The Earth moves about the Sun in a circular orbit with a radius of 150 * 10^6 m.

Question

The Earth moves about the Sun in a circular orbit with a radius of 150 * 10^6 m. 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 24th (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 * 10^6 m. Determine the acceleration of a point on the Earth's surface due to its rotation.

Explanation / Answer

Given data

  

radius of the circular orbit R = 150*10^6 m

   Earth can complete one orbit in one year so the distance covered in completion of one orbitis   

   circumferance of the circle = 2*pi*R= 2*3.14*150*10^6= 942*10^6 m
now the speed of the Earth is V = 942*10^6/(365*24*60*60)= 29.87 m/s

b) Acceleration of the earth is

       centripeatal acceleration a = v^2/R= 29.87^2/150*10^6 = 6*10^-6 m/s2

c)
   acceleration of the particle is a = v^2/r = (2pi*R /T)^2/R
                       = 4 pi^2 *R/T^2
                       = 4*3.14^2*6.37*10^6 / (86400)^2

                       = 0.034 m/s2

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