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Unit conversion

Convert Gravitational constant (G) from SI to CGS using dimensional analysis

6.674 × 10⁻¹¹ N m² kg⁻² = 6.674 × 10⁻⁸ dyne cm² g⁻². Gravitational constant is [M⁻¹ L³ T⁻²], so only the powers of mass, length and time decide the factor.

6.674 × 10⁻¹¹ N m² kg⁻² 6.674 × 10⁻⁸ dyne cm² g⁻²

Working

Step by step

  1. The dimension of gravitational constantGravitational constant has the dimensions [M⁻¹ L³ T⁻²]. Only the powers of M, L and T matter for the conversion.
  2. The conversion ruleA quantity with dimensions [Ma Lb Tc] has the number n₂ = n₁ [M₁/M₂]ᵃ [L₁/L₂]ᵇ [T₁/T₂]ᶜ in the new system. Here n₂ = n₁ [M₁/M₂]⁻¹ [L₁/L₂]³ [T₁/T₂]⁻².
  3. The size of each base unitM: 1 kilogram (kg) is 1000 gram (g). L: 1 metre (m) is 100 centimetre (cm). T: 1 second (s) is the same in both systems.
  4. Put the numbers inn₂ = 6.674 × 10⁻¹¹ [1 kg / 1 g]⁻¹ [1 m / 1 cm]³ [1 s / 1 s]⁻²
  5. Work out each bracket[M₁/M₂]⁻¹ = 1000⁻¹ = 0.001; [L₁/L₂]³ = 100³ = 10⁶; [T₁/T₂]⁻² = 1⁻² = 1
  6. Multiplyn₂ = 6.674 × 10⁻¹¹ × 0.001 × 10⁶ × 1 = 6.674 × 10⁻⁸
  7. The answer6.674 × 10⁻¹¹ N m² kg⁻² = 6.674 × 10⁻⁸ dyne cm² g⁻²
Questions

Gravitational constant G, SI to CGS: quick answers

How do you convert N m² kg⁻² to dyne cm² g⁻²?

Gravitational constant is [M⁻¹ L³ T⁻²]. Multiply by the ratio of each base unit raised to its power in the dimension. That gives 6.674 × 10⁻¹¹ N m² kg⁻² = 6.674 × 10⁻⁸ dyne cm² g⁻².

What is 6.674 × 10⁻¹¹ N m² kg⁻² in dyne cm² g⁻²?

6.674 × 10⁻¹¹ N m² kg⁻² = 6.674 × 10⁻⁸ dyne cm² g⁻².

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