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?

Answer 1

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 ${\displaystyle \left(a_c\right)=R{\omega }^2=\frac{5{\pi }^{2}R}{T^2}}$

= ${\displaystyle \frac{4\times {\left(\frac{22}{7}\right)}^2\times 1.5\times {10}^{11}}{{(3.15\times {10}^7)}^2}}$

= ${\displaystyle 5.97\times {10}^{-3}}$ m/s²

∴ ${\displaystyle \frac{a_c}{g}=\frac{5.97\times {10}^{-3}}{9.8}=\frac{1}{1642}}$