Astronomy and Planetary Motion (Menu Individual Procedures \ Chinese Remainder Theorem Applications)

The dialog Astronomy and planetary Motion  is an interactive visualization of the Chinese Remainder Theorem for an example of use in astronomy: Are the orbital periods and the current position known, when do all or a some of the planets come into perfect alignment?

One can model such questions as a system of simultaneous congruences, which can be solved using the Chinese Remainder Theorem. In this implementation, you can enter up to 9 equations x ai mod mi (i = 1,...,9) and a solution, (x), will be computed.

Suppose mi (i = 1,...,9) are pairwise relatively prime (coprime) positive integers and larger than 1, then the system of simultaneous congruences has a unique solution x.

One can use such equation systems to determine the number of days until certain planets become aligned.

One can also use such equation systems to build a code which allows any 3 of 5 key-holders to open a bank vault (Secret Sharing by CRT).