Saturn has a mass of 5.68 times 10^kg and a radius of 0.03 times 10^7 m. Assume

Question

Saturn has a mass of 5.68 times 10^kg and a radius of 0.03 times 10^7 m. Assume it is a uniform solid sphere. The distance of Saturn from the Sun is 1.43 times 10^12 m. (Assume Saturn completes a single rotation in 10.6 hours and orbits the Sun once every 1.08 times 10^4 Earth days.) What is the rotational kinetic energy of Saturn on its axis? What is the angular speed of Saturn as it rotates on its axis? Check your units for consistency. J What is the rotational kinetic energy of Saturn in its orbit around the Sun? J

Explanation / Answer

Here ,
a) for the moment of inertia of saturn

I = 0.4 * m * r^2

I = 0.4 * 5.68 *10^26 * (6.07 *10^7)^2

Now, for the kinetic energy

kinetic energy of saturn due to rotation on axis = 0.5 * I * w^2
kinetic energy of saturn due to rotation on axis = 0.5 * 0.4 * 5.68 *10^26 * (6.07 *10^7)^2 * (2pi/(10.6 * 3600))^2

solving

kinetic energy of saturn due to rotation on axis = 1.135 *10^34 J

part b)

Now, for the rotation around sun

kinetic energy = 0.5 * I * w^2

kinetic energy = 0.5 * m * r^2 * w^2

kinetic energy = 0.5 * 5.68 *10^26 * (1.43 *10^12)^2 * (2pi/(1.08 *10^4 * 24 * 3600))^2

kinetic energy = 2.633 *10^24 J

the kinetic energy of the saturn due to rotation around sun is 2.633 *10^24 J

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