Hohmann Transfer: Maximum Radii Ratio

[sadiethebull]

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?

 

[Filip Larsen]

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.