If we can reduce the travel time to Mars below the Hohmann transfer orbit's typical 258 days, would we still use the usual Hohmann launch window or delay launch accordingly? For example, if we followed Zubrin's plan and used additional fuel to make the trip in 180 days, would we launch at the usual launch window, or 78 days later? If we could use nuclear-plasma rockets to reach Mars in 40 days, would we launch at the usual launch window, or 218 days later? Thanks!
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2 Answers
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Below is a typical porkchop plot, showing the 2005 Earth to Mars opportunity.
A "Hohmann" transfer in its pure form only exists between co-planar orbits. Since Earth's and Mars' orbits are not coplanar, the 180° transfer would actually require a huge plane change, which results in the opportunity splitting into two pieces on either side of 180°. In a great stroke of imagination, mission designers decided to refer to those as Type 1 (for less than 180°), and Type 2 (for more than 180°).
On the porkchop plot you can see the contours of the Type 1 on the bottom and the Type 2 on the top. The solid red lines are constant transit times in days. The blue closed curves are constant $C_3$, which is the energy required for the transfer.
So the most efficient travel times are about 200 days (Type 1) and 400 days (Type 2), with the Type 2 being a smidge more efficient. 180 days is actually not bad at all for this particular opportunity, requiring only a little more $C_3$. In fact you could get a nice 20-day launch period with a transit time of 180 days for a $C_3$ of less than $18\,\mathrm{{km}^2/s^2}$.
40 days transit time is a completely different story. You would launch a few weeks before the Earth-Mars closest approach, and arrive a few weeks after. In 2005, the closest approach was Oct 29, at right end of the x-axis of that plot. You would be arriving almost one y-axis box below the plot. I don't know what that $C_3$ would be, but it goes up fast as you leave those wells.
answered Mar 12, 2019 at 6:02
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$\begingroup$ It would be interesting to see plots for a "worst case" and "best case" transfer window, since the fairly elliptical orbit of Mars results in quite a large variation in what is achievable for a given amount of delta-v. $\endgroup$ Mar 13, 2019 at 14:23
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$\begingroup$ That would depend on worst case for what parameter. The 2005 opportunity was one of the worst for $C_3$. 2003 was one of the best. You might want to ask a new question for that. $\endgroup$ Mar 13, 2019 at 15:28
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Earth and Mars really only align every 26 months or so. One particular instant in that is the Hohmann Transfer window, the rest is just close to it, in terms of time, delta-v, etc. If delta-v isn't an issue, we can launch any time, but it will be faster when Earth and Mars are close to each other, if it is an issue, but we have more than is current, we can launch a bit after the optimal transfer window and arrive there beforehand.
answered Mar 11, 2019 at 18:48
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1$\begingroup$ If delta-v isn't an issue you could accelerate to the speed of light, travel in a straight line and then stop when you get there :)! As the... crowsmic ray... flies? $\endgroup$ Mar 11, 2019 at 19:13
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1$\begingroup$ Pretty much, although it might not be that fast depending on the ability to manage large amounts of acceleration. $\endgroup$– PearsonArtPhoto ♦Mar 11, 2019 at 19:17
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$\begingroup$ Thank you. But I'm not sure I understand your response. If we have the delta-v to reduce the Hohmann trip of 258 days to Zubrin's 180 days, would we launch at (or about) the standard Hohmann launch window and arrive 78 days earlier than a Hohmann transfer - or would we launch 78 days after the Hohmann launch window and arrive at the normal time for a Hohmann transfer? Thanks! $\endgroup$ Mar 11, 2019 at 20:09
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2$\begingroup$ It is probably somewhere between. There is something known as a pork chop plot that might give you an idea of what that would look like. $\endgroup$– PearsonArtPhoto ♦Mar 11, 2019 at 21:32