Probability

[DrD]

Go figure:

Suppose an 8.5 ton Chinese space station went out of control, and re-entered the Earth's atmosphere. If the predicted debris impact zone could be anywhere within the boundaries of 43° North latitude, and 43° South latitude, and given this event occur's some time next year, with other orbital parameters not known at this time, what are the chances, any particular spot, within the boundary, will be hit with debris remnants?

Not being wise in the ways of this field of study, does this problem even have a feasible solution? Zoner's, keep your hard-hat ready!

https://www.thesun.co.uk/tech/4676492/ch...ist-warns/

[AlexFekken]

Back-of-the-envelope/gut-based calculation says: extremely small...

EDIT: this is taking into account the "law of conservation of debris", i.e. there is only so much debris that won't be burned up and hits earth.

[Didier Lachieze]

Here is a quick program to calculate, based on your estimated number of debris reaching earth, the probability to be hit by a debris on a 1m² area:

Code:

EXPORT Tiangong1(N)   //N: estimated numbers of debris reaching earth
BEGIN
LOCAL h,p,R,S;
R:=6371000;                 //Earth radius (m)
h:=2*SIN(43°00′00″)*R;      //Distance between 43° north and 43° south plans
S:=2*π*R*h;                 //Earth surface area where a debris can fall
p:=N*1/S;                   //Probability to be hit by a debris on any 1m² area within the boundaries
END;

EDIT: I initially wrongly multiplied p by 0.3 (70% of Earth being oceans) but the % of oceans doesn't change the probability of a given square meter area to be hit by a debris.

[DrD]

Didier,

I am always amazed at your knowledge, skills, and abilities. You have combined all three, to make this challenge simple and understandable! Thanks for taking the time to demonstrate a serious, but also entertaining use of the hp prime technology.

This forum has a lot of content concerning bug issues, or limitations, but I find it very interesting when the finer points of using the product for real world problem solving get some show time!

Very nice work!

-Dale-