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