Gravity

Gravitational Constant Conversion

The gravitational constant uses the following conversion process to convert from units in meters, kilograms, and newtons, to units in centimeters, kilograms, and newtons.

$$ G_{cm} = 6.674 * 10^{-11} \frac{Nm^2}{kg^2} * \frac{10,000cm^2}{1m^2} $$

$$ = 6.674 * 10^{-11} \frac{N * 10,000cm^2}{kg^2} $$

$$ = 10,000 * 6.674 * 10^{-11} \frac{N * cm^2}{kg^2} $$

$$ = 6.674 * 10^{-7} \frac{N * cm^2}{kg^2} $$

Alternatively, we can eliminate Newtons, as newtons are in meters ($1N = 1kg*m/s^2$)

$$ G = 6.674 * 10^{-11} \frac{m^3}{kg * s^2} $$

$$ G_{cm} = 6.674 * 10^{-11} \frac{m^3}{kg * s^2} * \frac{(100cm)^3}{1m^3} $$

$$ = 6.674 * 10^{-11} \frac{m^3}{kg * s^2} * \frac{1,000,000cm^3}{1m^3} $$

$$ = 6.674 * 10^{-11} \frac{m^3}{kg * s^2} * \frac{10^6cm^3}{1m^3} $$

$$ = 6.674 * 10^{-11} \frac{m^3 * 10^6cm^3}{kg * s^2 * 1m^3} $$

$$ = 10^6 * 6.674 * 10^{-11} \frac{cm^3}{kg * s^2} $$

$$ = 6.674 * 10^{-5} \frac{cm^3}{kg * s^2} $$