Hohmann Transfer: Maximum Radii Ratio

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To determine the maximum radius ratio R1/R0 of 15.6 for a Hohmann transfer, the discussion emphasizes calculating the total ∆V at both aphelion and perihelion. The approach suggested involves taking the derivative of the relevant equation and setting it to zero to find the maximum. While there may not be a shortcut, following this method should yield the desired value. Participants encourage thorough exploration of the mathematical process to achieve the result. Understanding the relationship between the orbits is crucial for solving the problem effectively.
sadiethebull
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Hello everyone,

I'm working on a problem where I had to find the ∆V's at the aphelion and perihelion for a Hohmann transfer, which I did. However, I am being asked to prove how for the total ∆V for the transfer has a maximum R1/R0 = 15.6 (R0 is the radius of the original circular orbit and R1 is the radius of the second circular orbit after the two boosts). I want to know how to obtain the value 15.6.

I was going to take a derivative of the equation, set it equal to 0, and solve for the maximum that way...but I'm thinking this is wrong...Any suggestions?
 
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Welcome to PF!

I am not aware if there is a shortcut somehow, but if you follow through on your own suggestion then you should
end up with the value you are supposed to.
 
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