There is no claim that the plane moved along the 40 degree arc in two dimensional space, only that it moved along the arc in three dimensional space. If every ping happened along the 40 degree arc all the means is that the plane held to the same altitude for 7 hours, nothing more.
Let's get something straight. The arc that we are presented with has nothing to do with 40 degrees except it happens to be a 40 degree arc. And it has nothing to do with the
path of the aircraft.
The arc is simply a line that marks the potential range of positions of the aircraft at a single, specific moment in time, based on a single ping from the satellite. It is the distance from the satellite computed based on the length of time from the time at which the satellite sends the ping until it receives the response. The aircraft's altitude would have very little effect on the position of the line... perhaps a couple of miles, but there is enough potential error that the altitude makes very little difference
The Inmarsat satellite does not have any azimuth information. The data that we are being presented with is simply a distance from the satellite at the moment of the last single ping. A radar works sort of the same way... the time it takes for the signal to return to the radar head determines the distance. The difference between radar and this type of information is that radar provides the azimuth (direction) of the signal based on the direction the radar antenna is facing at the moment the signal is received.
RADAR stands for
RAdio
Direction
And
Ranging. All this satellite can provide is RANGE and that's all the arc represents.
Thank goodness they didn't present the arcs from the other pings. It would have been even more confusing.