Respuesta :
Explanation:
It is given that,
The radius of the circular path, [tex]r=1.5\times 10^{11}\ m[/tex]
Mass of earth, [tex]m=5.97\times 10^{24}\ kg[/tex]
Time taken to complete one orbit, [tex]t = 365.26\ days =3.15\times 10^7\ s[/tex]
Firstly, finding the velocity of the Earth's orbital motion. It is given by :
[tex]v=\dfrac{2\pi r}{t}[/tex]
[tex]v=\dfrac{2\pi \times 1.5\times 10^{11}}{3.15\times 10^7}[/tex]
[tex]v=2.99\times 10^4\ m/s[/tex]
Let a is the centripetal acceleration of the Earth's orbital motion. The relation between the velocity and the acceleration is given by :
[tex]a=\dfrac{v^2}{r}[/tex]
[tex]a=\dfrac{(2.99\times 10^4\ m/s)^2}{1.5\times 10^{11}\ m}[/tex]
[tex]a=5.96\times 10^{-3}\ m/s^2[/tex]
Let F is the force necessary to cause this acceleration. It is equal to the product of mass and acceleration. It is given by :
[tex]F=m\times a[/tex]
[tex]F=5.97\times 10^{24}\ kg \times 5.96\times 10^{-3}\ m/s^2[/tex]
[tex]F=3.55\times 10^{22}\ N[/tex]
Hence, this is the required solution.
