Mathematical Modelling — Question 3

Step 1 : Formulation :

The speed at which the moon orbits the earth is = $\dfrac{\text{Length of the orbit}}{\text{Time taken}}$

Step 2: Finding the solution :

Since the orbit is nearly circular.

∴ Its length is its circumference

⇒ 2πr = 2 × π × 384000

= 2 × 3.14 × 384000 = 2,411,520 km

We know that,

The moon takes 24 hours to complete an orbit.

So, Speed = $\dfrac{\text{Distance}}{\text{Time}} = \dfrac{2411520}{24}$ = 100480 km/hour

Step 3 :Interpretation :

The speed is 100480 km/h.