Rotational Period of Large Body

[GypsySmash]

Homework Statement

The Sun rotates on its axis every 25 days. The sun currently has a radius of 7X10^8 m. When it expands into a Red Giant (in about 4 billion years) it will have a radius of 1.5X10^11 m. What will its rotational period be assuming the same mass for both, and they are both uniformly distributed spherical masses? (Note that these are not realistic assumptions)

Homework Equations

T = square root of (4 x pi^2 x r^3/ G x m)

G = 6.673x10^-11

The Attempt at a Solution

T = 3.167x10^7 sec, 366.59 yrs

Am I even answering the question asked?[/B]

 

[gneill]

The Sun is not in orbit about itself. So the period of an orbiting body about the Sun is not going to help here.

However, the Sun is rotating. What's conserved?

 

[GypsySmash]

ok, here's another shot.

If (2/5xmxr^2)(2pi/t) = (2/5xmxr^2)(2pi/t) I can just solve for the Tfinal.

I can cancel some stuff out and get R^2/T = R^2/T and cross multiply.

(1.5x10^11)^2 x 25 days = 5.625x10^23

5.625x10^23 / (7x10^8)^2 = 1147959.18 daysHow am I looking there?

 

[gneill]

Looking good!

 

[GypsySmash]

Would someone double check that for me?

 

[TSny]

It looks correct to me.

 

[gneill]

Despite your using the same variable names for both the initial and final radii and periods during your algebra working, you arrived at a correct result.

It would have been more clear if you had done all the work symbolically until the last step where you could plug in the numbers.