The blend file can’t explain the procedure of making and
the explanation itself is not very simple
Here are the the steps:
Creation of the particle emmiter.
1. Create a sphere (clear its rotation - Alt+R).
2. Add an Empty to its center (clear its rotation - Alt+R).
3. Enter Edit mode for the sphere and delete all vertices except for one at the pole - that is your particle emmiter object (PEO).
4. Create a particle emmiter modifier for PEO. Make sure you set the emmition from vertices!
5. Animate the rotation of PEO around its center - in my case I aniamted rotation from 0 to -180 degrees around Y axis (i.e. in front view). This will change the RotY parameter in IPO curves. RotX and RotZ aren’t changing so you can delete them.
6. Now it is important to transfer this animation to the dRotY parameter. For this - create one key for dRotY (Ctrl click in IPO editor window with dRotY channel selected), copy the curve from RotY channel in the buffer and paste it in the dRotY channel. Now you have to delete the RotY IPO curve!
Duplicating the particle emmiters
1. To get the effect of moving along longitude edges of the sphere you will need the desired number of particle emmiters. This could be done by duplicating and rotating the PEO several times.
2. Select the PEO in top view duplicate it (Shift+D) and rotate the copy at some degree (in my case it was 45 degrees around Z axis). Repeat this step until you create the desited number of PEOs. It is hard to notice the duplicates because they are single vertices rotated in place, but they are there.
3. Now you have PEOs that share the same particle system and its settings are applied to all emmiters.
4. It is time to play with the settings of the particle system and PEO’s material (which in my case was set as Halo material).
Adding extra motion effects
1. The Empty object that was created initially can play the role of rotating center of the PEOs.
2. Select all PEOs and parrent them to the Empty object.
3. Now you can animate the Empty too and get interesting variations of the movement over the sphere surface.
The visible blue sphere in the posted video was separate object, not related to the particle emmiters.
I hope the explanation is clear enough so you can post an nice video reply to mine.