Why gravitational potential is always negative
Potential at infinity is defined as zero. The gravitational field is attractive, so as a mass is brought in from infinity gravity does positive work and the external force does negative work. Hence φ (and U) fall below zero, and φ increases towards zero as r increases.
What this actually means
This is a two-mark explain that appears almost every year. The answer needs two ingredients: the zero of potential is at infinity by definition, and the field is attractive so the work done by the external force in bringing the mass in is negative.
Trace the logic slowly. The external force must oppose the displacement to stop the mass accelerating inwards, so F_ext points outwards while the mass moves inwards. Force opposite to displacement means negative work. Negative work done from a zero starting point lands you below zero.
Equivalently, gravity does POSITIVE work pulling the mass in. Energy has to leave the system for the mass to arrive with no extra kinetic energy, so the store ends up negative.
The consequence students most often get backwards: as r increases, φ INCREASES, because it goes from very negative towards zero. Less negative means larger. So a satellite moved to a higher orbit gains potential energy even though the number on your calculator gets closer to zero.
This is also why there is no positive gravitational potential anywhere in the universe. Electric potential can be either sign because charges repel as well as attract; gravity has only one sign of mass, so its potential has only one sign.
Marker's phrasing to copy: 'Since potential at infinity is defined as zero and the gravitational force is attractive, work is done BY the field in bringing a mass from infinity, so the potential at any finite point is negative.'
Saying φ 'decreases' as you move away, when it actually increases towards zero.
Prove it — watch it be true
- Look at the 3D potential well and note the flat zero plane far from the planet and the funnel dipping below it.
- Read the φ–r graph and check every value is below the axis, rising towards zero as r grows.
- Use the work-done two-marker tool from far out to close in and confirm the work comes out negative.