# Astrodynamic Canonical Units [closed]

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?

• All symbols need to be defined. DU? – Rob Jeffries Oct 11 '17 at 11:20
• Canonical Units and I admit $DU$ is a new one to me. – StephenG Oct 11 '17 at 12:25
• For Mu, you mean DU^3/TU^2 -- that might help – barrycarter Oct 11 '17 at 15:33
• DU is Distance Unit Which is the Equatorial radius of the Earth (6,378.1363KM) And yes Barry that is what i meant. – Nzjeux Oct 11 '17 at 19:35
• Thanks, @StephenG and Rob. I thought I was the only one who didn't understand "DU"… – pela Oct 12 '17 at 18:34

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.

• 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 Oct 12 '17 at 20:00
• @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 Says Reinstate Monica Oct 13 '17 at 7:01