Question

6.Calculate the centripetal acceleration of the Earth towards the Sun. (r = 1.5 x 1011 m)
I'm not really sure about this problem so I need some help

Answer 1

Given,

The radius of Sun, $r=1.5\times 10^{11}\ m$

To find,

The centripetal acceleration of the Earth towards the Sun.

Solution,

The centripetal acceleration of an object is given by the formula as follows :

$a=\omega^2 r$ ....(1)

Where

$\omega$ is angular velocity

First calculate the angular velocity.

$\omega=\dfrac{2\pi}{1\ \text{day}}\\\\=\dfrac{2\pi}{24\times 3600\ s}\\\\=7.27\times 10^{-5}\ s^{-1}$

Put all the values in formula (1)

$a=\omega^2 r\\\\=(7.27\times 10^{-5})^2\times 1.5\times 10^{11}\\\\=792.79\ m/s^2$

So, the centripetal acceleration of the Earth towards the Sun is $792.79\ m/s^2$.