The Earth\'s orbit around the sun is very nearly circular, with an average radiu

Question

The Earth's orbit around the sun is very nearly circular, with an average radius of 1.5 times 10^11 m. Approximate the orbit as circular for this question. Assume the sun does not move. The mass of the Earth is 5 97 times 10^24 kg. The mass of the sun is 1.99 times 10^30 kg. The choices for the blanks below are: tangential speed angular speed (2 pi radian/365 days)(1 days/86, 400 s) = 1.99 times 10^-7 rad/s gives the _____ of Earth as it moves around the sun. (2 pi radians/365 days)(1.5 times 10^11 m/1 radian)(1 day/86, 400 s) = 29, 900 m/s gives the _____ of Earth as it moves around the sun. The period T of the Earth's revolution is A. 2 pi radians B. 360 degree C. 2 pi radius middot 1.5 times 10^11 m D. about 365 days E. 1 rev/365 days The frequency f of Earth's revolution is A. 2 pi radians B. 360 degree C. (2 pi radians)(1.5 times 10^11 m) D. about 365 days E. (1/365 days)(1 day/86, 400s) = 3.17 times 10^-8 Hz Using the values given above calculate the magnitude of the Earth's average centripetal acceleration as it orbits the sun. What is the centripetal force acting on the earth?

Explanation / Answer

29 e)

The period which the Earth orbits around the Sun is: (365.26 day)(24 hr/day)(3600 s/hr) = 31558464 s
The centripetal acceleration of the Earth in its orbit around the sun will be: a = v2/r = (2r/T)2/r = 42r/T2
Then, acceleration, a = 42 (1.5x1011m)/(31558464 s)2 = 0.005946m/s2 = 0.0059 m/s/s toward the Sun

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