mathrm{d}^2 u}{\mathrm{d}\theta^2} $ ?
PM 2Ring
CC BY-SA 4.0
2019-06-05T14:42:22.060Z
@PM2Ring I've transcribed the OP's equation from the original [screen shot](https://i.sstatic.net/LRJaT.png) 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
<orbit><astrophysics><mercury><precession>
How to write a normalized, dimensionless form of Binet's relativistic equation?
zircon
# How to write a normalized, dimensionless form of Binet's relativistic equation?

(Asked by: username_0 on 2019-06-04)

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

This is [Binet's relativistic equation](https://en.wikipedia.org/wiki/Binet_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](https://astronomy.stackexchange.com/q/32067/7982) and for doing so I would like to use a dimensionless form of this expression.

**Tags:** orbit, astrophysics, mercury, precession
> **Comments:**
> **username_1**: I've converted your [screen shot](https://i.sstatic.net/LRJaT.png) to [MathJax](https://math.meta.stackexchange.com/q/5020/284619) 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!*  
> **username_2**: What's the problem with simply doing $u=av$ where $a$ is an arbitrary constant with units of length$^{-1}$ and $v$ is dimensionless ?  
> **username_3**: Shouldn't $\frac{\delta^2 u}{\delta^2 \theta^2}$ be written as $\frac{\mathrm{d}^2 u}{\mathrm{d}\theta^2} $ ?  
> **username_1**: @PM2Ring I've transcribed the OP's equation from the original [screen shot](https://i.sstatic.net/LRJaT.png) 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.  

---

## 0 answers

