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I just watched a National Geographic documentary on ExoMars. In it, they mentioned there were 2 launch windows in early 2016 for the TGO/Schiaparelli launch, one in January and one in March.

Quote from ESA site showing this is not just a gaffe by NatGeo:

The later window is open 14-25 March and, thanks to the relative orbital positions of Earth and Mars, the mission will still arrive at Mars in October, just as if launched in January.

How does that work? As I understand it, there is one optimal date every 780 days, with the required launch energy going up slowly either side of the optimal date. So where do two launch windows, 2 months apart, come from?

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    $\begingroup$ I'm not certain, but I think it has to do with the eccentricity of Mars's orbit (about six times Earth's, small but not negligible). If both Earth and Mars were on perfectly circular orbits there would be one optimum, but depending on where Mars is in its orbit there's a tradeoff between delta-v to intercept and delta-v to enter Martian orbit, and trajectories other than pure Hohmann become more advantageous, yielding two different local optima. $\endgroup$ – Russell Borogove Nov 3 '16 at 21:07
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Depending on how you define "optimal", there are usually two local minima in the impulsive trajectory characteristics for a given opportunity, called "Type 1" and "Type 2". The Type 1 trajectories go a bit less than 180° around the Sun, and the Type 2 trajectories go a bit more than 180° around the Sun. This bifurcation occurs due to the relative inclination of the orbit of Earth and the orbit of Mars. If the orbits of Earth and Mars were coplanar, there would be one local minima going 180° around the Sun.

This can be seen in the traditional "pork chop" plots, which show various trajectory characteristics, such as departure $C_3$ or arrival $V_\infty$, as a function of departure and arrival dates. Here is an example from the 2005 opportunity:

2005 Earth-Mars pork chop plot

The Type 1 is the smaller region on the bottom, and the Type 2 is the larger region on the top.

TGO changed from a Type 2 to a Type 1, when they moved their launch out two months, but kept the same arrival date. TGO had a large deep space maneuver, so the pork chop plot doesn't have enough dimensions to represent the trade space, and the trajectories weren't the classic Type 1 and Type 2 impulsive trajectories (i.e. a single burn at Earth). But the basic principles still apply.

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    $\begingroup$ Ah, so it's the inclination difference more than the eccentricity that breaks the optimum? I was so close... $\endgroup$ – Russell Borogove Nov 4 '16 at 0:52
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    $\begingroup$ Yes. Even a tiny inclination difference results in requiring a 90° plane change in order to do a 180° transfer. (If you think about it, that's the only plane through the Sun that connects those two points.) That huge increase in energy is what causes the rift between the Type 1 and Type 2 trajectories. $\endgroup$ – Mark Adler Nov 4 '16 at 2:10

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