Answer:
diameter = 21.81 ft
Explanation:
The gravitational force equation is:
Where:
- F => Gravitational force or force of attraction between two masses
- M => Mass of asteroid 1
- m => Mass of asteroid 2
- R => Distance between asteroids 1 and 2 (from center of gravity)
We also know that the asteroids are identical so their masses are identical:
- M=m
Since R is the distance between centers of the two asteroids and their diameters are identical (see attachment), we can conclude that:
- R=d=2r
We don´t know the mass of the asteroids but we know they are composed of pure iron, so we can relate their masses to their density:
- m=ρV
This is going to be helpful because the volume of a sphere is:
And know we can write our original force of gravity equation in terms of the radius of the asteroids:
Now let´s plug in the values we know:
mutual gravitational attraction force
gravitational constant
Solve for r and multiply by 2 because 2r = diameter
Result is d = 21.81 Feet
