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Orbit related equations

  • #1

Homework Statement


I'm just trying to rearrange a few equations for gravity, period, radius etc., and am a tad confused.

Homework Equations


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

Want to rearrange for T and R. :)

The Attempt at a Solution


I got T to a point of...

T^2 = (4*pi^2*R)*(R^2)/GM
I think that's right, but I'm sure it can be further simplified.


Any halp? :)
 

Answers and Replies

  • #2
rock.freak667
Homework Helper
6,230
31
[tex]\frac{GM}{R^2} = \frac{4 \pi^2 R}{T^2}[/tex]


[tex]\frac{GM}{R^3} = \frac{4 \pi^2}{T^2}[/tex]


now re-arrange again.
 
  • #3
Thanks! Just what I needed! Can't believe I forgot it actually, silly me.

ANYWAY, therefore...

[tex]
{T^2} = {4 \pi^2} \frac{R^3}{GM}
[/tex]

Yes??

and...

[tex]
{R^3} = {GM} \frac{4 \pi^2}{T^2}
[/tex]

and...

[tex]
{M} = \frac{4 \pi^2 R^3}{G T^2}
[/tex]

Just wondering if I could get these verified...
 
  • #4
The second equation is wrong...rest is fine!
 
  • #5
dynamicsolo
Homework Helper
1,648
4
When in doubt, check the units. The gravitational constant G has the units N·(m^2)/(kg^2) = (m^3)/[kg·(sec^2)].

So the second equation couldn't be right, since the kg and the (sec^2) in the denominator of G have to be canceled out somehow in order to leave the (m^3) for R^3 on the left-hand side. The correct form must have the combination GM(T^2)...
 
  • #6
So it'd be ..

R^3 = GMT^2? on 4pi^2

Oh, and I just rearranged the lorentz factor to subject v^2

v^2 = c^2(1-(1/lorentz)^2)

How's that?

Thanks guys
 
Last edited:
  • #7
Kurdt
Staff Emeritus
Science Advisor
Gold Member
4,812
6
Both look fine.
 

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