<p>It's not entirely clear what your problem is, but the best way is to stick to a certain unit system for your variables and use the correct physical relations. Then, if you want to express the variables in another unit, you must convert them. The standard (SI) units are inconvenient in astronomy, as they give some unwieldy numerical values, hindering intuitive understanding/interpretation.</p>

<p>If you are interested in the Solar system or other planetary systems, a useful unit system is as follows.</p>

<pre><code>distances in AU (astronomical unit)
masses in Solar masses
time in years
</code></pre>

<p>Then Newton's constant of gravity is $G=4\pi^2$ and the velocity $V_c=\sqrt{GM/r}$ is in AU/yr.</p>

<p>Of course, you can use another unit set (for example one for which $G=1$ at the expense of a strange mass or time unit), but you should not switch between different unit systems.</p>

CC BY-SA 3.0
2017-10-12T20:00:05.250Z
It seems the 48 cool down period of not working on it seems to make it work because i just looked at the entire thing again and got it. Thanks for answering.
Nzjeux
CC BY-SA 3.0
2017-10-13T07:01:42.553Z
@Nzjeux if you're happy with Walter's answer, you should give it a tick. This is something only the person who asked the question can do. :-)
Chappo Hasn't Forgotten
CC BY-SA 3.0
2017-10-12T18:05:56.787Z
2017-10-12T18:05:56.787Z
Walter
<p>Maybe this is more appropriate for the Physics or Maths, but anyway.</p>

<p>I am struggling with applying Canonical units with formulas. I am struggling specifically with how they are used, am I to convert all the time? Use the whole numbers?</p>

<p>An example is a a simple velocity of a circular orbit: <code>v= SQRT Mu/r</code></p>

<pre><code>r  =2DU (12,756.23KM)
Mu =1DU3/TU3 (3.9860KM3/s2)

v = 4.5641KM/S or 0.707DU 
</code></pre>

<p>In order to convert it back to DU I had to use a percentage calculator (I'm bad at fractions). Is there a simpler way of converting back and forth?</p>

CC BY-SA 3.0
2017-10-11T11:20:37.093Z
All symbols need to be defined. DU?
ProfRob
CC BY-SA 3.0
2017-10-11T12:25:32.997Z
[Canonical Units](https://en.wikipedia.org/wiki/Canonical_units) and I admit $DU$ is a new one to me.
StephenG - Help Ukraine
CC BY-SA 3.0
2017-10-11T19:35:45.860Z
DU is Distance Unit Which is the Equatorial radius of the Earth (6,378.1363KM) And yes Barry that is what i meant.
Nzjeux
CC BY-SA 3.0
2017-10-12T18:34:22.687Z
Thanks, @StephenG and Rob. I thought I was the only one who didn't understand "DU"…
pela
<orbit><astrophysics><units>
Astrodynamic Canonical Units
Nzjeux
# Astrodynamic Canonical Units

(Asked by: username_0 on 2017-10-11)

Maybe this is more appropriate for the Physics or Maths, but anyway.
I am struggling with applying Canonical units with formulas. I am struggling specifically with how they are used, am I to convert all the time? Use the whole numbers?
An example is a a simple velocity of a circular orbit: v= SQRT Mu/r
r  =2DU (12,756.23KM)
Mu =1DU3/TU3 (3.9860KM3/s2)

v = 4.5641KM/S or 0.707DU 

In order to convert it back to DU I had to use a percentage calculator (I'm bad at fractions). Is there a simpler way of converting back and forth?

**Tags:** orbit, astrophysics, units
> **Comments:**
> **username_1**: All symbols need to be defined. DU?  
> **username_2**: [Canonical Units](https://en.wikipedia.org/wiki/Canonical_units) and I admit $DU$ is a new one to me.  
> **username_0**: DU is Distance Unit Which is the Equatorial radius of the Earth (6,378.1363KM) And yes Barry that is what i meant.  
> **username_3**: Thanks, @StephenG and Rob. I thought I was the only one who didn't understand "DU"…  

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## 1 answers

### Answer by username_4 on 2017-10-12. Score: 2

It's not entirely clear what your problem is, but the best way is to stick to a certain unit system for your variables and use the correct physical relations. Then, if you want to express the variables in another unit, you must convert them. The standard (SI) units are inconvenient in astronomy, as they give some unwieldy numerical values, hindering intuitive understanding/interpretation.
If you are interested in the Solar system or other planetary systems, a useful unit system is as follows.
distances in AU (astronomical unit)
masses in Solar masses
time in years

Then Newton's constant of gravity is $G=4\pi^2$ and the velocity $V_c=\sqrt{GM/r}$ is in AU/yr.
Of course, you can use another unit set (for example one for which $G=1$ at the expense of a strange mass or time unit), but you should not switch between different unit systems.

> **Comments:**
> **username_0**: It seems the 48 cool down period of not working on it seems to make it work because i just looked at the entire thing again and got it. Thanks for answering.  
> **username_5**: @Nzjeux if you're happy with Walter's answer, you should give it a tick. This is something only the person who asked the question can do. :-)  

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