# How will be changed Hill's radius and Kepler's formulas in case of 2D space instead of 3D?

Imagine that Flatland habitats go into space. All stars and planets are the circles instead of spheres and gravity law is $$F=Gm_1m_2/R$$ instead of $$F=Gm_1m_2/R^2$$.

How the other formulas will be changed in this case?

This image of a $$F=-1/r$$ orbit was produced by "central force workbench" by Juan M. Aguirregabiria.
The potential is now of the form $$V= \ln|r|$$. The only formula that is unchanged is Kepler's second law: Equal areas are swept out in equal time, as this is true for all central forces.