Answer:
[tex]0.00594\ m/s^2\ \text{towards the Sun}[/tex]
[tex]3.54737\times 10^{22}\ N[/tex]
Explanation:
r = Distance between Earth and Sun = [tex]1.5\times 10^{11}\ m[/tex]
Time taken to complete one rotation around Sun is given by
[tex]T=365.25\times 24\times 3600[/tex]
Centripetal acceleration is given by
[tex]a=\dfrac{v^2}{r}\\\Rightarrow \\\Rightarrow a=\dfrac{(\dfrac{2\pi r}{T})^2}{r}\\\Rightarrow a=\dfrac{4\pi^2r}{T^2}\\\Rightarrow a=\dfrac{4\pi^2\times 1.5\times 10^{11}}{(365.25\times 24\times 3600)^2}\\\Rightarrow a=0.00594\ m/s^2\ \text{towards the Sun}[/tex]
The centripetal acceleration of the Earth in its orbit is [tex]0.00594\ m/s^2\ \text{towards the Sun}[/tex]
Force is given by
[tex]F=ma\\\Rightarrow F=5.972\times 10^{24}\times 0.00594\\\Rightarrow F=3.54737\times 10^{22}\ N[/tex]
The force on the Earth is [tex]3.54737\times 10^{22}\ N[/tex]
