Librations

I just realised Thursday that none of the five Libration Points are stable. Not even L4 and L5; what these two do give you, are orbits in a kidney-bean shape. I've been going through and editing my older posts, to fit.

Here are the Earth-centred Librations fore and aft our Moon. We're, here, concerned with planetary Librations, centred at the Sun.

The exit-ramp over the planet runs past outer L2. This metastable and shadowed Libration, itself, for this purpose features a navigational buoy-beacon and also a nice store of ice. The L4 (leading, "Greek") and L5 (trailing, "Trojan") foci have similar beacons. L1 gets one too, for inner-planets and for solar-observations. And to catch fry-by passengers swinging up from sunside.

If people orbiting above the planet are going home, then another shuttle pushes them up further (to the hundred-thousands of km in Venus' case; the Earth-Moon system's outer edge is higher still). This spaceport is prograde to ecliptic, to lift off when that outer L2 buoy is in view. Retrograde if on an inner-planet mission, toward L1. Or if serving L5.

The stations here traffic amongst each other and with their planet between them via a parabolic, alias a ballistic.

I assume, crayon-on-tissue-paper, that since L4 and L5 are a sixth of the way fore and aft of our orbiting body, that when calculating Hohmann transit-dates to these Librations, that we divide the synodic year by a sixth, and subtract and add that (respectively for L4 and L5) to the date we want.

Trying this out for Venus' 583.92 days: 97.3 days. The acceleration sunward from Venus semimajor is GM/r² = 6.67428 × 1.9891 × 10¹⁹ × 10^-22 / 1.1708971264 = about 0.011338 ms^-2. (This is a good deal more than at Earth 0.0059, but not insurmountable.)

Both L4 and L5 can serve for overflow staging areas. The key to remember: an inner planet orbit is faster. Trailing L5 can send Hohmann travelers from said planet to the outer and slower planets, like criminals or the impatient or lame-duck outworld politicians, earlier; they also get incoming slowpokes from wherever. Leading L4 can let outbound fools get where they need to go, later.

I still have to figure out how wide the L4 / L5 kidney-beans are UPDATE 1/6: L4/5 beans extend 30 degrees fore and aft, of each. Also I hear that L1-3 can be orbited, as “halo”; but these aren’t all that stable either.