Question

Two asteroids are 100,000 m apart. One has a mass of 3.5 106 kg. If the force of gravity between them is 1.05 10-4 N, what is the mass of the other asteroid?

Answer 1

`4.5\cdot 10^9 kg`

Step-by-step explanation:

The gravitational force between the two asteroids is given by:

`F=G(m_1 m_2)/(r^2)`

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:

`G=6.67 \cdot 10^(-11) m^3 kg^(-1) s^(-2)`

`m_1 = 3.5 \cdot 10^6 kg`

`F=1.05 \cdot 10^(-4) N`

`r=100,000 m=10^5 m`

So, we can re-arrange the equation to find the mass of the second asteroid:

`m_2 = (Fr^2)/(Gm_1)=((1.05 \cdot 10^(-4))(10^5)^2)/((6.67\cdot 10^(-11))(3.5\cdot 10^6))=4.5\cdot 10^9 kg`