Hohmann Transfer: Maximum Radii Ratio

In summary, the conversation was about finding the ∆V's at the aphelion and perihelion for a Hohmann transfer and proving that the total ∆V has a maximum of R1/R0 = 15.6. The individual discussing the problem was considering taking a derivative of the equation to solve for the maximum value.
  • #1
sadiethebull
1
0
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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  • #2
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:

FAQ: Hohmann Transfer: Maximum Radii Ratio

1. What is a Hohmann Transfer?

A Hohmann Transfer is a type of orbital maneuver used in space travel to transfer a spacecraft from one circular orbit to another by using the least amount of fuel.

2. What is the maximum radii ratio in a Hohmann Transfer?

The maximum radii ratio in a Hohmann Transfer is approximately 11.94. This means that the final orbit will have a radius 11.94 times larger than the initial orbit.

3. How is the maximum radii ratio calculated in a Hohmann Transfer?

The maximum radii ratio can be calculated using the formula (2*R2)/(R1+R2), where R1 is the radius of the initial orbit and R2 is the radius of the final orbit.

4. Why is the maximum radii ratio important in a Hohmann Transfer?

The maximum radii ratio is important because it determines the amount of fuel needed for the maneuver. A higher ratio means less fuel is required, making the transfer more efficient and cost-effective.

5. Are there any limitations to using a Hohmann Transfer with the maximum radii ratio?

Yes, there are limitations to using a Hohmann Transfer with the maximum radii ratio. This method is only applicable for transferring between circular orbits and assumes that the gravitational pull of the central body is the only force acting on the spacecraft. In reality, there may be other forces that can affect the transfer and alter the maximum radii ratio.

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