The Earth moves about the Sun in a circular orbit with a radius of 150 times 10^

Question

The Earth moves about the Sun in a circular orbit with a radius of 150 times 10^6m. It takes one year for the Earth to complete one orbit. Find the speed of the Earth as it orbits the Sun. Determine the acceleration of the Earth in its orbit. Now consider that the Earth spins about its own axis once every 24h (so a point on the surface of the Earth moves in a circle whose center is the center of the Earth). The radius of the Earth is 6.37 times 10^6m. Determine the acceleration of a point on the Earth's surface due to its rotation.

Explanation / Answer

a) Speed of the Earth V = (2*pi*r)/T = (2*3.142*150*10^6)/(365*24*60*60) = 29.88 m/sec

b) accelaration is a = v^2/r = (29.88^2)/(150*10^6) = 5.95*10^-6 m/s^2
c) a = r*w^2

r = 6.37*10^6 m

w = (2*pi/T) = (2*3.142)/(24*60*60) = 7.27*10^-5 rad/sec

a = r*w^2 = 6.37*10^6*(7.27*10^-5)^2 = 0.03366 rad/s^2

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