Semi-major axis equation question

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Homework Statement



Hi there, this isn't a homework question but I need some help with this equation since I'm not the best at mathematics. I would like to rearrange this equation so I can solve for "a"

Homework Equations



Equation P = 2π√(a³/(GM)), giving the orbital period P in terms of the semi-major axis a, gravitational constant G and mass M.


The Attempt at a Solution



?
 
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eXmag said:

Homework Statement



Hi there, this isn't a homework question but I need some help with this equation since I'm not the best at mathematics. I would like to rearrange this equation so I can solve for "a"

Homework Equations



Equation P = 2π√(a³/(GM)), giving the orbital period P in terms of semi-major axis a, gravitational constant G and mass M.


The Attempt at a Solution



?

Well, start by squaring both sides. That will get rid of the square root. How bad at mathematics are you?
 
eXmag said:
Im really bad at it!

Good to know. What happens if you try squaring both sides? Do your worst.
 
eXmag said:
so you're saying

Handwritten or typeset equation p^2 = 2π(a^3/GM)^2, where p is period, a is semi-major axis, G is gravitational constant and M is mass.

That's pretty bad. You forgot to square the ##2 \pi##. And if you square a square root then you eliminate the square root. ##(\sqrt{x})^2=x##. Try and fix it up a little.
 
eXmag said:
Ok then, another attempt.

Handwritten equation: P squared equals 2 pi squared times the fraction a cubed over GM.

Closer. Just write ##(2 \pi)^2## instead of ##2 \pi^2##. They mean different things don't they? I hope you know that much? The next step is to move everything except for ##a^3## to the left side of the equation. Know ANY algebra?
 
Well considering I haven't taken a math course since high school which was about 8 years ago so I'm a little rusty as you can tell. But it's starting to come back to me somewhat. So should this be the final solution then?

Equation a = cube root of GM(P^2/(2pi^2)), written as a = ∛(GM(P²/(2π²))).


edit it should be (2pi)squared like u said
 
eXmag said:
Well considering I haven't taken a math course since high school which was about 8 years ago so I'm a little rusty as you can tell. But it's starting to come back to me somewhat. So should this be the final solution then?

Equation a = cube root of GM(P^2/(2pi^2)), written as plain typeset mathematics.


edit it should be (2pi)squared like u said

Yes, that's right. Glad you got it if you write (2pi)^2. I didn't think you were going to make it for a while. Keep reviewing the algebra. It's not that hard and you need to know it.
 
eXmag said:
OK, thanks for you're help!

You're welcome. Um, it's 'your help' not 'you're help' if you want to do grammar too. :)