Two identical spherical objects are placed with their centers 2*10^4 m apart. The gravitational force between the two objects is 2.668*10^22 N. Calculate their mass.
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The gravitational force of attraction between two objects at a distance r from each other and with mass m1 and m2 is equal to `F = (G*m1*m2)/r^2` where G is a constant equal to `6.673*10^-11` N/(kg^2*m^2)
The two objects with equal mass m are `2*10^4` m apart and the force of attraction between them is equal to `2.668*10^22` N.
`2.668*10^22 = (m^2*6.673*10^-11 )/(2*10^4)^2`
=> m = `sqrt((2.668*10^22*(2*10^4)^2)/(6.673*10^-11))`
=> m = `3.9*10^20` kg
Each of the objects has to have a mass of approximately 3.9*10^20 kg for the gravitational force between them to be what it is.
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