Problem 1-10: The average speed of the earth in its orbit in kilometers per second and in meters per second

Advertisements
Advertisements

PROBLEM:

a) The average distance between the Earth and the Sun is  108 km. Calculate the average speed of the Earth in its orbit in kilometers per second. 

b) What is this is meters per second?

Advertisements
Advertisements

SOLUTION:

Part A

We assume that the earth revolves around the sun in a circular manner. Therefore, the distance between the earth and the sun will be the radius of its orbit.

The total distance traveled the earth in full revolution is

\begin{align*}
d & =2\pi r \\
& = 2\pi \left(10\right)^8\:\text{km} \\
\end{align*}

The total time of travel is

\begin{align*}
t & =365.25\:\text{days}\left(\frac{24\:\text{hr}}{1\:\text{day}}\right)\left(\frac{3600\:\text{s}}{1\:\text{hr}}\right) \\
& = 3.15576\times 10^7\:\text{sec} \\
\end{align*}

Therefore, the average speed is

\begin{align*}
\text{speed} & =\frac{\text{distance}}{\text{time}}=\frac{d}{t} \\
 & = \frac{2\pi \left(10\right)^8\:\text{km}}{3.15576\times 10^7\:\text{s}} \\
& = 19.91\:\text{km/s} \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right)
\end{align*}

Therefore, the average speed of the earth is 19.91 km/s.

Part B

Convert 19.91 km/s to m/s.

\begin{align*}
s & =\left(19.91\:\frac{\text{km}}{\text{s}}\right)\left(\frac{1000\:\text{m}}{1\:\text{km}}\right) \\
& =19\,910\:\text{m/s} \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right) \\
\end{align*}

Therefore, the velocity is 19 910 m/s. 

Advertisements
Advertisements