Awkwardly phrased title aside, the question is as follows:

If you wished to launch from Earth to head to Mars at the moment when the two planets are furthest apart, would you arrive sooner if you left immediately or if you waited until the planets were closer together?

To put this another way, what closes distance faster, a rocket-propelled spacecraft, or the planets?

Bonus: what is the minimum speed a spacecraft would have to travel at in order to make it win this "contest"?

  • $\begingroup$ Are you assuming a near-Hohmann transfer orbit, or something more fuel-guzzling? $\endgroup$ – Nathan Tuggy Jun 14 '16 at 1:05
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    $\begingroup$ What engine technology are you using? What's your fuel budget? $\endgroup$ – Mark Jun 14 '16 at 1:11
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    $\begingroup$ This is known as a conjunction trajectory, and is useful for missions that stay on Mars for a year or so. Look for instance at this paper. $\endgroup$ – kim holder Jun 14 '16 at 1:30
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    $\begingroup$ If you want to depart for a Hohmann transfer, you need to launch when Mars is about 45 degrees ahead of the earth. $\endgroup$ – HopDavid Jun 14 '16 at 22:49

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