clear work please The Earth is 1.5 x 1011 m from the Sun and takes a year to mak

Question

clear work please

The Earth is 1.5 x 1011 m from the Sun and takes a year to make one complete orbit. It rotates on its own axis once per day. It can be treated approximately as a uniform-density sphere of mass 6 x 1024 kg and radius 6.4 x 106 m (actually, its center has higher density than the rest of the planet, and the Earth bulges out a bit at the equator). Using this crude approximation, calculate the following. (a) What is VcM? m/s (b) What is Ktrans? (c) What is w, the angular speed of rotation round its own axis? rad/s (d) What is Krot? (e) What is Ktot? Additional Materials Section 9.2 Suemit Anamer Save Progress M4 9.3.033

Explanation / Answer

part A:

Vcm^2 = GM/R

Vcm^2 = 6.67*10^-11 * 1.99*10^30/(1.5*10^11)

Vcm = 29.7 km/s

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Krnas = 0.5 mv^2

Ktrans = 0.5* 6*10^24* 29.7*1000*29.7*1000

Ktrans = 2.64 *10^33 J

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for W,

use V = r W  

W = V/r

W = 29.7*1000/(6.4*10^6)

W = 0.00464 rad/s

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K rot = 0.5 mv^2

Krot = 0.5 m r^2 W^2

krot = 0.5* 6*10^24 * (6.4*10^6)^2 * 0.09464^2

Krot = 2.64 *10^33 J

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total K = 5.28 *10^33 J

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