# Rotational Period of Large Body

1. Mar 11, 2015

### GypsySmash

1. The problem statement, all variables and given/known data
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)

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

G = 6.673x10^-11

3. The attempt at a solution

T = 3.167x10^7 sec, 366.59 yrs

2. Mar 11, 2015

### Staff: Mentor

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?

3. Mar 11, 2015

### 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 days

How am I looking there?

4. Mar 11, 2015

### Staff: Mentor

Looking good!

5. Mar 13, 2015

### GypsySmash

Would someone double check that for me?

6. Mar 13, 2015

### TSny

It looks correct to me.

7. Mar 13, 2015

### Staff: Mentor

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.