Rearranging Equations for Centripetal Force and Mass of Orbiting Objects

[Sharr-zeor]

i fail miserably at rearranging equations. how would i rearrange GM/r^2 = v^2/r to make M the subject?
this is to do with centripetal force, and the mass of a planet a space probe is orbiting
after working out the answer to v^2/r (which is 1.35ms^-2) I am left with GM/r^2 = 1.35ms^-2 i wasnt sure if it would be M = 1.35G/r^2...

as i said, i am terrible at rearrangements. any help would be appreciated

 

[berkeman]

i fail miserably at rearranging equations. how would i rearrange GM/r^2 = v^2/r to make M the subject?



this is to do with centripetal force, and the mass of a planet a space probe is orbiting



after working out the answer to v^2/r (which is 1.35ms^-2) I am left with GM/r^2 = 1.35ms^-2 i wasnt sure if it would be M = 1.35G/r^2...

as i said, i am terrible at rearrangements. any help would be appreciated

Well, per the PF rules (see the link at the top of the page), we can't just give you the answer.

So, what steps do you normally use to re-arrange equations? If you multiply both sides by the same thing, does the equality still hold? Divide both sides by the same thing? Multiply one side by 1? (using something like 1=x/x)

 

[Sharr-zeor]

Well, per the PF rules (see the link at the top of the page), we can't just give you the answer.

well i only need the equation to work out the answer to my coursework question. I've taken the steps to find the necessary equation, i just can't rearrange it.

i didntunderstand the second part of your reply.
i don't know if I am multiplying or dividing anything

oooh, if i multiply 1.35 by r^2 i get GM?
therefore 1.35r^2/G = M ?

if this is right I am going to kick myself for not thinking aboutthe multiplication/division. i always forget the simple bits...

 

[berkeman]

well i only need the equation to work out the answer to my coursework question. I've taken the steps to find the necessary equation, i just can't rearrange it.

i didntunderstand the second part of your reply.
i don't know if I am multiplying or dividing anything

oooh, if i multiply 1.35 by r^2 i get GM?
therefore 1.35r^2/G = M ?

if this is right I am going to kick myself for not thinking aboutthe multiplication/division. i always forget the simple bits...

It's hard for me to check your work -- where did the 1.35 come from? It would be easier for us to check your work if you just left the equation symbollic until the end.

So if you start with GM/r^2 = v^2/r

and leave it symbollic, what do you get for M = ?

 

[Sharr-zeor]

leaving it symbolic i get (v^2 / r) r^2 / G = M ?

would that work out as v^2 r / G = M

v [squared] r [divided by] G [equals] M

 

[berkeman]

leaving it symbolic i get (v^2 / r) r^2 / G = M ?

would that work out as v^2 r / G = M

v [squared] r [divided by] G [equals] M

Good job!

 

[Sharr-zeor]

so v^2 r / G = M?

it seems so simple now >.<

thanks for the help, i guess i need to just go through it step by step instead of rushing to an answer :)