Answer:
The mass of the other asteroid is [tex]m_2=6.49\times 10^9\ kg[/tex].
Explanation:
Given that,
Mass of one asteroid, [tex]m=5\times 10^8\ kg[/tex]
The separation between two asteroids, r = 50,000 m
The force of gravity between asteroids, [tex]F=8.67\times 10^{-2}\ N[/tex]
We need to find the mass of the other asteroid. The gravitational force acting between two masses is given by :
[tex]F=G\dfrac{m_1m_2}{r^2}[/tex]
[tex]m_2[/tex] is the mass of other asteroid
[tex]m_2=\dfrac{Fr^2}{Gm_1}[/tex]
[tex]m_2=\dfrac{8.67\times 10^{-2}\times (50000)^2}{6.67\times 10^{-11}\times 5\times 10^8}[/tex]
[tex]m_2=6.49\times 10^9\ kg[/tex]
So, the mass of the other asteroid is [tex]m_2=6.49\times 10^9\ kg[/tex]. Hence, this is the required solution.
