Answer
\[ \begin{align*} a_N &= 8.41 \times 10^{10}. \end{align*} \]
Work Step by Step
Step 1 Since speed is $2.9 \times 10^5 \, \text{km/s}$ and radius is $1 \, \text{km}$, then \[ \begin{align*} v &= \frac{ds}{dt} \\ &= \frac{2.9 \times 10^5 \, \text{km/s}}{1 \, \text{km}} \\ &= 2.9 \times 10^5 \, \text{km/s}. \end{align*} \] Step 2 \[ \begin{align*} a_N &= \kappa \left(\frac{ds}{dt}\right)^2 \\ &= \rho^{-1} \left(\frac{ds}{dt}\right)^2 \\ &= (2.9 \times 10^5)^2 \\ &= 8.41 \times 10^{10}. \end{align*} \] Result \[ \begin{align*} a_N &= 8.41 \times 10^{10}. \end{align*} \]
