Given data:
* The mass of the first spherical object is,
[tex]m_1=3.1\times10^5\text{ kg}[/tex]* The mass of the second spherical object is,
[tex]m_2=6.5\times10^3\text{ kg}[/tex]* The force of attraction between the objects is,
[tex]F=65\text{ N}[/tex]Solution:
The gravitational force of attraction between the spherical object in terms of the distance between their centers is,
[tex]F=\frac{Gm_1m_2}{d^2}[/tex]where G is the gravitational constant and d is the distance between the centers of spherical objects,
Substituting the known values,
[tex]\begin{gathered} 65=\frac{6.67\times10^{-11}^{}\times3.1\times10^5\times6.5\times10^3}{d^2} \\ d^2=\frac{6.67\times10^{-11}\times3.1\times10^5\times6.5\times10^3}{65} \\ d^2=2.07\times10^{-11+5+3} \\ d^2=2.07\times10^{-3} \end{gathered}[/tex]Thus, the distance between the centers is,
[tex]\begin{gathered} d=\sqrt[]{2.07\times10^{-3}} \\ d=\sqrt[]{0.207\times10^{-2}} \\ d=0.455\times10^{-1} \\ d=0.0455\text{ m} \end{gathered}[/tex]Hence, the distance between the centers is 0.0455 meters or 4.6 centimeters.
