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$\begingroup$ It appears they wait until just before Mars close approach. $\endgroup$– BrendanLuke15Commented Aug 19, 2021 at 11:56
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13$\begingroup$ @BrendanLuke15: That's because it's most efficient to launch a probe so that it departs from Earth when it's on one side of the Sun and arrives at Mars when it's on the other side of the Sun. See this diagram. And since Mars goes around in its orbit slower than Earth does, it works out that the optimal launch point is a few months before Earth "passes" Mars in its orbit. (Orbital mechanics is weird.) $\endgroup$– Michael SeifertCommented Aug 19, 2021 at 12:39
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3$\begingroup$ @MSalters: The fact that Mars goes slower has no bearing on the Hohmann launch window, but it does matter in the sense that it leads to the coincidental nature of a launch window opening at around the same time of a closest approach between the planets. Since Mars moves slower, Earth should be almost overtaking Mars during the launch window, but not quite overtaking it yet (cfr the graph). This is all pure coincidence due to the relative orbital velocity of both planets. $\endgroup$– FlaterCommented Aug 20, 2021 at 10:55
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9$\begingroup$ My issue with this answer is that its phrasing implies the closest distance defines the launch window. It doesn't. What defines the launch window is the time needed for the ship and planet to meet each other at the end of the interplanetary transfer, which defines a specific position for the target planet based on its relative velocity to the starting planet. For Mars, this happens to work out nearby to a closest approach, but that is pure coincidence. $\endgroup$– FlaterCommented Aug 20, 2021 at 11:02
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1$\begingroup$ What @Flater said. Somewhat simplified, a minimum-energy transfer takes half an elliptical orbit going from the orbital radius of Earth to that of Mars, arriving on the opposite side of the sun from where it launched from Earth at the same time Mars passes that location. That means Mars and Earth were about to make their closest approach when it departed, but attaching any importance to that is looking at things rather backwards...it's the position of Mars and the spacecraft at the far end of the transfer orbit that determines the launch window. $\endgroup$– Christopher James HuffCommented Aug 20, 2021 at 14:50
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