Earth orbits the sun at an average distance of about $150$ million kilometres every $365.2564$ mean solar days, or one sidereal year. What is the linear velocity of the earth in kilometres per hour?
I did:
$\frac{2 \pi}{8760}$ (hours in a year) = $0.0002283 \pi /\text{hr}$
$\frac{150 \pi}{0.0002283} \text{km}/\text{hr} = 2064026.39405 \text{km}/\text{hr}$
I couldn't find a place to check my answer, if I am wrong can anyone help me with this question? My teacher is on break.
The linear velocity of a point on a rotating body is $$v=\omega r,$$ where $\omega$ is the angular speed of the system. Angular speed is defined in terms of the angular displacement $\Delta\theta$, and since speed is the distance per unit of time, $$\omega=\frac{\Delta\theta}{\Delta t}.$$
The Earth makes one revolution around the sun every 365.2564 days (8,766.154 hours), giving an angular speed of $$\omega=\frac{2\pi}{8,766.154}=7.17*10^{-4}\;\text{radians/hr;}$$ we then find that $$v=(7.17*10^{-4})(1.5*10^8)=107,550\;\text{km/hr.}$$