How would you go about calculating an orbital inclination when accounting for the rotation of Droo? Is there a formula that can be used to get a certain inclination, or is it more trial and error.
Ex: if I wanted to put a satellite at a 43 degree inclined orbit, what would I have to set the navball at to counteract the rotation of droo? Thanks!
I take it you're talking about launching into an inclined orbit as opposed to making a plane change maneuver in orbit since Droo's rotation would be irrelevant in the latter case.
Droo's rotation imparts ~150 meters per second of horizontal velocity when launching from the launchpad. Orbital velocity for 100km Droo orbit is 3400 m/s. Therefore if you point at 43 degrees and launch up to 100km circular orbit that 150 m/s will be responsible for some of your forward motion and a small change in your trajectory. Theoretically you can use trig to figure out how much. If you launch at 43 degrees the component of velocity due to rotation that is going to change your trajectory is going to be 150 * sin(47) and given that the angle of deflection going to be arctan(150 * sin(47) / 3400 which is 1.85 degrees. So you could just adjust your trajectory -1.85 degrees, however the amount of deflection at this new trajectory will be slightly different. I feel like it should be possible to define this equations in terms of a target and some error, and then solve for error, but it's late and I'm not coming up with it in my head.
FWIW I think my trig is correct, but there must be a practical consideration I'm missing, because experimentally the error is quite a bit lower. When I launched at a heading of 43 degrees I wound up with an inclination of 46.5, only 0.5 degrees off from what you would get if there were no adjustment due to rotation.