Solved problem: Average speed of the Moon

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Statement

difficulty

Knowing that the Moon takes 28 days to make one complete revolution around the Earth, calculate its average speed.

Datum: Consider the trajectory of the Moon as circular with a radius of 384,000 Km.

Solution

First, we change the 28 days to seconds.

$28 days \times 24 h / day \times 60 min / h \times 60 s/ min = 2419200 s$

Then we calculate the length of the circumference, which is the distance traveled by the Moon in its journey of 28 days. Considering R = 384,000 Km = 384,000,000 m:

$L = 2 \cdot π \cdot R = 2412743157.95696256 m$

Finally, we calculate the speed:

$V_{avg} = \frac{∆ s}{∆ t} = \frac{2412743157.95696256}{2419200} = 997.331 m/s$

Formulas worksheet

These are the main formulas that you must know to solve this exercise. If you are not clear about their meaning, we recommend you to check the theory in the corresponding sections. Furthermore, you will find in them, under the Formulas tab, the codes that will allow you to integrate these equations in external programs like Word or Mathematica.

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V_{avg} = \frac{∆ s}{∆ t} = \frac{s_{2} - s_{1}}{t_{2} - t_{1}}

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Average speed of the Moon

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