How long does it take for 3 planets to align themselves at an angle

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The discussion focuses on calculating the time required for Earth, Mars, and Jupiter to align at a specific separation angle for a Hohmann transfer mission. Key factors include the original positions of the planets and the individual alignment times between Mars and Earth, Mars and Jupiter, and Earth and Jupiter. The participants emphasize the importance of using orbital data expressed in angle units to determine the alignment timing. The challenge lies in finding the exact moment when all three planets achieve the desired configuration for optimal mission execution. Accurate calculations are crucial for the success of the proposed gravity assist maneuver.
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How long does it take for earth, mars, and Jupiter to line themselves up to a certain separation angle.
Background information: I am doing this project where we are trying to do a Hohmann transfer from Earth's stationary orbit to Mars and doing a flyby gravity assist at Mars and shoot for Jupiter. Now we are at the point where we have to find out the exact time it takes for all three planets to lineup at a perfect angle for this whole mission to be completed.

Knowns: -the original positions we need for all three planets to be.
- the time it takes for Mars to lineup with earth
- the time it takes for Mars to lineup with Jupiter
- the time it takes for Earth to lineup with Jupiter

Unknowns: the time it takes for all above scenarios to happen. For example, the grand tour alignment, however this time it is only 3 planets.
 
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Welcome to PF;
Use the information you have on their orbits - expressed in angle units.
 
Welcome to PF;
Use the information you have on their orbits - expressed in angle units.
 

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