2.4 Orbit Circularization

Explanation

So far we have launched from the lunar base and are currently coasting towards apoapsis. We need to perform a boost at apoapsis in order to not fall back towards the moon. At apoapsis we will simply aim the nose straight ahead in prograde (direction of flight) and fire the engines for a few seconds. 

In general, it's easiest to change the eccentricity of an orbit at either periapsis or apoapsis. This is because at these points, the radial component of the spaceship's velocity is 0. This simplifies the orbital equations and allows you to adjust the orbit by firing the engines in either the prograde or retrograde direction. Firing at apoapsis will modify periapsis, and firing at periapsis will modify apoapsis. 

The speed needed to have a circular orbit has already been computed; it is identical to the space station speed, since we are at the same altitude. So, we know how much we need to accelerate. For flight planning we also computed the fuel required for this burn. We will show the computation below. We performed this computation twice, using two methods: first considering the ship as a point mass model, and second by just using the ideal rocket equation. 

Computation

Here is the computation that was used in the flight plan:

Here are the printouts:

Flight Results

Arriving at Apoapsis, our cockpit view is shown in the image below. Note that the physical view is black because our apoapsis is on the dark side of the moon. In the orbit MFD, the apoapsis is indicated with a tiny green circle, and the MFD indicates that we are 4.61 seconds from reaching the apoapsis (ApT = Time to Apoapsis in seconds). 

Note how the eccentricity has dropped close to 0, and the apoapsis and periapsis radii nearly match. The fuel remaining is 25,600 kg:

On the Orbit MFD we can set our space station target in order to compare it to our ship's orbit. Note that the space station lags the ship position by a few minutes, and the orbits are progressing anti-clockwise in the images:

In the next section we will show how we change our ship's orbital plane to match the target space station's orbital plane.