Im very confused About these two equations?
Ok, I've been very confused for the last few days. my question: look at the two equations below.
1) P^2= 4pi^2 x r^3/G(M1+M2)
2) M1+M2=A^3/P^2
Ok, I have a few questions about these equations.
1) aren't these equations the same? They both look for the same thing, the orbital period( or if you rearrange the equation they can also both be looking for mas or distance), but either way they look for the same answers and they use the same factors too, semi-major axis cubed, mass of the 2 objects. The only difference is the G and the 4pi^2. So when I do the same problem using both equations, I should get the same answer, but I don't, why am I getting different answers when the equations are the same. What am I doing wrong? Or am I wrong and are these equations actually different and used for different situations? please explain?
2) When you need to find the orbital period you just do a^(3/2) right? So how come they have more complex equations like that when you can just find the orbital period or semi-major axis the short way?
3) and if these equations are used for different situations, which is for which? and if they aren't used for different situation's then does it matter what equation I use if im looking for mass, distance, or orbital period of a planet or a star?
I know these are a lot of questions, but I want to make everything clear and straightened out, because im very confused, so can You please try and answer the question and explain thoroughly
Thank You!