Big spheres are not spherical

Hello, I'm trying to make a game/simulator in unity of the universe that includes interactions with planets.
I haven't done the usual thing and made a terrain for the planet's surface, instead, I tried to make a huge sphere that represents the planet itself the radius of the planet was 10000 unity units.
The problem was that the sphere wasn't spherical and I could see flat surfaces over the sphere, I'm trying to make the sphere behave and look more spherical, does anybody got a suggestion about how to do that?

I know that it's possible with unity because Kerbal Space Program is a game that developed with unity and it has spherical planets.

 

So there is no such thing as a true sphere in 3D modeling, at least as used in game development. Meshes are a collection of triangles that combine to form whatever you want it to appear as. So a sphere is still a collection of triangles. To make a model appear smooth, that is done by increasing its detail (more and smaller triangles) and through the smoothness of the materials applied to the model. Just taking a built in Unity primitive shape and scaling it up to planet size is going to have less than ideal results.