Question

Calculate the cenrtripetal acceleration of the Earth in

itsorbit around the Sun, and the net force exerted on the Earth.
Whatexerts this force on the Earth? Assume that the Earth's orbit
isorbit is a circle of radius 1.50 x 10-11m.

Answer 1

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

`3.54737* 10^(22)\ N`

Step-by-step explanation:

r = Distance between Earth and Sun =
`1.5* 10^(11)\ m`

Time taken to complete one rotation around Sun is given by

`T=365.25* 24* 3600`

Centripetal acceleration is given by

`a=(v^2)/(r)\\\Rightarrow \\\Rightarrow a=(((2\pi r)/(T))^2)/(r)\\\Rightarrow a=(4\pi^2r)/(T^2)\\\Rightarrow a=(4\pi^2* 1.5* 10^(11))/((365.25* 24* 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* 10^(24)* 0.00594\\\Rightarrow F=3.54737* 10^(22)\ N`

The force on the Earth is
`3.54737* 10^(22)\ N`