Gravitational field — common mistakes

Remember to pay close attention to the negative signs for gravitational potential and potential energy. They indicate that work is done by the field, and energy is released as objects move closer. This is crucial for understanding energy changes within gravitational systems.

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

They are negative because gravitational attraction is an attractive force. By convention, potential at infinity is zero. As a mass moves from infinity into a field, work is done by the field, meaning energy is released. This release of energy results in a lower, negative potential and potential energy relative to zero at infinity, signifying a bound system.

Both follow an inverse square law (proportional to $1/r^2$) and are proportional to the product of the interacting properties (masses for gravity, charges for electrostatics). However, gravity is always attractive, while electrostatic forces can be either attractive or repulsive. Also, gravity is significantly weaker than the electrostatic force.