Explanation:
how to solve for M ?
that means we have to transform the equation, so that we end up with
M = ...
or
... = M
remember, whatever we do to one side of the equation we have to do also to the other side, so that the balance of the original equation remains.
T² = 4×pi²×a³/(G×M)
first, we want to bring M up from the denominator side of the fraction, and maybe already to the less crowded side of the equation.
we do this by multiplying both sides by M :
M×T² = 4×pi²×a³/G
now, all that is in our way to get the expression in the above mentioned form is the T² factor on the left.
so, we simply divide both sides by T² :
M = (4×pi²×a³/G)/T² = 4×pi²×a³/(G×T²)