Answers

2015-09-28T22:36:43+05:30
Distance of artificial satellite (d)= 3400 km
Radius of earth(R) = 6400 km = 6.4×10⁶ m
Radius of orbit(r) = R+d = 10,000 km = 10⁷ m
g = 9.8 m/s²
Orbital velocity, V_o=\ ?
Period of revolution, T = ?

(i) Orbital velocity

V_o= \sqrt{ \frac{GM}{r} }= \sqrt{ \frac{GM}{r} \times  \frac{R^2}{R^2}  }= \sqrt{ \frac{GM}{R^2} \times  \frac{R^2}{r}  }=  \sqrt{g\times  \frac{R^2}{r} }

\Rightarrow V_o= \sqrt{9.8 \times  \frac{(6.4 \times 10^6)^2}{10^7} } \\ \\\Rightarrow V_o= \sqrt{40.14 \times 10^6 } \\ \\ V_o=6.33 \times 10^3\ m/s

(ii) Time period
T= \frac{2 \pi r}{V_o} = \frac{2 \times 3.14 \times 10^7}{6.33 \times 10^3} =9.93 \times 10^3\  seconds
1 5 1