Orbital Elements or State Vectors?

For many years the space community has used orbital elements at epoch to define orbits.  Yes, it does allow you to easily visualize the orbits; however, these are only valid for Earth orbits that have no perturbations due to lunar and solar gravity, Earth bulge, or atmospheric drag.

To solve this problem, we have proposed that TLEs (Two-line Elements) also include state vectors. State vectors are spacecraft position and velocity in 3 dimensions at epoch.  These are valid for any orbit that uses the ECI (Earth-centered Inertial) coordinate frame, including cislular orbits.

The objection used by leaders in the space community is that mean values cannot be assigned to state vectors but can be applied to all orbital elements except True Anomaly. Our response to this is that “estimates” can be calculated for state vectors based on current and past observations using the following process that is similar to a Kalman filter state estimator:

1) Take an observation (radar and/or telescope) to establish a state vector at the current epoch.

2) Propagate past observed state vectors, using the equation of motion method used by SOS, to the current epoch.

3) Combine the past and present state vectors with weighting based on the age of the observed state vectors.

We believe that our suggestion is based on common technical sense and will make TLEs more useful in the future.

Andrew Motes

Using the Satellite Path script functions and records in Mission Planner

When defining orbits with the functions and records within the Mission Planner, you will find that there are different groups with different levels of functionality.

At the highest level we have the “Satellite Path” group. We define a path as a fully defined orbit in space and time, with a beginning and an end (the last path doesn’t require the end to be defined). With these functions and records, each of paths of the satellite are automatically linked to each other. Changing the start time of one path will amend the start time of the other paths. The DeltaV to go between each path is worked out for you.

There are three projects that come with SOS that demonstrate their use:

  • Change inclination with Mission Planner
  • Mission using SatellitePath records
  • Moon Orbits using Mission Planner

The first project is the simpler one and the second demonstrates the use of all the satellite path functions. The third demonstrates a Hohmann transfer and inclination change while orbiting the Moon.

Achieving accurate orbit prediction

There can be a world of difference between designing an orbit using Orbital Elements and how the satellite’s orbit truly is. The reason is fairly obvious, Orbital Elements only account for the one force, the gravity of the object that the satellite is orbiting around. In the real world, there are many other forces at play, which need to be considered.

SOS tries to allow for these forces, as much as it practically can. Some forces are quite trivial to account for. For instance, the Earth’s bulge (due to its spin), has been mathematically modelled and can be accounted for. The Moon’s gravity is not hard either. Other forces, such as Solar Pressure and Atmospheric Drag, require knowledge of the satellite in question, but SOS has mathematical models for these too. Unfortunately, these models can not account for the day to day Solar Weather. This can lead to several effects like causing more atmospheric drag than predicted. SpaceX had this very problem when launching a batch of satellites in February 2022. It lost 38 of 49 satellites due to a geomagnetic storm – see link for more details. Fortunately, these instances are quite rare and any unforeseen forces like these can be picked up and allowed for using normal orbit maintenance manoeuvres.