2.5 Orbital Planes Alignment

Explanation

Now that we are established in a circular orbit, we can turn our attention to synchronizing with our target space station. Looking at the map and orbit MFDs, we can see that we need to make two adjustments:

• our orbital planes are not aligned 

• we are leading the target by several minutes, and at these speeds this adds up to a very large distance apart 

We will take care of the planes first.

On the map we can see two points at which our ship's orbital plane crosses the target orbital plane. These are called the ascending and descending nodes. 

Using the Align Planes MFD, we can see the relative inclination (RInc) between our orbital planes is 14.29°. This is close to the value we expected from our flight plan, 14.27°.

Once we reach an ascending or descending node, we will fire our engines to redirect our velocity vector to match the target orbital plane. We are going to try and aim in such a way that the resulting velocity has changed only in direction, not magnitude. In other words, looking at the diagram below, we want to get as close as possible to|v1| == |v2|. This is called a "pure rotation of the velocity vector". 

To do this we are going to use the normal and anti-normal autopilot modes to get the spaceship pointed perpendicular to its flight path, and then adjust slightly to achieve the correct angle. If the spaceship is aimed correctly, the diagram above will reform into an isosceles triangle with v1 == v2. 

Computation

Here is the computation that was used in the flight plan. Note that the relative inclination value we used for the flight plan was taken from the Align Planes MFD while the spaceship was still on the launch pad. We decided it was acceptable to use this value as long as we used an eastbound (090°) launch azimuth. 

Here is the printout:

Note how much more fuel is required for this maneuver than for the circularization maneuver. Plane changes are very fuel-intensive if the speeds are high. So, they tend to be more economical if you perform them at higher altitudes. 

Flight Results

Here are the results in our flight after performing the plane change burn. Note the aiming was not perfect, so our orbit's circularity has been disturbed. We will correct the circularity with short adjustments at the next crossing of periapsis and apoapsis. Fuel for the correction burns was included in the flight plan budget. 

Here is our view coasting to the ascending node:

Here we are arriving at the ascending node and have positioned the ship for the plane change burn. Note that the ship's nose is aimed about 7 degrees above the prograde direction, and that we are going to use the hover engines to perform this burn. 

The alignment burns were not aimed perfectly, so the circularity of our orbit was disturbed. After correcting, we can see that our orbit is once again circular, and that on the map MFD, the two orbital planes have merged into the same track, meaning the orbital planes are now aligned:

In the next section we will show how we synchronize the phase of the ship and space station orbits.