In our Universe Centripetal Force can be expressed by the equation
If we assume an equivalent for Gravity in other numbers of dimensions the equation for gravity in 4d would be and in 2d the equation for gravity would be So in 4d gravity would increase much more rapidly when the distance decreases while in 2d gravity would increase more slowly as distance decreases. If the equation for centripetal force was instead of then the Centripetal Force of an object would increase more rapidly with Velocity so increasing the Velocity by a smaller amount would increase the Centripetal Force more while if the equation for Centripetal Force was the Centripetal Force would increase more slowly with Velocity.
If in 4d the equation for Centripetal Force was instead of would that balance out the more rapid increase in gravitational attraction with distance and produce stable orbits in 4d? And if in 2d the equation for Centripetal Force was would that balance out the slower increase in gravitational attraction with distance and produce stable orbits in 2d?
where F is the Centripetal Force, M is the Mass, V is the Velocity, and r is the radius. The equation for gravity is where F is the Force of Gravity, G is a gravitational constant, M is the Mass, and d is the distance between the two objects. When there are two objects orbiting each other the centripetal force between them can be expressed by the equation is the same as the Angular Acceleration meaning that for the Angular Acceleration the Velocity is squared. Centripetal Force is really just another form of gravity which pulls objects apart whether than pulling them together. In both the equation of Gravitational Attraction and Centripetal Force there is a value that is squared. In the equation for Centripetal Force the Velocity is squared while in the equation for Gravity the distance is squared. In order for two objects to stay in orbit around each other the Centripetal Force between them must be equal to the gravitational attraction between them.