Newton's law of gravitation and field strength

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Every two masses attract each other with a force $F = G\dfrac{m_{1}m_{2}}{r^{2}}$ — proportional to each mass and to the inverse square of the distance r between their centres.

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The gravitational **force per unit mass** on a small mass placed in the field: $g = \dfrac{F}{m}$. Unit: **N kg⁻¹**.

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$g = G\dfrac{M}{r^{2}}$ — given in the data booklet. M is the source mass, r the distance from its centre.

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**N kg⁻¹** — numerically the same as the free-fall acceleration in m s⁻².

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Because F = mg and F = ma, so a = g. The falling mass cancels, so g is the acceleration — independent of the mass that falls.

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**Inward**, towards the mass — gravity is always **attractive**.

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g is divided by **3² = 9** (g is proportional to 1/r², the inverse-square law).

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**No** (ignoring air resistance) — the acceleration g = GM/r² doesn't depend on the falling mass, so all masses fall equally fast.

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The **gravitational constant**, G = 6.67 × 10⁻¹¹ N m² kg⁻² — the same everywhere in the universe.

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About **9.8 N kg⁻¹** (or 9.8 m s⁻²) — found from g = GM/r² using Earth's mass and radius.

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g is **inversely proportional to r²** (inverse-square): double r → quarter g; triple r → one-ninth g.