Question

the earth circles the sun once a year how much work would have to be done on the earth to bring it to rest realtive to the sun given yhe mass of the earth is 6×10 kg and the distance between sun and earth is 1.5 ×10 km​

Answer 1

Given

M = Mass of Earth = $6\times 10^{24}\ \text{kg}$

R = Radius of orbit = $1.5\times 10^8\ \text{km}$

To find

The work done to bring Earth to stop revolving around the Sun.

Solution

Circumference of the orbit

$2\pi r=2\pi 1.5\times 10^8\\ =942477796.077\ \text{m}$

t = Time taken to complete one revolution = $365.25\ \text{years}$

Orbital velocity

$v=\dfrac{2\pi r}{t}\\\Rightarrow v=\dfrac{942477796.077}{365.25\times 24\times 60\times 60}\\\Rightarrow v=29.865\ \text{m/s}$

Kinetic energy of the Earth

$K=\dfrac{1}{2}mv^2\\\Rightarrow K=\dfrac{1}{2}\times6\times 10^{24}\times 29.865^2\\\Rightarrow K=2.67\times 10^{27}\ \text{J}$

So, the energy required to bring the Earth to rest relative to the Sun is $2.67\times 10^{27}\ \text{J}$.