Question

Calculate the cenrtripetal acceleration of the Earth in

Answer 1

Answer:

$0.00594\ m/s^2\ \text{towards the Sun}$

$3.54737\times 10^{22}\ N$

Explanation:

r = Distance between Earth and Sun = $1.5\times 10^{11}\ m$

Time taken to complete one rotation around Sun is given by

$T=365.25\times 24\times 3600$

Centripetal acceleration is given by

$a=\dfrac{v^2}{r}\\\Rightarrow \\\Rightarrow a=\dfrac{(\dfrac{2\pi r}{T})^2}{r}\\\Rightarrow a=\dfrac{4\pi^2r}{T^2}\\\Rightarrow a=\dfrac{4\pi^2\times 1.5\times 10^{11}}{(365.25\times 24\times 3600)^2}\\\Rightarrow a=0.00594\ m/s^2\ \text{towards the Sun}$

The centripetal acceleration of the Earth in its orbit is $0.00594\ m/s^2\ \text{towards the Sun}$

Force is given by

$F=ma\\\Rightarrow F=5.972\times 10^{24}\times 0.00594\\\Rightarrow F=3.54737\times 10^{22}\ N$

The force on the Earth is $3.54737\times 10^{22}\ N$