How to calculate and reach a given orbital inclination

[gilflo]

Hi everybody

You can see on this pic, the 1st one, 3 ships with 3 different orbits around EVE. As you can see the ship on the blue orbit is inclined to 24°. The ship above and on the left has got the same inclination, orbit is just shorter. Inclination being the lowest latitude you can reach, choosing the same inclination as the ship you want to rendez-vous does not means you will have same orbit !!! I just realize this now....

As you can see on the 1st Pic, lat 24 is reach at Longitude -247

On the 2nd pic lte lat 24 is reached at longitude 46

So I have 3 questions:

-What means longitude -247°: Is it E113° (360-247), West being positive? Lat S seems to be positive While Lat N seems to be negative.

-When in transfert for another planet, is there a trick to choose the inclination of your future orbit? My 2 first launches to Eve gave me on final the 2 grey perpendicular orbits on the 1st pic, which were each time the minimum burn and they are different from 90°. I used MechJeb and protractor to help.

-For the 3rd launch, I burnt a lot of extra fuel, after EVE rendez vous, long before approaching Periapsis, just to get a 24° inclination, but I won't be able to reach the 24° inclination of the other orbit as I will be short of fuel. So is there also a trick to solve this before braking to establish orbit?

[Taki117]

as soon as you enter the SoI of your target body is when you should make your initial plane change, this will save tons of dV. As far as LAT and LON I really have no idea nad tend to ignore them anyway. Also, I seriously doubt that either of your craft in the first pic (The ones on the grey orbits) are in a 24 deg orbit. If they were then they would be on the same orbital plane as the blue orbit. Just because MechJeb says they are at the same inclination doesn't mean they are relative to eachother. Your best bet here is to send a refueler.

[gilflo]

I agree with the refueler.

Inclination is angle of your orbit with equator, so you can have same inclination North or south from equator and not being on same orbit. I think mechJeb does not lie, it's a question of signs - positive or negative, which is not included.

[alexmun]

So I have 3 questions:

-What means longitude -247°: Is it E113° (360-247), West being positive? Lat S seems to be positive While Lat N seems to be negative.

-247 should mean the exact same thing as 113, it's just a wrapping error. I'd assume positive is East, but I don't know for sure.

-When in transfert for another planet, is there a trick to choose the inclination of your future orbit? My 2 first launches to Eve gave me on final the 2 grey perpendicular orbits on the 1st pic, which were each time the minimum burn and they are different from 90°. I used MechJeb and protractor to help.

-For the 3rd launch, I burnt a lot of extra fuel, after EVE rendez vous, long before approaching Periapsis, just to get a 24° inclination, but I won't be able to reach the 24° inclination of the other orbit as I will be short of fuel. So is there also a trick to solve this before braking to establish orbit?

This is the cheapest way I know to set your inclination after an interplanetary transfer:

1. After entering the SoI (or even before, if you're really good with fine tuning maneuver nodes) adjust your orbit so that the latitude of your periapsis is close to the equator. If you're trying to match the orbit of another vessel, target it and adjust your periapsis to be at a node (ascending or descending) with the other orbit.
   
2. When you get to periapsis, burn retrograde until your apoapsis is just inside the sphere of influence.
   
3. When you get to apoapsis, burn normal/antinormal to get the inclination you want. This should take only a few m/s of delta-v because you will be moving very slowly.
   
4. Finally, when you get back to periapsis, you can circularize into your final orbit.
   

You can calculate how much delta-v a plane change costs using:

dv = 2 * v * sin(theta / 2)

Where v is your orbital velocity when you perform the maneuver and theta is the angle by which you want to change your orbit. If you target your other ship, you can read that angle off the node and calculate whether you have enough left to do the plane change. For large plane change maneuvers, you can also use a bi-elliptic strategy, where you would burn prograde at a node (ascending or descending) until your apoapsis is near the edge of the sphere of influence, coast to apoapsis, do the plane change there (which will be much cheaper due to the lower orbital velocity), then re-circularize at periapsis.

Finally, the reason your two 24 degree inclination orbits don't line up is that your orbital plane is defined by two numbers, inclination and longitude of ascending node (which is where the orbit crosses the equator, and confusingly has nothing to do with terrestrial longitudes). So even though your two orbits have the same inclination, they have different longitudes of ascending nodes (238 vs 167), and so they're on different planes.

[gilflo]

Well, Alexmun, thank's a lot for those explanations, great help.