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.

Step-by-step 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* 10^(-2)\ m/s^2`

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

`a_c=(v^2)/(r)`..........(1)

Where,

v is tangential velocity

r is the radius

Putting all values in equation (1)

`3.41* 10^(-2)\ m/s^2=((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.