# Rearranging an equation

well i have my equation T^2/R^3 = 4pi^2/GM

and i want to find 'M' on its own, (i never have been good at this) but here is my attempt:

M = 4pi^2/G(T^2/R^3)

is this correct?

Filip Larsen
Gold Member
No (not as I read your notation). Note that when you "move" something like a/b to the other side of an equation it becomes b/a.

It may help to transform your equation only one step at a time. If you are in doubt about the transformation rules, then remember that you are transforming the two sides by doing the same thing on both sides, i.e. to "move" the term $a$ in $a+b$ you actually add $-a$ to both sides so that the original side becomes $a-a+b = 0+b = b$; to "move" the factor $a$ in $a \cdot b$ you actually multiply with $1/a$ on both sides that on the original side becomes $(a/a) \cdot b = 1 \cdot b = b$.

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after having a look at it for a while, i tried one step at a time and i came out with:

M = (4*pi^2)(T^2/R^3)/G

is this any better? please dont take offence if i didnt understand your post.

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Filip Larsen
Gold Member
This is the same result you got the first time, so its still not correct.

The problem is with $T^2/R^3$. Originally that factor is on one side of the equation and must at some transformation step be moved to the other side. You seem to move it verbatim to the other side so it ends up being the same $T^2/R^3$ which is not correct.

Note that the factor is in the form of a fraction (i.e. a/b) and you should carefully consider what happens when you move such a fractional factor to the other side of an equation. If you have a text book you may want to look up reciprocal.

so you're saying that i need to turn the expression into R^3/T^2?

then would the equation be:

M = (4pi^2)(R^3/T^2) / G ?

am i any closer?

You were initially correct in your first post, just remember to bring R^3 to the numerator to simplify things.

Filip Larsen
Gold Member
so you're saying that i need to turn the expression into R^3/T^2?

then would the equation be:

M = (4pi^2)(R^3/T^2) / G ?

am i any closer?

Now it looks right, yes.

ok thank you very much :)
i have a fair bit of trouble with rearrangements,

so thanks for the help! =)