The first one is simple spherical coordinates. You may have seen this on youtube on some other engines maybe. It looks great, but has one deciding disadvantage: the planet is not full 3D. It\'s just a simple visual effect. The planet surface is a plane that is warped (kind of like very wide lense photo cameras) by converting all the points into spherical coordinates and make the ends repeat (so it loops). But a plane has as we all know only one up direction, and while you could have the visual effect of it even rotating, other objects would have to be warped in the same way as the planed surface. It looks like it\'s working, but without a real 3d space, there will be logic problems with every other object not in that planet\'s context.
Well, personally I think it\'s the way to go. You\'d have to try to implement a transition layer in planet\'s entity, to make \"out-of-context\" objects don\'t interfere with a planet, and objects entering the area-of-influence (atmosphere) of a planet to acquire the planar dimension to avoid logic issues. You would be able to pick an area of approach from within, but it would just move you to appropriate location over the plane, like it works with void-sys transition. To avoid logic issues from the planet view you can limit the vision to display only stars on night, and maybe only Beacon lights from objects outside, while you can\'t see anything in the daylight atmosphere, but the star which provides it.
It would likely require other major changes to happen, like increasing sector dimensions and decreasing their number, to make planets as more viable objects (though there\'s several other points why it should be done that way). It\'s okay this to be just a visual effect as long as you just can\'t approach the planet from the bottom, which is main issue in my opinion.