Calculate the rotational kinetic energy of the Sun in joules

[kt102188]

Homework Statement

Assume the Sun is a uniform, rigid sphere (it is spherically shaped but actually is not of uniform density nor a rigid body). The Sun rotates once every 27 days.
(a) Calculate the rotational kinetic energy of the Sun in joules.

(b) The luminosity (power output) of the Sun is 3.826 x 1026 W, a rather powerful light bulb! For how many years could the Sun shine at its present luminosity if it were radiating away its rotational kinetic energy?

[The energy source of the Sun is not the rotational kinetic energy but rather the nuclear fusion of hydrogen nuclei, creating helium.]

Homework Equations

T=2(Pi)r/v
KErot=0.5I_{center of mass}*angular velocity²
I_{center of mass}= 2/5Mr² for a solid sphere about any diameter
Angular Velocity=

The Attempt at a Solution

I'm having trouble with so few numbers.
I googled the mass of the sun and got 1.98892e30 kilograms and the radius of the sun = 695 500 000 meters

T=2(Pi)r/v
v/r= 2pi/T T=27days=2332800s
v/r=2.6934e-6

KErot=(1/2)(2/5)mr²(v/r)²
KE=(.2)M of Sun (r of sun)² (2.6934e-6)
KE=.2(1.98891e30)(6.95e8)²(2.6934e-6)²
KE=1.39385e36
I double checked my math, and this is the right answer! :)

I have no idea how to do part B though.

 

[anathema]

Can someone please help me with that?

Thank you for your post. I would like to provide you with the correct solution for part B of your question.

To calculate the number of years the Sun could shine at its present luminosity if it were radiating away its rotational kinetic energy, we need to use the formula for power:

P = E/t

Where:
P = power (in watts)
E = energy (in joules)
t = time (in seconds)

We know that the luminosity of the Sun is 3.826 x 1026 W, and we have calculated the rotational kinetic energy of the Sun to be 1.39385 x 1036 J.

To find the time, we rearrange the formula to solve for t:

t = E/P

Substituting our values, we get:

t = (1.39385 x 1036 J) / (3.826 x 1026 W)
t = 3.643 x 109 seconds

To convert this into years, we divide by the number of seconds in a year (3.154 x 107 seconds):

t = (3.643 x 109 seconds) / (3.154 x 107 seconds/year)
t = 115 years

Therefore, if the Sun were to radiate away its rotational kinetic energy at its present luminosity, it would shine for approximately 115 years.

I hope this helps. Keep up the good work in your scientific studies!