Cue Column:

• Field vs Potential?
• Sign of potential?
• Relation between them?

Notes: Gravitational field intensity: E = $\frac{F}{m}$ = -GM/$r^2$ (vector, directed toward mass) Gravitational potential: V = -GM/r (scalar, always negative at finite distance) Relation: E = -dV/dr

Gravitational PE of two-mass system: U = -GMm/r

• At r = infinity: U = 0
• As r decreases: U becomes more negative (system is more tightly bound)

At Earth's surface: g = $\frac{GM_E}{R_E}$^2 = 9.8 m/$s^2$, V = -$GM_E$/$R_E$ = -$gR_E$

Summary: Field is a vector (force per unit mass). Potential is a scalar (PE per unit mass). Potential is always negative for gravity.