# Which orbital elements are normally targeted at launch?

Say you launch a rocket for rendezvous with the ISS.

You'll want to set the target orbital inclination and longitude of ascending node. These will ensure the rocket is in the plane of the ISS.

You'll also want to set the target altitude and velocity. These will ensure your rocket enters a stable orbit from which to transfer closer to the ISS.

Are there any other parameters you'd want to set? Would orbital eccentricity be important? If so, any comments on how you'd determine its appropriate value?

What about the argument of periapse and true anomaly? Would you set any of these? Comments on how to set them?

Plane changes are expensive in terms of fuel consumption, making it essential that any launch intended for rendezvous with the ISS must target an orbit whose orbital plane is very close to that of the ISS. This requires launching a vehicle in roughly the right direction, and at roughly the right time. The question mentions that this addresses only two of the orbital elements. What about the remaining elements?

There are several rules regarding rendezvous with the ISS. One is that even if the visiting vehicle goes completely dead at exactly the wrong time, it will not come close to the ISS within an extended period of time. Another is that the visiting vehicle needs to take advantage of the fact that the ISS is a cooperative target; the ISS has multiple navigation aids explicitly intended to make rendezvous easier. The combination of these two means that rendezvous is a slow process. The fastest rendezvous takes six hours from launch to rendezvous; some vehicles take several days.

I'll discuss the concept of phase angle before I answer the question. The ISS is in such a nearly circular orbit that argument of perigee and true anomaly aren't that well defined. What is well defined is the argument of latitude, the sum of argument of perigee and true anomaly. The phase angle between two spacecraft is the difference between the those spacecrafts' arguments of latitude.

The answer to the question depends very much on the rendezvous strategy used by the vehicle's mission planners. Some of the issues include

• Whether the vehicle launch window is designed to allow for fixable issues. SpaceX and Russia use nearly instantaneous launch windows (one second launch windows). Others have more flexible launch windows. A delay of just one second means the ISS is 7.7 kilometers ahead of where it would have been had the launch occurred at exactly the planned time.
• Whether the amount of time that passes between launch and docking/berthing is a few hours or several days. Some vehicles take several days, others, just six hours. Taking several days adds a lot of flexibility, but at the expense of taking several days.
• Whether phasing orbits used after orbit insertion have semi major axes that are greater than or less than that of the ISS. Phasing orbits that are above the ISS need to have the vehicle be ahead of the ISS so that orbital mechanics will eventually bring the vehicle closer to the ISS. The reverse is true for phasing orbits below the ISS; phasing from below requires the vehicle to be behind the ISS.
• Whether the final few orbits have semi major axes that are slightly greater than or slightly less than that of the ISS. The same basic concepts for phasing orbits apply, but the phase shift needs to be much smaller for those final few orbits.

I'll look first at the many orbits (several days) approach to rendezvous. These approaches use phasing orbits whose orbital period is slightly larger (approach from above) or slightly smaller (approach from below) than that of the ISS so as to eventually reduce the phase difference. The launch targets matching the orbital plane, but has a non-zero phase difference, the sign of which depends on whether the approach is from above or from below. A properly designed rendezvous strategy reduces the magnitude of the phase angle with each orbit.

With this many orbits strategy, changes in the spacecraft's orbit are initially entirely up to mission planners, and in real time, to mission controllers on Earth. Those mission controllers know the orbits of the ISS and of the visiting vehicle. The goal is to eventually bring the visiting vehicle to the point where it is somewhat close to the ISS and in somewhat the same orbit as the ISS. The approach to far field must keep the visiting vehicle from having any reasonable chance of colliding with the ISS. The transition from far field to near field rendezvous marks the point at which the visiting vehicle can finally see and communicate with the ISS. Visiting vehicle navigation transitions from absolute navigation to relative navigation at this point.

The visiting vehicle will be slightly behind the ISS at this transition point if the last few orbits follow an approach from below strategy, slightly ahead if it follows an approach from above strategy. Regardless of strategy, each orbit will take the visiting vehicle closer to the ISS. Eventually the visiting vehicle will be close enough to perform its final steps; how long is vehicle-specific.

What about faster rendezvous designs? Those designs must necessarily eliminate many of the intermediate steps and must drastically reduce steps from far field to near field to final approach. But even these fast rendezvous designs are a bit conservative. Unlike sci-fi, where rendezvous happens shortly after launch, even the fastest of rendezvous require multiple orbits between launch and rendezvous.

• +1, very informative Mar 13, 2021 at 16:49
• Thanks, @David_Hammen! I learned a few things from your answer. If the initial orbit (at insertion) has nonzero eccentricity, meaning that the argument of periapse is well defined, is the argument of periapse normally set (or at least known) before launch? Or do you enter orbit at some random argument of perigee? Thanks!!!
– user39728
Mar 13, 2021 at 18:49

The orbital insertion targets for shuttle were

• Inertial velocity magnitude
• Altitude
• Inertial flight path angle
• Orbital plane

From Unified Powered Flight Guidance page 1-3 (see also table on 3-3)

Some explanation:

We will tackle the second difficulty by deciding on a non-rotating Earth-centric XYZ coordinate frame: X and Y axes will lie in the equatorial plane (X aligned with the 0° meridian at some given time), Z will point north. It's easy to convert spherical coordinates (longitude, latitude & altitude) into XYZ - we just have to remember that the Earth constantly rotates, thus the launch site coordinates will also be continuously changing. Converting Keplerian coordinates of the target orbit into XYZ is more difficult. Since it is not a single, unique point in position&velocity space but rather a set of points, we can only express the desired state in terms of constraints. We will write them in the following form:

• plane - defined by desired inclination and longitude of ascending node,

• altitude - desired radius at MECO,

• velocity - magnitude of the desired velocity vector,

• flight path angle - angle between desired velocity vector and local horizontal.

The first constraint can be easily and uniquely written in XYZ form as a vector normal to the target plane (we can use Euler formulas to calculate it knowing INC and LAN angles), explicitly describing where the orbit will be and what will be the direction of motion. Next three describe what the orbit will look like: knowing altitude (radius) and corresponding velocity and angle, we can draw an ellipse in a unique way.

From here - written by a person who sat down and wrote their own version of PEG by poring through the shuttle documents

• +1 I'm a hack at this but let's see... with a velocity magnitude and two angles (flight path angle and orbital plane) you can have a velocity vector. With an altitude and an orbital plane and a known velocity vector you either have a circle (if eccentricity is zero) or two possible points if it's not zero. This certainly seems pretty complete except an epoch (time) for phasing; one wouldn't want to end up on the same orbit as the ISS except for being 45 minutes early/late.