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:
2pi/8760(hours in a year) = 0.0002283pi/hr
150pi/0.0002283*km/hr = 2064026.39405km/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.
$\endgroup$ 21 Answer
$\begingroup$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 $$v=(7.17*10^{-4})(1.5*10^8)=107,550\;\text{km/hr.}$$
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