Problem 7 Earth is approximately a solid sphere, has a mass of 5.98 × 1024 kg an

Question

Problem 7 Earth is approximately a solid sphere, has a mass of 5.98 × 1024 kg and a radius of 6.38 × 106 m, and completes one rotation about its central axis each day. 1) Calculate the translational kinetic energy of Earth as it orbits the Sun once each year (the Earth-Sun distance is 1.50 × 1011 m). (Express your answer to two significant figures.) J Submit 2) Calculate the ratio of the translational kinetic energy to the rotational kinetic energy. (Express your answer to two significant figures.) Submit

Explanation / Answer

a) earth orbital speed V = 2*10^30*6.67*10^-11/(1.50*10^11) = 29,822 m/sec
Ek = 1/2m*V^2 = 2.99*10^24*2.98^2*10^8 = 2.66*10^33 joule

b) J = 2/5mr^2
= 2PI/T = 6.2832/(3600*23.93) = 0.0000729 (7.29*10^-5)
Ek = 1/2J*^2 = 5.98*10^24/5*6.38^2*10^12*7.29^2*10^-10 = 2.59*10^29 joule

Ratio = 2.66*10^33/2.59*10^29 = 1.027*10^4

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