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Question
Earth also moves in circular orbit around sun once every year with on orbital radius of 1.5 × 1011 m. What is the acceleration of earth (or any object on the surface of the earth) towards the centre of the sun? How does this acceleration compare with g = 9.8 m/s2?
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Solution
The orbital radius of the earth around the sun (R) = 1.5 × 1011 m
Time period = 1 yr = 365 day
= 365 × 24 × 60 × 60 s
= 3.15 ×107 s
Centripetal acceleration `(a_c) = Rω^2 = (5pi^2R)/T^2`
= `(4 xx (22/7)^2 xx 1.5 xx 10^11)/(3.15 xx 10^7)^2`
= `5.97 xx 10^-3` m/s2
∴ `a_c/g = (5.97 xx 10^-3)/9.8 = 1/1642`
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