Gravitational field of a point mass — common mistakes

Pay close attention to whether the question asks for gravitational force, field strength, or potential/potential energy. Each has a distinct formula and often different units. Remember the inverse square law applies to force and field strength ($1/r^2$), but potential depends simply on $1/r$. Also, don't forget to use the radius from the centre of the mass (e.g., planet's radius + altitude) in your calculations.

Gravitational field strength ($g$) is a vector quantity representing the force per unit mass, showing the direction and magnitude of the pull. Gravitational potential ($\phi$) is a scalar quantity representing the work done per unit mass to bring an object from infinity to that point, indicating the energy state.

For external points outside the sphere, the net gravitational effect of all its constituent particles is mathematically equivalent to having all its mass concentrated at its geometric centre. This simplifies calculations greatly, especially at a distance.

Theoretically, the gravitational force only becomes exactly zero at an infinite distance from the mass. In practical terms, it becomes negligibly small at very large distances, but never truly reaches zero in a finite space.

The negative sign indicates that the gravitational force is attractive. It means that work is done by the field when two masses are brought together from infinity. The system loses potential energy as the masses get closer. Zero potential energy is defined at infinite separation.