It's a consequence of the orbit's eccentricity - the perigee (low point) in the orbit is to the south. The satellite is moving faster around the perigee, and slower near the apogee (high point) over Japan.

More info here: https://gssc.esa.int/navipedia/index.php/QZSS

It's a version of the tundra orbit ( https://en.wikipedia.org/wiki/Tundra_orbit )

In https://en.wikipedia.org/wiki/Tundra_orbit#/media/File:Anima... its the green orbit.

The figure 8 shape can be seen in https://commons.wikimedia.org/wiki/File:Qzss-01-120s2.gif though it isn't quite as extreme in its eccentricity as orbits that are trying to service further north.

The shape is based on what is known as "apogee dwell" - that from the ground perspective a satellite at apogee (the furthest distance from earth) will be moving the slowest compared to the ground view. When the satellite is closer to Earth that same velocity will be covering more ground distance (there will also be some actual change in velocity based on how far down Earth's gravity well it goes in and out of, though I haven't done enough orbital mechanics to say with certainty). Judging by https://en.wikipedia.org/wiki/Quasi-Zenith_Satellite_System it changes by about 10% as it gets closer to earth.

The main issue (and you'll see this if you use GPS in a city) is that GPS can have difficulty in canyons - either urban or natural.

https://www.traffictechnologytoday.com/news/connected-vehicl...

You need line of site to GPS in order to get an accurate fix. If there's mountain or building in the way, it can have difficulty. Japan's cities are susceptible to this.

The QZSS system is designed to have a satellite directly overhead of Japan so that when you are in a city there is a satellite visible.

> The primary purpose of QZSS is to increase the availability of GPS in Japan's numerous urban canyons, where only satellites at very high elevation can be seen. A secondary function is performance enhancement, increasing the accuracy and reliability of GPS derived navigation solutions. The Quasi-Zenith Satellites transmit signals compatible with the GPS L1C/A signal, as well as the modernized GPS L1C, L2C signal and L5 signals.

It's the narrow bit over Japan that is intended, but as it happens the orbit tracks closest to the most populated parts of Australia, on the coast. The central parts (tan on the map) are more or less unpopulated.