# Math, Doppler And The Missing Jetliner

I just finished reading some technical data from Inmarsat and Ministry of Transport Malaysia concerning the analysis of satellite data transmissions from MH370. It’s this data that’s shifted the searchers from MH370’s planned route to a tract in the Southern Indian Ocean well west of Australia–nearly the opposite direction expected!

It is a brilliantly concocted method to get usable information from what should have been meaningless housekeeping transmissions.

Radio signals travel at the speed of light. If we know how long those signals take to go satellite-to-plane (or vice versa) we can start doing calculations and find the distance between the two.

Inmarsat was then able to calculate the range of the aircraft from the satellite, and the time it took the signal to be sent and received, to generate two arcs of possible positions – a northern and a southern corridor.

As you probably know the northern track was thrown out. But why? That’s where the plane should have been flying. It was the most logical direction.

Enter Doppler!

Because the satellite and plane were both moving, their radio waves were subject to Doppler shift. This is an expected part of satellite work and equipment to compensate for it is built into the system.

The Inmarsat technique analysed the difference between the frequency that the ground station expected to receive and the one actually measured, known as the Burst Frequency Offset.

Because the satellite wasn’t at the midpoint of the two project tracks, the expected northbound offset or shift was different than the southbound shift. What was actually seen only matched the southern track.

Depending on the plane’s speed the same Doppler shift could indicate slightly different positions. Unfortunately, that’s an unknown. It’s a good guess to estimate 400-450 knots. That’s why the area now being searched isn’t a single point, but a larger area.

Obviously, the plane hasn’t been found, there’s still no real explanation for what went wrong. However, this clever use of math helps bring those looking one step closer.

I know this is somewhat complex. I’m not 100% sure my explanation will be clear to everyone. Questions are welcome.

## 3 thoughts on “Math, Doppler And The Missing Jetliner”

1. Carole says:

Geoff, I wish I could ask my brother-in-law some questions about this flight, because he has flown over the area numerous times over the years. He recently passed away. He flew as a commerical pilot around the world several times a month.

2. Jeffrey Eric Grant says:

Geoff, the way I understand it, the satellite is 22K+ miles above the earth and that the ‘ping’ indicates a connection with the plane. A track of possible locations could be drawn on the earth, and that track would be a circle (ring). Your two arcs are two parts of that circle, all of which is equidistant from the satellite. The ring is not dependent upon topography or eccentricity of the roundness of the earth surface. The connection is momentary and is established once/hour. The last one was at 0811, and there were 4-6 others (depends upon who you ask). If the first one was when the aircraft was in the Malacca Strait, please tell me how they got down by Perth in 6 hours of flight. I am sure you are assuming the flight path was straight. If the flight path was controlled, it could have been zig-zaged, and another location on that last ring could be established. In fact, there could be up to 64 different locations on that last ring. Could it be determined by a Doppler shift? If so, I need a better explanation. My calculations indicate there is no discernible way to determine where the aircraft is located on the ring.
Thanks, Jeff

1. Look at the third graphic, which compares the expected Doppler shift at 450 kts constant with what was received. As you see, they correlate really well. From that, constant speed/course can be safely implied.