Rotational Kinetic Energy Question (Regarding the Earth)

[zmoose27]

Homework Statement

What is the Kinetic Energy of the Earth Orbiting Around the Sun in Joules?

Homework Equations

E rotation = (1/2)* I * w^2

where I = moment of Inertia
where w = angular velocity

The Attempt at a Solution

Well, this is my predicament: I don't know whether my professor wants me to use the above equation or not, but I don't know any other way to solve it. My answer is comes out to somewhere around 10^29, while his is around 10^33. So obviously something must be wrong...

My solution:
Earth's period = 23.93 hours
Therefore, its angular velocity is 7.29×10^ -5 rad·s-1.
Assuming that the Earth is perfectly spherical and uniform in mass density, it has a moment of inertia, I = 9.72×10^37 kg·m2.
Therefore, it has a rotational kinetic energy of 2.58×10^29 J.

Is this right? Or am I missing something completely?

Thanks a lot.

 

[Doc Al]

You found the rotational KE of the Earth revolving on its axis. But you were asked to find:

What is the Kinetic Energy of the Earth Orbiting Around the Sun in Joules?

 

[calef]

And if you think about it, it makes sense that the Earth's translational kinetic energy is several orders of magnitude greater than its rotational. In fact, if you were only solving the net kinetic energy of the Earth to a couple decimal places, you could neglect the rotational kinetic energy entirely.