physics (1 Viewer)

maths lover · Jul 12, 2011

i have a physics portfolio to do

, and one of the questions asks you to derive Kepler's third law of periods. i cant seem to find any resources that give a derivation that i can understand even slightly. any help would be greatly appreciated.
r^3/T^2=GM/4pi^2

SpiralFlex · Jul 12, 2011

Centripetal force is provided by gravitational attraction force.

Let this be $Fc$ and $Fg$ respectively.

We can say that these are equal,

$Fc= Fg$

$Fc = \frac{mv^2}{r}$

Law of universal gravitational attraction,

$F= G \frac{m1m2}{d^2}$

Our $M$ is our centre mass and we will use $r$ for radius.

So our new equation is,

$Fg= G \frac{mM}{r^2}$

Now,

$\frac{mv^2}{r} = G \frac{mM}{r^2}$

$v^2 = \frac{GM}{r}$

$v = \sqrt{\frac{GM}{r}}$

Our tangential velocity is given by,

$v = \frac{2 \pi r}{T}$

Substituting this into our $v^2 = \frac{GM}{r}$

$(\frac{2 \pi r}{T})^2=\frac{GM}{r}$

$\frac{4 \pi^2 r^2}{T^2}=\frac{GM}{r}$

$\frac{r^3}{T^2} = \frac{GM}{4 \pi ^2}$

We can say that $\frac{GM}{4 \pi ^2}$ is a constant. Don't you agree?

[Note: Someone should check my algebra since it's after 9 pm which is the time Spiral makes mistakes.]

SpreadTheWord · Jul 12, 2011

maths lover said:
i have a physics portfolio to do, and one of the questions asks you to derive Kepler's third law of periods. i cant seem to find any resources that give a derivation that i can understand even slightly. any help would be greatly appreciated.
r^3/T^2=GM/4pi^2

http://www.physicsclassroom.com/Class/circles/u6l4a.cfm

Hope this helps man.

s2 SEductive · Jul 12, 2011

Ye perfect Spiralflex

SpiralFlex · Jul 12, 2011

s2 SEductive said:
Ye perfect Spiralflex

Human.

maths lover · Jul 13, 2011

thank you so much spiralflex and spreadtheword. spiralflex you sure seem to know all your derivations.
edit:it wont let me rep you. sorry!

maths lover · Jul 13, 2011

spiralflex how did you get from here to there.
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Alkanes · Jul 13, 2011

[tex.] [/tex.] without the '.'

SpiralFlex · Jul 13, 2011

Sorry, I was having a house inspection.

I interchanged the distance with " $r$ " and the m2 with our centre mass of " $M$ ".

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