Introduction
Having discerned a suitable satellite constellation for coverage over specific user-defined regions of interest in part two, part three will see us compute a conjunction analysis for the proposed LEO constellation.
Threat Ellipsoid for LEO satellite conjunction analysis
Computing Conjunction Analysis
Crucial to the success of our LEO constellation is the ability to maintain our operational satellites for the entire mission duration. Unsurprisingly, much of the industry talk about LEO orbits finds itself centred around the congested and contested nature of this domain. With modern LEO constellations growing both in number and in sheer size per constellation, ensuring an accurate method to plan for potential collision events is paramount to any satellite’s longevity.
Ansys STK facilitates detailed conjunction analysis for any publicly tracked object in space, drawing on the public NOAA databases and updated multiple times a day to reflect the most up to date tracking information. Moreover, should a user possess more detailed tracking information for a particular object, or the proposed orbit for an upcoming satellite launch, this data can be incorporated into STK’s conjunction analysis procedures.
In this instance, we will analyse our 12 satellite LEO constellation against all publicly tracked space objects. The default database included with STK includes active and decommissioned satellites as well as tracked debris and is updated frequently with up-to-date tracking information. Each satellite and database object is assigned a threat ellipsoid. This accounts for the uncertainty in a satellites exact position, as measurement data will always possess some degree of inaccuracy.
In this instance, the threat ellipsoids are defined as a fixed size. However, the “class” dropdown above offers several input types, including an altitude-based lookup table, where the threat ellipsoid will change size based on satellite apogee and perigee. For even more detail, let us look at how we can incorporate real-world or simulated tracking uncertainties for the conjunction analysis.
Incorporating Tracking Uncertainties
Within STK, the user can apply known tracking uncertainties for any objects in their STK analysis. For example, if the user has access to more detailed tracking data for a particular satellite, this will often include time-dependent covariance data. Depending on the frequency of tracking measurements, accuracy of equipment, and type of tracking data this can result in significant variations in the threat ellipsoid. For example, the screenshot below shows a satellite which is currently being tracked by ground facility. At this point in time the uncertainty in the satellite’s position is relatively low, depending largely on the quality of the tracking equipment available.
Threat ellipsoid (red) is relatively small as a current tracking measurement from the ground facility with access minimises the uncertainty in tracking position.
However, as time progresses the satellite moves to a portion its orbit during which no ground facilities are able to see and track the satellite. In turn, the uncertainty in its exact location grows extensively due to a multitude of factors affecting the satellites real world trajectory. Below, we can see the red threat ellipsoid has grown significantly.
Threat ellipsoid (red) has grown considerably due to the lack of recent measurements to correct the increasing uncertainty in the satellites exact position.
Factoring this dynamic tracking data into the conjunction analysis can allow for increased accuracy in determining near miss or potential collision events. Notably, these tracking uncertainties can be simulated using tools such as Ansys Orbit Determination Tool Kit (ODTK), allowing for detailed satellite orbit planning before any real-world launch.
For more information on ODTK be sure to check out our full DME blog. Or contact us for more information, including a demo of how ODTK and STK might apply to your specific needs.
Exploring Conjunction Events
With the threat ellipsoids defined for all satellites of concern, STK can compute the conjunction analysis for any desired analysis period. In this case we have opted for a 24hr window, as tracking data is to be updated multiple times a day, and we can simply reopen STK, update the analysis timeframe and rerun this computation when more up to date information becomes available. The computation itself completes in a handful of seconds on a modest workstation laptop.
Once complete we can compose any custom report or graph required, but in this instance, we will start our analysis with a premade “Close Approach by Min Range” report. This will sort all intersect and close approaches detected over the analysis window, allowing us to focus on the conjunction events most likely to cause problems for our satellite at the top of the report.
Snapshot of a Close Approach by Minimum Range report, showing the objects that come closest to one of the proposed LEO satellites along with information for each conjunction event.
A snapshot of the report above shows each object that presents a close encounter with our LEO satellites. Information includes the common name of the object from the tracked database, where “deb” refers to a piece a debris, time in, out and time at minimum separation, as well as the minimum range at this time and overall calculated collision probability. Collision probability is based on one of four methods available in STK, each using established methods in space-research literature. We are also free to select any of these conjunction events and scrutinise them further in the STK GUI. This can be achieved by right clicking on any of the above timestamps and selecting “Set Animation Time.”
Below, we can see “LEOSat62” approaching another tracked object, in this case “Rubin-3 seen in the conjunction report above. As the two objects near their threat ellipsoids become orange, indicating a heightened potential for collision.
Visualisation of one potential conjunction event. Yellow threat ellipsoids are one of the primary LEO satellites and one secondary database satellite, whilst other database satellites in green travel in the background. Yellow threat ellipsoids indicate the two objects have entered within a user-defined “threshold” distance to one another.
A few seconds later the threat ellipsoids change to red, as the two begin to intersect. Referring to our earlier report, the minimum separation between these two satellites drops to just 3.2km. Whilst the fixed threat ellipsoids used here are quite generous due to the lack of “real-time” tracking covariance data, this close proximity may prompt our satellite operators to consider available actions targeted reducing the collision probability between our satellite and this identified threat.
Stepping forward in time from the previous image, the threat ellipsoids now intersect, turning red to indicate this change. Once they separate further they will turn yellow and then green once more.
Additionally, we can analyse any individual conjunction event via a premade “Encounter Warnings” report. This provides further insight into the nature of a potential collision, including relative velocity and direction between the two objects during their close encounter. Here we can gather that the approach angle between LEOSat62 and a near miss with some “Cosmos 2251 Debris” is calculated as 29.15 deg, with a relative velocity of 227km/s at the time of closest approach.
Encounter Warnings report which describes each possible conjunction event in terms of time and relative position/velocity between the two satellites. Also lists the uncertainty in tracking data of the two satellites, which remains fixed in this particular example
Combined with the additional data available here this can provide further insight into the best possible course of action for a satellite operator, such as whether to reorient their satellite to a lower or higher drag generating attitude. Of course, doing so may compromise the availability or performance of sensing and communication equipment aboard the satellite, all of which can be analysed by the interconnected mission model in STK.
Conclusion
This series has endeavoured to explore a handful of the design challenges facing LEO satellite problems. Whilst we have yet to explore many other challenges, including cyclic thermal loading and orbital decay management, the Design Reference Mission assembled in STK across this series lays the foundation for even more detailed analysis as the engineering project progresses. Be sure to check out our full LEAP Australia DME Blog, and feel free to reach out to us to see how DME solutions can enhance your missions.