Question

Hint:

To calculate satellite velocity in a circular orbit, use \( V = \sqrt{GM/r} \), ensuring that the radius \( r \) includes the Earth's radius plus the satellite's height.

Answer 1

To find the orbital velocity of a satellite, we use the formula:
\[ V_s = \sqrt{\frac{GM_e}{r}} \]
where:

\(G = 6.67 \times 10^{-11}\) m\(^3\)kg\(^{-1}\)s\(^{-2}\)
\(M_e = 5.972 \times 10^{24}\) kg
\(r = r_e + h = (6378 + 1000) \times 10^3 = 7378000\) m

Now plug in the values:
\[ V_s = \sqrt{ \frac{6.67 \times 10^{-11} \times 5.972 \times 10^{24}}{7378000} } \approx \sqrt{5.403 \times 10^7} \approx 7349 \, \text{m/s} = 7.35 \, \text{km/s} \]

So, the final velocity of the satellite is:
\[ \boxed{7.35 \, \text{km/s}} \]