Answer
$20.2\ m/s^2$
Work Step by Step
Given:
Radius of circular turn $ r = 3220 km= 3220 \times 10^{3} m$
Speed of spaceship $v = 29000\ km/h =29000\times \frac{1000m}{3600 s }=8055.55\ m/s$
The angular speed is:
$\omega = \frac{v}{r}$
$\omega = \frac{8055.55\ m/s}{3220 \times 10^{3} m}$
$\omega = 2.5\times 10^{-3}\ rad/s$
The radial acceleration is given by:
$a_r = \omega^2r$
$a_r=( 2.5\times 10^{-3}\ rad/s)^2\times 3220 \times 10^{3}\ m$
$a_r = 20.2\ m/s^2$
