(455) Gravitational fields and force [IB Physics SL/HL]

Definition: Gravitational field lines represent the direction a test mass would move under the influence of gravity.
- A test mass shows where it would go when placed in a gravitational field.
Drawing Gravitational Field Lines:
- Arrows are drawn pointing towards the center of a mass (e.g., Earth).
- The number of field lines indicates the strength of the gravitational field: more lines = stronger field.
- Field lines radiate inwards toward the center of the mass.

Fundamental Principle: Every object with mass attracts every other object with mass.
Gravitational Force Equation: F = G (M1 M2) / R²
- F: Force of attraction (in Newtons)
- M1, M2: Masses (in kilograms)
- R: Distance between the centers of the masses (in meters)
- G: Gravitational constant (6.67 x 10⁻¹¹ N(m²/kg²))
Interpretation of the Equation:
- Force is directly proportional to the product of the two masses.
- Force is inversely proportional to the square of the distance between the masses.

Situation: Two planets are separated by distance R; determine new force when distance increases to 4R.
- Using the Equation (Brute Force):
  - F2 = G (M1 M2) / (4R)² = G (M1 M2) / 16R²
  - F2 / F = (G M1 M2 / 16R²) / (G M1 M2 / R²) = 1/16.
- Simplified Approach: The force is proportional to 1/R², thus:
  - For 4R: F ∝ 1/(4)² = 1/16.
Conclusion: The new force is 1/16th of the original force.

Gravitational field lines point inward towards the center of mass and indicate strength by the number of lines drawn.
Newton's law explains how objects with mass attract each other based on mass and distance.