Question

# Two identical spherical asteroids (mass 3.07x1018 kg, radius 5.5x103 m) are initially at rest, with their...

Two identical spherical asteroids (mass 3.07x1018 kg, radius 5.5x103 m) are initially at rest, with their centers 6.01x105 m apart. Ignore all other objects in the universe, and friction. The two asteroids accelerate toward each other, due to gravity, until they finally crash together. At what speed, in m/s, will each asteroid be moving when they collide (just touch on their outer edge)?

NOTE: when the asteroids collide, the distance between the centers of the asteroids is not zero!

let
m = 3.07*10^18 kg
r = 5.5*10^3 m

initial distance between the asteroids, d1 = 6.01*10^5 m
final distance between the asteroids, d2 = 2*r

= 2*5.5*10^3

= 1.10*10^4 m

let v is the speed of asteroids when they collide.

Apply conservation of energy

KEf + PEf = KEi + PEi

2*(1/2)*m*v^2 - G*m^2/d2 = 0 - G*m^2/d1

m*v^2 = G*m^2*(1/d2 - 1/d1)

v^2 = G*m*(1/d2 - 1/d1)

v = sqrt(G*m*(1/d2 - 1/d1) )

= sqrt(6.67*10^-11*3.07*10^18*(1/(1.1*10^4) - 1/(6.01*10^5))

#### Earn Coins

Coins can be redeemed for fabulous gifts.