You can calculate various astronomical things yourself:
The formulas that I give on the mentioned pages are mathematical
formulas. To be able to use them in computer programs you need to
take into account how those computer languages and compilers work.
For example, if you copy the formula
s a whole number) without changes into a program
that can handle whole numbers only, then the result can depend on the
order in which the calculations are done, because in such a program
the intermediate results can only be whole numbers, too, and any
fractional parts are discarded. If intermediate results are too
large, then parts of them can be discarded as well, and then the
results won't fit the mathematical results, either.
s = 400. Then the mathematical result is
4000*400⁄1461001 = 1600000⁄1461001 = 1 +
138999⁄1461001. If this is calculated in a program that can
handle whole numbers only, and if the multiplication is performed
first, then the intermediate result is
4000*s = 1600000
and the second calculation
1600000⁄1461001 then yields
the end result 1, because the fractional part of the result is
discarded. If the division is done first, then the first calculation
s/1461001 = 400⁄1461001 which yields 0, because the
remainder of the division is discarded. The second calculation is then
0*4000 = 0 so the end result is 0. The end result
depends on the order in which the calculations are done.
Many astronomical formulas involve angles. If you turn around once and end up facing in the same direction, then you've swung through an angle of 360 degrees. So, two directions that differ by a multiple of 360 degrees are equivalent, and you can always reduce any angle to an equivalent angle that is between 0 and 360 degrees, by subtracting a suitable multiple of 360 degrees. For example, an angle of 19462.44 degrees can be reduced to the equivalent angle of 22.44 degrees. The difference between the two is 19440 degrees, which is exactly 54 times 360 degrees.
One way to do that is as follows:
In a computer program, you'd use the "modulus" function or operator,
19462.44 % 360 or
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Last updated: 2016-02-07