Answer
(a) It takes 1.65 hours to complete one orbit.
(b) The speed of the spacecraft is 7.50 km/s.
Work Step by Step
(a) If the spacecraft is 705 km above the surface of the earth, the radius $R$ of the orbit is 705 km + 6380 km, which is 7085 km. We can find the time $T$ it takes for one orbit.
$T = 2\pi~\sqrt{\frac{R^3}{G~M}}$
$T = 2\pi~\sqrt{\frac{(7.085\times 10^6~m)^3}{(6.67\times 10^{-11}~m^3/kg~s^2)(5.98\times 10^{24}~kg)}}$
$T = 5933~s = 1.65~hours$
It takes 1.65 hours to complete one orbit.
(b) We can find the speed of the spacecraft.
$v = \frac{distance}{time}$
$v = \frac{2\pi~R}{T}$
$v = \frac{(2\pi)(7085~km)}{5933~s}$
$v = 7.50~km/s$
The speed of the spacecraft is 7.50 km/s.
