We can apply our new improved understanding of gravity to work out circular motion problems involving orbits:
And just like we needed a new equation for gravitational force, we need a new one for gravitational potential energy.
This could cause some people confusion… negative energy?! The key here is realizing that there is no actual “built-in” energy just because of where an object is located. Position is always relative. All potential energy measurements are always comparisons between two locations – so we can call any point we like “zero potential energy”. It makes a lot of sense to set that point at infinite distance – thus negative potential energy: