Estimate the kinetic energy of the Earth with respect to the Sun as the sum of t

Question

Estimate the kinetic energy of the Earth with respect to the Sun as the sum of two terms, that due to its daily rotation about its axis [Assume the Earth is a uniform sphere with mass = 6.0 times 10^24 kg, radius = 6.4 times 10^6 m, and is 1.5 times 10^8 km from the Sun.] Express your answer to two significant figures and include the appropriate units. KE_daily = that due to its yearly revolution about the Sun Express your answer to two significant figures and include the appropriate units. KE_yearly =

Explanation / Answer

(a) kinetic energy of the earth due to its daily rotation about the axis:
KE(daily)=1/2* I* w^2
I is moment of inertia
w is angular velocity
I for a solid sphere =2/5*m*r^2
=.4*6*10^24*(6.4*10^6)^2=9.8304*10^37 kgm^2
w =2*pi/(24*60*60)=7.27 *10^-5 radian/second
KE(daily)=2.6 *10^29 Joule

(b)kinetic energy of the earth due to its yearly revolution about the sun
KE(yearly)=1/2*m*v^2
v=2*pi*r/t
=2*pi*1.5 x 10^11/(3600*24*365.25)
=29865.31916 m/sec
KE(yearly)=.5*6.0 x 10^24 *29865.31916 ^2
KE(yearly)=2.8 *10^33 Joule

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