The locations of Inmarsat-3F1 during the flight of MH370
Duncan Steel
2015 March 18
A whole year ago now I first became specifically interested in the tragic loss of MH370 and all on board due to my background in satellite orbits, because I realised that the positions of Inmarsat-3F1 being represented in the media (and some official investigation reports) were incorrect: there is no such thing as a truly geostationary satellite (they all unavoidably move around compared to an absolutely geostationary position above the equator), and I3F1 is good illustration of that fact, because a shortage of station-control fuel has meant that its orbital inclination has been left of necessity to drift upwards over the past few years.
Rather tardily I am now updating my ephemeris for I3F1 during the interval of the MH370 flight, in case this ephemeris might be useful to others. As noted in the preceding post here, the Independent Group (IG) has an intent to post and document a range of developments and improvements in our understanding of the constraints on the route taken by MH370, these having been arrived at through work conducted pro bono over the past many months. Different members of the IG concentrate on different aspects of the problem, and in part this leads to difficulties in reaching a consensus view on things to be published in a timely fashion in the open literature (e.g. on this website) under the collective heading of the IG, and so instead the plan is to post discrete facets of the investigations conducted by IG members in a piecemeal fashion. The point is that a dozen or more people debating specific words to use in an email wave that rolls around the globe daily means that time is taken up on trivialities rather than pushing the analysis forward, whereas two or three people can arrive at a final text on a more-restricted topic rather more quickly.
The present post conforms to that general idea. Briefly, the situation is as follows.
Throughout my earlier modelling of the orbit of I3F1 (and thus ping rings, and so on) I used within the STK application an orbit for the satellite which was downloaded from the AGI/STK server. Such orbits are based on optical and radar observations made by US military sensors and issued through the JSpOC (formerly NORAD and USSPACECOM), being issued in a form known as the “NORAD Two-Line Elements” (TLEs) and available through various public websites such as CelesTrak, which is associated with AGI.
Orbits for various epochs are/were available, and I settled on using the orbit for epoch 2014 March 09 [sic] on the basis that it was known that a manoeuvre had been conducted shortly before the MH370 flight, by coincidence, and so I needed to use an orbit determination from well after that manoeuvre. Within STK I then back-integrated that orbit (using SGP4/SDP4) so as to obtain a set of positions for I3F1 during the interval 2014 March 07 at 16:00 UTC through to March 08 at 00:30 UTC (i.e. covering the flight of MH370). I will refer to this as Ephemeris A.
In the ATSB report MH370 – Definition of Underwater Search Areas as Table 3 on page 56 is given a set of positions and velocity components for I3F1 as supplied by Inmarsat from its own knowledge of its own satellite (i.e. not based on the JSpOC observations, which might be anticipated to be less precise in terms of orbit definition). The eleven positions for I3F1 published there run from 16:30 through to 00:20.
Using those eleven positions Dr Henrik Rydberg, a member of the IG, kindly did a parametric fit so as to determine a second-by-second ephemeris for I3F1 across the interval 16:00 UTC to 02:30 UTC [sic], which he labels PAR5. I have inducted that ephemeris into STK so as to represent the positionss of I3F1 as indicated by Inmarsat’s own knowledge of the orbit across the interval of interest. I will term this Ephemeris I for clarity (rather than ‘Par5’).
The first thing to note is that the differences in positions for I3F1 as derived from Ephemeris A and Ephemeris I vary systematically during the flight of MH370 by between almost 2 km and almost 4 km. This implies that errors in the ping rings based on Ephemeris A (as previously used by the IG, and perhaps others) include an error component that could be as much as 4 km, which is non-negligible but nevertheless reassuring in that other sources of error are rather larger in terms of the cross-ping-ring overall uncertainty. It would appear that using a slightly-inaccurate orbit for I3F1 contributes at most 20 per cent of the cross-ping-ring uncertainty,
Should others wish to use the ephemeris (i.e. Ephemeris I) derived as above, I am hereby making it available for download from here. It covers the interval 2014 March 07 at 16:00 UTC through to March 08 at 00:30 UTC. So far as I know, this is the best (i.e. most precise) ephemeris (set of positions and speed components) available. Positions are given for each second of time, in terms of the latitude and longitude plus radial distance from Earth’s centre, to six decimal places (although their actual precision should not be imagined to stretch that far). The speed components in latitude and longitude are given in units of arcseconds per second of time [NB], and for the radial component in metres per second.
Update: Some users might prefer the ephemeris and velocity components in Cartesian coordinates, and so I have made this available here.