Estimate how many stars are likely to hit when two Milky Way

Estimate how many stars are likely to hit when two Milky Way - like galaxies collide. Assume each galaxy has 200 billion stars (2 * 10^11) and that all stars have the same diameter as the sun. The Probability of a particular star of one galaxy hitting any star of the other is proportional to area covered by stars divided by the total area of the galaxy. The area covered by stars is the area of one star times the numbers of stars. The probable numbers of hits is the product of the probability for one hit multiplies by the number of potential hitters.

Solution

Total number of stars = 2*2*10^11 = 4*10^11

Each hit requires 2 stars, therefore number of potential hitters = 2*10^11

Probability of hitting = Area covered by stars/Area of the galaxy

= (2*10^11*(Area of one star))/Area of the galaxy

In this case,

=(2*10^11)*(Area of sun)/Area of the milky way galaxy

=(2*10^11)*pi*(1392000)^2/4*Area of milky way

Assuming the milky way galaxy to be circular, its area = (pi/4)*(1,000,000,000,000,000,000)^2/

Therefore,

required probability = 3.875*10^-13

Therefore, number of stars hitting = 3.875*10^-13*2*10^11 = 0.077~0

Therefore, probabile number of hits = 0