What is Gravitational field strength? — Physics

Definition 4.11 High School Physics · Chapter 4 — Universal Gravitation and Weight

The quantity $g = G M / R^2$ , in newtons per kilogram, is the gravitational field strength at the star’s surface: the star pulls on each kilogram with $g$ newtons. On Earth, $g = 9.81\,\mathrm{N}/\mathrm{kg}$ .

Surface gravitational field strength on four worlds: the same 1\, kg bag of sugar weighs 1.6\, N on the Moon and 25\, N on Jupiter. — Surface gravitational field strength on four worlds: the same $1\,\mathrm{kg}$ bag of sugar weighs $1.6\,\mathrm{N}$ on the Moon and $25\,\mathrm{N}$ on Jupiter.

“Down” is a local notion: at every point of the globe the weight vector points toward the center O. Two antipodean walkers both stand upright — feet toward each other. — “Down” is a local notion: at every point of the globe the weight vector points toward the center $O$ . Two antipodean walkers both stand upright — feet toward each other.

Examples

Example 4.12 (Computing $g$ )

For the Earth ( $M = 5.97 \times 10^{24}\,\mathrm{kg}$ , $R = 6.37 \times 10^{6}\,\mathrm{m}$ ):

g = \frac{6.67 \times 10^{-11} \times 5.97 \times 10^{24}}{(6.37 \times 10^{6})^2} = \frac{3.98 \times 10^{14}}{4.06 \times 10^{13}} \approx 9.81\,\mathrm{N}/\mathrm{kg}.

For the Moon ( $M = 7.35 \times 10^{22}\,\mathrm{kg}$ , $R = 1.74 \times 10^{6}\,\mathrm{m}$ ) the same computation gives $g_{\text{Moon}} \approx 1.62\,\mathrm{N}/\mathrm{kg}$ — six times less: the Moon is far lighter, and being smaller does not make up for it. For Mars, $g_{\text{Mars}} \approx 3.73\,\mathrm{N}/\mathrm{kg}$ .

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