Answer:
The average speed of the earth in its orbit is [tex]29.86km/s[/tex]
Explanation:
The average distance between the Earth and the Sun is [tex]1.50x10^{8} km[/tex].
The average speed of the earth in its orbit can be found by the next equation :
[tex]v = \frac{2 \pi r}{T}[/tex] (1)
Where r is the radius and T is the period.
In this case, the orbit of the Earth can be considered as a circle
([tex]r = 1.50x10^{8}km[/tex]) instead of an ellipse.
It takes 1 year to the Earth to make one revolution around the Sun. Therefore, its period will be 365.25 days.
Notice that to express the period in terms of seconds, the following is needed:
[tex]365.25d . \frac{86400s}{1d}[/tex] ⇒ [tex]31557600s[/tex]
Then, equation 1 can be used:
[tex]v = \frac{2 \pi (1.50x10^{8}km)}{31557600s}[/tex]
[tex]v = 29.86km/s[/tex]
Complete Question
The average distance between earth and the sun is 1.50 x10^8 km. Calculate the average speed of the Earth in its orbit in kilometres per second.
Answer:
The value is [tex]v = 29.89 \ km/s [/tex]
Explanation:
From the question we are told that
The average distance is [tex]r = 1.50 *10^{8} \ km[/tex]
The average speed is mathematically represented as
[tex]v = \frac{2 \pi r}{t}[/tex]
Here t is the time taken to circle round the sun which is equal to 1 year
Now converting this to seconds we have
[tex]t = 1 * 365 * 24 * 60 * 60 = 3.154*10^{7} \ s[/tex]
So
[tex]v = \frac{2 *3.142 *1.50 *10^{8} }{3.154*10^{7}}[/tex]
[tex]v = 29.89 \ km/s [/tex]
