(455) Gravitational field strength [IB Physics SL/HL]

Definition of Gravitational Field Strength

• Gravitational field strength (g)

  • Defined as the gravitational force per unit mass experienced by a point mass.

  • Equation: g = F/m where F is the gravitational force and m is mass.

Equation Derivation

• Relationship: g = F = G * M * m / R² (where G is gravitational constant, M is mass of the object generating the field, and R is the distance from the center of mass)

  • Simplified to: g = G * M / R² by cancelling mass (m).

Units of Gravitational Field Strength

• Units derived from force divided by mass: Newtons (N) per kilogram (kg).

  • Since 1 N = kg·m/s², thus units simplify to m/s².

• g on Earth: approximately 9.81 m/s².

Application of Gravitational Field Strength

• Can be calculated for any celestial body by plugging in mass and radius into g = G * M / R².

• Example: Moon and other planets (e.g., Mars).

  • On the Moon, gravitational field strength can be calculated similarly by using its mass and radius.

Example Calculation: Deimos (Moon of Mars)

• Given: mass = 1.5 * 10¹⁵ kg, radius = 6.2 * 10³ m.

• Using g = G * M / R², plug in values:

  • g = (6.67 × 10⁻¹¹ N m²/kg²) * (1.5 × 10¹⁵ kg) / (6.2 × 10³ m)².

  • Result: g = 0.263 m/s².

Example Calculation: Planet with 10x Earth's Mass

• Given: mass = 10 * m_e (Earth's mass), radius = 20 * r_e (Earth's radius).

• Start with: g = (G * 10 * m_e) / (20 * r_e)².

  • Simplified: g = (1/40) * (G * m_e / r_e²).

• Substitute known value for g on Earth: 9.81 m/s².

  • Result: g = 9.81 / 40 = 0.24525 m/s² ≈ 0.25 m/s².

Conclusion

• Gravitational field strength (g) can be applied to any mass with corresponding radius, providing insight into how gravity varies in different contexts.