Inclination equation

[SRB]

Is there an equation to calculate the heading I need to fly to reach an orbit of a certain inclination, based of the latitude of the launch site?

[Superfluous J]

As it depends so much on your ascent path, I'm not sure how much any equation would help.

I'd say to launch it once with a guess, don't deviate from that guess until orbit, then check your deviation and relaunch.

Or if you're aiming at something, target it and spend the launch in map mode watching your an and dn. This is what I do hitting an asteroid or orbiter.

[bewing]

I believe there is such an equation -- but there are some problems. The first problem is that simply hitting a particular inclination is often not useful, unless you also hit some particular LAN -- which is basically impossible with just an equation.

The second problem is that it is mathematically impossible to hit an inclination which is less than your starting latitude.

You can guess at a heading (as a deviation from east = 90), I suppose, by just subtracting your starting latitude from your desired inclination.

 

Edited June 15, 2019 by bewing

[FleshJeb]

You can figure it out using this by substituting the appropriate orbital velocity and inclination. (Someday I'll redraw this):

[Kryxal]

You're solving a triangle for which you have SSA (side side angle), S1=174.5, S2=2300, A=desired inclination

https://www.triangle-calculator.com/?what=ssa&a=174.5&b=2300&b1=45&submit=Solve

Now take 180 - C and you have your launch inclination.