Using dimensional analysis to create dimensionless equation

astrofunk21
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Homework Statement


I am tasked with solving and creating a dimensionless equation from a differential equation given.

Homework Equations


This is the given equation:

render.png

The Attempt at a Solution


When doing the dimensional analysis I see that we are left with units of [m-3][kg1][s-2].

These units are actually the units of the inverse of the gravitational constant G. So to make this equation dimensionless would I just multiple both sides by G? So we get this dimensionless equation (but not really since the left side isn't exactly dimensionless):

render.png


Would appreciate help on where to go with this! Thanks in advance
 
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Please give the problem exactly as stated.
 
Orodruin said:
Please give the problem exactly as stated.
Question: Solve and make a dimensional analysis in order to ensure the equation is really dimensionless.
 
That is not the entire problem. It sounds like the very end of the problem text.
 
What is c in the equation?
 

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