Question

2. The Moon orbits the Earth in a nearly circular orbit at a distance of about240,000 miles.b. If the Moon takes approximately 27.3 days for one round trip, whatis its average velocity in km/hr?

Answer 1

For this case we know that the Moon orbits the Earth in a circular orbit at a distance of about 240000 miles, we also know that for one complete trip it takes about 27.3 days and we want to estimate the average velocity in km/hr

The first step here is convert the miles into km and the days into hours and we got this:

$r=240000mi\cdot\frac{1.609Km}{1mi}=386160Km$$27.3\text{days}\cdot\frac{24hr}{1day}=655.2hr$

After this we know that the total circumference of a circle is given by:

$S=2\pi r$

And from here is possible to find the distance covered in one orbit:

$S=2\pi(386160Km)=2426314.838Km$

And then we can use the definition of velocity given by:

$v=\frac{S}{t}=\frac{2426314.838Km}{655.2hr}=3703.167\operatorname{km}/hr$

So for this case we can conclude that the average velocity for the Moon is given by 3703.167 Km/hr