(455) HL Important gravitational field equations [IB Physics HL]

Gravitational Potential Energy (E_P)

• Definition: Work done to assemble a system from infinite separation.

• Equation:[ E_P = -\frac{G \cdot M_1 \cdot M_2}{R} ]

• Units: Joules (J)

• Key Point: Use ( R ) (not ( R^2 )) in potential energy calculations.

• As ( R ) approaches infinity, ( E_P = 0 ) (asymptotic behavior).

Gravitational Potential (V)

• Definition: Work done per unit mass.

• Equation:[ V = -\frac{G \cdot m}{R} ]

• Units: Joules per kilogram (J/kg).

• Relationship: Work done is given by[ \text{Work done} = m \cdot \Delta V_g ]

• Notes: To increase gravitational potential, one must move away from the mass (potential well analogy).

Gravitational Field Strength (g)

• Equation:[ g = -\frac{\Delta V_g}{\Delta R} ]

• Units: Newtons per kilogram (N/kg).

Equipotential Lines

• Definition: Locations where gravitational potential (V_g) is constant.

• Properties:

  • Perpendicular to gravitational field lines.

  • No work is done when moving along equipotential lines.

• Visualization: Equipotential lines indicate the same gravitational potential at different points.