Say I have launched a nice, sun-facing satellite with inclination of 90 degrees, give-or-take. From this orbit, I want to beam energy and/or data to a shaded pseudosatellite at SVL2. Should I let my satellite sit here, that satellite's sidereal longitude will change, day to day, returning to form in 224.701 days. Say I am at 600000 km. This will meet back up with its original position in 48.1 days. I want to stay at 600000 km, whence I worry it shall escape Venus' influence should its angle go too far Sunward. For that, I need delta-V, when it returns to the orbital nodes which are near the north or south poles, every 24.05 days.
That span is over a tenth of the freakin' Venus year. I need to adjust 38.53° in that time. I think I have a fixed Ω, the longitude of the ascending node. I need to push that. I need to do... maths, again. As they say, no time like the present:
Aside 1: On assumption of near zero eccentricity the 38.53° inclination equation leads to delta-V of 8232.84 x cos(ω+f) km per day, max 95.2875 m/s. "'cause - ohhh WTF", indeed. Them orbital mechanics ain't just whinin' when they complain about pushing inclination.
Since I'm circular, I don't have periapsis so I can neglect ω. "ω+f" (or ω+ν) boils down to argument of latitude, u: my angle from the ascending node.
Aside 2: as to how this relates to true longitude: let us talk Right Ascension of Ascending Node. Ascending Node of the sun's [apparent] orbit would be the day of vernal equinox; Right Ascension is that relative longitude.
The sun rises over the equator; RAAN (or O0) is where my satellites rise on that day. If I have a polar orbit those suckers are rising north or south, fixing their RAAN to some function of 90° or 270°. Here is an Earth example: RAAN 247.3207°, less than a trigonometric minute off 270° minus Earth's 23.45° obliquity.
Over Venus I think my polar's RAAN is 92.6°.
Against the ecliptic, my sat's angle is purest 90°. I'll take the cosine of 92.6°. Its Delta-V for adjusting 38.53° at 600000 km altitude, is 7.3276 m/s.
As I keep saying, I do not expect my life to be perfect. For my sat's orbit I don't expect its eccentricity to be zero - especially when I first get such satellites going, which I will likely be doing The Pioneer 12 Way. Still, even a 8 m/s is not that bad: it's like jumping off Deimos, or driving 17-18 mph. It's much worse for us here at LEO, clearly. Best of all over Venus I take 2620 Wm-2 from the Sun and some density of "solar-wind" with it. If I can amortise this 8 m/s over 24 days, and my payload is light: solar sails would do the job.
DERP 1/13: I mistook inclination, always polar; for the face it shows to the sun, which is longitude. So: just read Kerbal fora.
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