Two identical spheres (of equal mass) a distance of 10 meters apart exert a force of gravity of 0.00050 N on each other. What are their masses?

The gravitational force between two objects is written as:

F = G*m1*m2/r^2

Where:

G = 6.67*10^(-11) m^3/kg*s

m1 and m2 are the masses of the objects.

r is the distance between the objects.

In this case, we know that:

F = 0.0005 N

r = 10m

and because the two spheres are identical, we have that:

m1 = m2 = M

then we have the equation:

0.0005 N = (6.67*10^(-11) m^3/kg*s)*(M^2/(10m)^2)

0.0005 N*(10m)^2/(6.67*10^(-11) m^3/kg*s) = M^2

√( 0.0005 N*(10m)^2/(6.67*10^(-11) m^3/kg*s) ) = M = 27,379.3 kg

The mass of each sphere is 27,379.3 kg

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