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Originally Posted by David Hall
And all that is assuming that the star is even heading our way, which when you think about all the possible directions it could be travelling in, is very, very, very unlikely.
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To which my evil mind asks how unlikely.
Assuming that the speed of light is 5,865,696 x 10 ^6 miles, the object is 45,752,428.8 x 10^6 miles away.
The distance from the sun to Pluto is 369,595 x 10^4 miles.
If we visualize this as a pythagorean triangle with the distance from the sun to Pluto as the opposite and the distance from the sun to the object as the adjacent, tanA = opposite/adjacent where tan A is the angle subtended by the object. Crunching the maths (and assuming my TI calculator works) gives us angle A is 1.4 x 10^-10 degrees. However, thats using a radius for the diameter of the solar system. To calculate the angle subtended for the object to pass within the solar system, we have to double that answer giving us 2.8 x 10^-10 degrees.
Assuming the object is heading in the right plane, the chance of it heading in that angle out of the 360 degrees possible is 360/2.8 x 10^-10 or 1.285 x 10^12.
In other words there is 1 chance in 1,285,000,000,000 that the object is heading on a course that would bring it within the orbit of Pluto - assuminga two-dimensional universe.
However, space being three dimensional, we have to allow for the vertical as well as the horizontal plane so the actual probability is 1 chance in 1,651,225,000,000,000,000,000,000.
All of which is meaningless of course because it doesn't matter how improbable it is since if it is on a collision course, it just means we were incredibly unlucky.