Friday, March 26, 2021

Everyone messed up Mars

Russell and Ocampo's 2.0 km/s for V insertion to Mars at 2-1-1-5 aphelion is, frankly, a joke.

For vinf: the cycler at the outer planet needs to target that ones' speed at that distance from the Sun, not a fictional planet's circular speed at its semimajor (possibly) millions of kilometers thence. And the cycler needs that angle - which, where the planet isn't himself at peri', is never circular 0°. (Tho' 'tis a sight closer than is the cycler's - obviously, or Mars would be a cycler...)

Mars, coming off his own 1.385 AU peri', is going faster than he will at 1.54 AU. At 1.45 AU that factor is 1.09775756.

We next have to consider cycler/Mars γ-angle. The cycler at aphelion is, itself, γ=0 with respect to the circle. So the angle we want is that angle Mars is going with respect to that circle. It's actually not so different from circular, especially this close in: only 0.00350 radians. And he's tilting for us.

It's the destination planet's speed which is killing us: where 2-1-1-5 and Mars meet, Mars is going 26475 m/s. This is decidedly midway semimajor-Mars : Earth 24.07 : 29.78 km/s. So 2-1-1-5 V @Mars = 1788 m/s.

For McConaghy et al. 1L1, 2L2, and 3L4 still check out. But... 2L3 is V 2678 m/s at aphelion (290 days), against McConaghy's 3.05 km/s. Sorry to say, we'd all got the cycler-Mars vinfs wrong for Mars where the cycler doesn't reach semimajor.

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