Question

a space vehicle is orbiting mars in a circular orbit. what radian measure corresponds to (a) 3.5 orbits? (b) $\frac{5}{6}$ orbit? (a) the radian measure corresponding to 3.5 orbits is . (type an exact answer in terms of $pi$. type an integer or a simplified fraction.) (b) the radian measure corresponding to $\frac{5}{6}$ orbit is . (type an exact answer in terms of $pi$. type an integer or a simplified fraction.)

Explanation:

Step1: Recall radian - orbit relationship

One full orbit corresponds to $2\pi$ radians.

Step2: Calculate for 3.5 orbits

For 3.5 orbits, we multiply the number of orbits by $2\pi$. So the radian measure is $3.5\times2\pi = 7\pi$.

Step3: Calculate for $\frac{5}{6}$ orbit

For $\frac{5}{6}$ orbit, we multiply $\frac{5}{6}$ by $2\pi$. That is $\frac{5}{6}\times2\pi=\frac{5\pi}{3}$.

Answer:

(a) $7\pi$
(b) $\frac{5\pi}{3}$