Answer:
[tex]4.5\cdot 10^9 kg[/tex]
Explanation:
The gravitational force between the two asteroids is given by:
[tex]F=G\frac{m_1 m_2}{r^2}[/tex]
where
G is the gravitational constant
m1 and m2 are the masses of the two asteroids
r is the distance between the two asteroids
In this problem, we have:
[tex]G=6.67 \cdot 10^{-11} m^3 kg^{-1} s^{-2}[/tex]
[tex]m_1 = 3.5 \cdot 10^6 kg[/tex]
[tex]F=1.05 \cdot 10^{-4} N[/tex]
[tex]r=100,000 m=10^5 m[/tex]
So, we can re-arrange the equation to find the mass of the second asteroid:
[tex]m_2 = \frac{Fr^2}{Gm_1}=\frac{(1.05 \cdot 10^{-4})(10^5)^2}{(6.67\cdot 10^{-11})(3.5\cdot 10^6)}=4.5\cdot 10^9 kg[/tex]
