Hohmann Transfer: Maximum Radii Ratio

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SUMMARY

The discussion centers on calculating the maximum radius ratio (R1/R0) for a Hohmann transfer, specifically proving that this ratio equals 15.6. The user successfully calculated the ∆V's at aphelion and perihelion but seeks confirmation on deriving the maximum ratio. The suggested method involves taking the derivative of the relevant equation and setting it to zero to find the maximum value, which is the correct approach to obtain the desired result.

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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.
 
Last edited:

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