Question

Calculate the centripetal acceleration of the Earth in its orbit around the Sun. Assume that the Earth's orbit is a circle of radius 1.50×1011m. Express your answer using three significant figures and include the appropriate units.

Answer 1

Answer:

0.00594 m/s²

Explanation:

r = Radius of Earth's orbit = $1.5\times 10^{11}\ m$

T = Time taken to complete one revolution around the Sun

$\omega=\frac{2\pi}{T}\\\Rightarrow \omega=\frac{2\pi}{365.25\times 24\times 60\times 60}$

$a=\omega^2r\\\Rightarrow a=\left(\frac{2\pi}{365.25\times 24\times 60\times 60}\right)^2\times 1.5\times 10^{11}\\\Rightarrow a=0.00594\ m/s^2$

The centripetal acceleration of Earth in its orbit around the Sun is 0.00594 m/s²