Answer:
mass of the other asteroid = [tex]4.49*10^9kg\\[/tex]
Explanation:
We use the definition for the force between two celestial objects under the action of the gravity they produce using newton's general gravitational constant: [tex]G=6.674*10^{-11} \frac{N*m^2}{kg^2}[/tex]
The force between the two asteroids will then be given by:
[tex]F_G=G*\frac{M_1*M_2}{d^2}[/tex]
where G is Newton's gravitational constant, the asterioid's masses are M1 and M2 respectively, and d is the distance between them.
We replace the known values in he equation above, and solve for the missing mass:
[tex]F_G=G*\frac{M_1*M_2}{d^2}\\1.05*10^{-4}N=6.674*10^{-11} \frac{N*m^2}{kg^2} \frac{3.5*10^6kg*M_2}{(10^5m)^2} \\1.05*10^{-4}=2.3359*10^{-14} * M_2\\M_2=\frac{1.05*10^{-4}}{2.3359*10^{-14}} =4.49*10^9kg[/tex]
Since the units for the given quantities are all in the SI system, our resultant units for the unknown mass of the asteroid will be in kg.
