Question

Two asteroids are 100,000 m apart. One has a mass of 3.5 x 106 kg. If the

force of gravity between them is 1.05 x 10-4 N, what is the mass of the other
asteroid?

Answer 1

4.5*10^9

Step-by-step explanation:

Answer 2

mass of the other asteroid =
`4.49*10^9kg\\`

Step-by-step 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:
`G=6.674*10^(-11) (N*m^2)/(kg^2)`

The force between the two asteroids will then be given by:

`F_G=G*(M_1*M_2)/(d^2)`

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:

`F_G=G*(M_1*M_2)/(d^2)\\1.05*10^(-4)N=6.674*10^(-11) (N*m^2)/(kg^2) (3.5*10^6kg*M_2)/((10^5m)^2) \\1.05*10^(-4)=2.3359*10^(-14) * M_2\\M_2=(1.05*10^(-4))/(2.3359*10^(-14)) =4.49*10^9kg`

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.