Question

An astronomer at the equator measures the Doppler shift of sunlight at sunset. From this, she calculates that Earth's tangential velocity at the equator is 465 m/s. The centripetal acceleration at the equator is 3.41 * 10^-2 m/s2. Use this data to calculate Earth's radius.

Answer 1

Answer : Radius of Earth is 6,340 Km.

Explanation

It is given that,

Tangential velocity of Earth at the equator, v = 465 m/s

Centripetal acceleration at the equation is, $a_c=3.41\times 10^{-2}\ m/s^2$

We know that the relation between centripetal acceleration and tangential velocity is :

$a_c=\dfrac{v^2}{r}$..........(1)

Where,

v is tangential velocity

r is the radius

Putting all values in equation (1)

$3.41\times 10^{-2}\ m/s^2=\dfrac{(465 m/s)^2}{r}$

$r=6340909\ m$

or

$r=6,340\ Km$

The Earth's radius is 6,340 Km. Hence, this is the required solution.