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Law of Gravitation

Part of the Mechanics section of Coddy's Physics journey. Lesson 87 of 97.

Every two masses pull on each other, along the line joining their centres:

F=G m1m2r2F = G\,\frac{m_1 m_2}{r^2}

rr runs centre to centre, and G=6.67×10−11 N⋅m2/kg2G = 6.67 \times 10^{-11}\ \mathrm{N \cdot m^2/kg^2}. Both bodies feel the same size of force, toward each other.

Two round bodies m1 and m2 pulling on each other with equal forces F along the line between them, with the distance r measured between their centres

Equal pulls toward each other; r runs centre to centre.

The force falls with the square of the distance: twice as far gives 1/22=1/4\relax 1/2^2 = 1/4 of the force, three times as far 1/32=1/9\relax 1/3^2 = 1/9. Doubling one of the masses doubles the force.

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Challenge

Two asteroids far out in space attract each other with 40 N40\ \mathrm{N}. One of them grows to three times its mass, and the distance between their centres doubles. Draw the force on the bigger asteroid after the change, then find the new force FF.

Try it yourself

Physics diagram: planet, vec; arrows 40 N, 40 N

Solve for FF

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