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Mechanics Formula

What is Newton's Law of Gravitation?

Any two masses attract each other with a force inversely proportional to the square of their separation.

Formula: F = \frac{Gm_1m_2}{r^2}

Plain-English Meaning

Every object with mass pulls on every other object. The bigger the masses, the stronger the pull. The further apart they are, the weaker the pull — and it drops off very fast (with the square of the distance). G = 6.674 × 10⁻¹¹ N·m²/kg² is an incredibly tiny constant, which is why we only notice gravity from planet-sized objects.

Mechanics questions usually become easier once you identify whether the problem is about force balance, kinematics, energy, or conservation.

Deeper Explanation

Newton's law is an inverse-square law: F = Gm₁m₂/r², where r is the centre-to-centre separation. It describes orbits (Kepler's laws deriving from this), tides, and the shape of galaxies. The gravitational field g = GM/r² is the force per unit mass at distance r from mass M.

Worked Example

Problem: Calculate the gravitational force between Earth (M = 5.97 × 10²⁴ kg) and a 70 kg person standing on its surface (R = 6.37 × 10⁶ m).

  • F = Gm₁m₂/r²
  • G = 6.674 × 10⁻¹¹ N·m²/kg²
  • F = (6.674×10⁻¹¹ × 5.97×10²⁴ × 70) / (6.37×10⁶)²
  • Numerator ≈ 2.788 × 10¹⁶, denominator ≈ 4.058 × 10¹³

Result: F ≈ 687 N (close to mg = 70 × 9.8 = 686 N ✓)

At A Glance

Category: Mechanics

Levels covered: High School, College, Masters, PhD

Best use: Start with the formula meaning, then move to the worked example and quiz so the equation turns into a tool instead of a memorised line.